Skip to content
Subjects

A-Level Computer Science

Tips

A-Level Computer Science (9618) is two halves that feel like different subjects. The theory half runs from information representation and communication through hardware, processors, system software, security, databases and ethics. The practical half is algorithms, data structures, programming and software development, and A2 adds recursion and object-oriented programming.

The theory papers are marked far more literally than students expect. There is a correct vocabulary — register names, addressing modes, normal forms, the exact difference between validation and verification — and a paraphrase usually scores nothing. Learn the definitions in the syllabus wording.

The programming papers reward writing code by hand until it compiles in your head.

A-Level Computer Science Past Papers

  • 1

    Information representation

    1.1

    Number systems

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of binary magnitudes and the difference between binary prefixes and decimal prefixes Understand the difference between and use: • kibi and kilomebi and megagibi and gigatebi and tera
    Show understanding of different number systems Use the binary, denary, hexadecimal number bases and Binary Coded Decimal (BCD) and one’s complement and two’s complement representation for binary numbers
    Convert an integer value from one number base/ representation to another
    Perform binary addition and subtraction Using positive and negative binary integers
    Show understanding of how overflow can occur
    Describe practical applications where Binary Coded Decimal (BCD) and Hexadecimal are used
    Show understanding of and be able to represent character data in its internal binary form, depending on the character set used Students are expected to be familiar with ASCII (American Standard Code for Information Interchange), extended ASCII and Unicode. Students will not be expected to memorise any particular character codes

    Source: Cambridge International syllabus

    Counting in binary: 0 to 15

    The three number systems 数制 you must use:

    • denary 十进制 (decimal, base 10) — uses digits 0–9. Place values are powers of ten.
    • binary 二进制 (base 2) — uses 0 and 1. Place values are powers of two. Every byte 字节 is 8 bits.
    • hexadecimal 十六进制 (base 16) — uses 0–9 then A–F for 10–15. Each hex digit 数位 stands for exactly 4 bits.
    Beads on a traditional abacus
    An abacus represents numbers by place value — the same idea behind decimal, binary and hexadecimal

    Conversions

    Denary → binary: keep dividing by 2 and record the remainders, read bottom-up. Or subtract the largest place value 位值 (power of 2) that fits.

    Example: $558_{10}$: $558 = 512 + 32 + 8 + 4 + 2 = 2^{9} + 2^{5} + 2^{3} + 2^{2} + 2^{1}$. In 12 bits: 0010 0010 1110.

    Binary → hex: group the bits into nibbles 半字节 (4 bits) from the right and convert each. 0010 0010 11102 2 E22E.

    Hex → binary: replace each hex digit with its 4-bit pattern. Hex → denary: multiply each digit by its place value. 22E $= 2 \times 256 + 2 \times 16 + 14 = 558$.

    Worked example. Convert denary 200 to 8-bit binary, then to hexadecimal.

    $200 = 128 + 64 + 8$, so the binary is 11001000. In nibbles, 1100 1000 $= 12$ and $8$, i.e. $\text{C}$ and $8$, so the hexadecimal is C8.

    A binary place-value chart for 200: the columns 128, 64, 32, 16, 8, 4, 2, 1 hold the bits 1,1,0,0,1,0,0,0; the two 4-bit nibbles 1100 and 1000 become the hex digits C and 8, so 200 = 11001000 = C8
    Reading 200 from its place values, then grouping the bits into nibbles to get hex C8

    How many bits?

    Exam questions fix the register width 寄存器宽度 (8, 12 or 16 bits). Pad with leading zeros to that width: $558$ in 12 bits is 0010 0010 1110, never 10 0010 1110.

    To find the minimum number of bits that can store a value, ask which place values you need:

    • an unsigned integer from $0$ to $2^{n} - 1$ needs $n$ bits: $200$ needs 8 bits (the top is $255$), $1000$ needs 10 bits (the top is $1023$), $16$ needs 5 bits (4 bits stop at $15$).
    • a signed two's-complement integer from $-2^{n-1}$ to $2^{n-1} - 1$ needs $n$ bits: $-200$ needs 9 bits, because 8 bits stop at $-128$.
    • one hexadecimal digit needs 4 bits, one BCD digit needs 4 bits, and one ASCII character needs 7 bits (8 for extended ASCII).

    Binary vs decimal prefixes

    Two prefix families look similar but differ — decimal (powers of 10) and binary (powers of 2):

    Decimal (SI) Binary (memory)
    kilo $= 10^{3}$ kibi (Ki) $= 2^{10} = 1024$
    mega $= 10^{6}$ mebi (Mi) $= 2^{20}$
    giga $= 10^{9}$ gibi (Gi) $= 2^{30}$
    tera $= 10^{12}$ tebi (Ti) $= 2^{40}$

    So a tebibyte (TiB) is slightly more than a terabyte (TB). A "1 TB" drive holds $10^{12}$ bytes, but an operating system that reports in TiB shows a smaller number.

    Explore

    Binary, denary and hex

    Type a number and see it in binary, denary and hexadecimal at once — and how the place values add up.

    Vocabulary Train
    English Chinese Pinyin
    number system 数制 shù zhì
    binary 二进制 èr jìn zhì
    denary 十进制 shí jìn zhì
    digit 数位 shù wèi
    place value 位值 wèi zhí
    byte 字节 zì jié
    bit wèi
    hexadecimal 十六进制 shí liù jìn zhì
    nibbles 半字节 bàn zì jié
    nibble 半字节 bàn zì jié
    register width 寄存器宽度 jì cún qì kuān dù
    Exercise sheet
    1.1

    Binary arithmetic

    Binary addition

    Add column by column from the right, carrying as in denary:

    Bit A Bit B Carry in Sum bit Carry out
    0 0 0 0 0
    0 0 1 1 0
    0 1 0 1 0
    0 1 1 0 1
    1 1 0 0 1
    1 1 1 1 1

    Overflow 溢出 happens when the result needs more bits than the register 寄存器 can hold — the carry-out of the leftmost column is the overflow bit.

    Worked example. Add the 8-bit unsigned integers $10110101$ and $01101100$, and comment on the result.

    $10110101 + 01101100 = 1\,00100001$. The answer needs 9 bits, so it does not fit in an 8-bit register: overflow has occurred. A full answer names the error and says why, using the word size the question gave: "Overflow: the true result ($289$) is larger than the largest value an 8-bit register can hold ($255$), so the carry out of the most significant bit is lost and the stored result ($00100001 = 33$) is wrong."

    Binary subtraction

    The usual way is two's complement 补码 addition: to do $A - B$, form the two's complement of $B$ (invert every bit and add 1), then add, and discard any final carry-out.

    To subtract $00011110$ from $01100100$ (unsigned 8-bit):

    • two's complement of $00011110$: invert → $11100001$, add 1 → $11100010$.
    • add to $01100100$: result $1\,01000110$ (9 bits) — discard the leading 1 → $01000110 = 70_{10}$. Check: $100 - 30 = 70$. ✓

    Two's complement signed integers

    In an $n$-bit two's-complement number:

    • the most significant bit 最高有效位 (MSB) is the sign bit 符号位: 0 = positive, 1 = negative.
    • to read a negative number: invert every bit, add 1, then negate.

    So $11100010$ is negative; invert → $00011101$, add 1 → $00011110 = 30$, so it is $-30$. This is a signed integer 有符号整数 (unlike an unsigned 无符号 one). The range for $n$ bits is $-2^{n-1}$ to $+2^{n-1} - 1$; for 8 bits, $-128$ ($10000000$) to $+127$ ($01111111$).

    The same bits mean different numbers depending on the agreed reading. As an unsigned integer every bit is a place value, so 8 bits run from $0$ to $255$; as a signed two's-complement integer the top bit is the sign, so the same 8 bits run from $-128$ to $+127$. The pattern $11111111$ is $255$ read one way and $-1$ read the other — nothing in the bits themselves says which.

    A table of four 8-bit patterns read twice: 00000000 is 0 either way, 01111111 is 127 unsigned and +127 signed, 10000000 is 128 unsigned but -128 signed, and 11111111 is 255 unsigned but -1 signed
    The same byte read as unsigned and as signed: only the agreed interpretation tells them apart An 8-bit two's-complement number line from -128 (10000000) to +127 (01111111); numbers with sign bit 1 are negative and those with sign bit 0 are positive, with -1 = 11111111 sitting just below 0 = 00000000 8-bit two's complement: the sign bit splits the range into negative ($-128$ to $-1$) and positive ($0$ to $127$)

    Worked example. What denary value does the 8-bit two's-complement number $10110100$ represent?

    The MSB is 1, so it is negative. Invert → $01001011$, add 1 → $01001100 = 76$, so the value is $-76$. Check with place values: $-128 + 32 + 16 + 4 = -76$.

    Worked example. Write $-108$ as a 12-bit two's-complement integer.

    Start from $+108$ in 12 bits: $108 = 64 + 32 + 8 + 4$, so 0000 0110 1100. Invert every bit: 1111 1001 0011. Add 1: 1111 1001 0100. Check with place values, where the top bit is worth $-2^{11} = -2048$: $-2048 + 1024 + 512 + 256 + 128 + 16 + 4 = -108$. ✓

    For 12 bits the range is $-2048$ (1000 0000 0000) to $+2047$ (0111 1111 1111). Questions that ask for the smallest and largest values want these two patterns, so learn the rule: the most negative number is a 1 followed by zeros; the most positive is a 0 followed by ones.

    An arithmetic shift 算术移位 moves every bit left or right but keeps the sign: a shift right by one place halves the value and copies the sign bit into the empty space on the left, so a negative number stays negative (1111 1001 0100 shifted right three places is 1111 1111 0010, which is $-14$: $-108 / 8 = -13.5$, and a shift right rounds down). A shift left doubles the value. Shifts belong to the assembly instruction set in topic 4, but this question is asked with the number work here.

    Overflow in signed arithmetic happens when the true result falls outside this range — spotted when the sign bit flips wrongly (two positives giving a negative, or two negatives giving a positive).

    One's complement

    Before two's complement, an older scheme called one's complement 反码 represented a negative number by simply inverting every bit of the positive — there is no "add 1" step.

    • $+30 = 00011110$, so in one's complement $-30 = 11100001$ (just the inverse).
    • Drawback: it has two zeros$00000000$ ($+0$) and $11111111$ ($-0$) — which wastes a bit pattern and makes arithmetic awkward.

    Two's complement (invert and add 1) removes the negative zero: it has a single zero and lets addition and subtraction use the same circuit. That is why modern computers store signed integers in two's complement, not one's complement.

    Explore

    Binary & signed integers

    byte = Σ place values

    See how an 8-bit pattern maps to a number (and how it would overflow past 255).

    Explore

    Two's complement signed bits

    The leftmost bit carries a negative place value. Flip any bit — or hit Negate (invert every bit, then add 1) — and watch the signed value change.

    Vocabulary Train
    English Chinese Pinyin
    register 寄存器 jì cún qì
    unsigned 无符号 wú fú hào
    overflow 溢出 yì chū
    most significant bit 最高有效位 zuì gāo yǒu xiào wèi
    two's complement 补码 bǔ mǎ
    signed integer 有符号整数 yǒu fú hào zhěng shù
    sign bit 符号位 fú hào wèi
    arithmetic shift 算术移位 suàn shù yí wèi
    one's complement 反码 fǎn mǎ
    1.1

    Binary Coded Decimal (BCD)

    In BCD 二进码十进数, each denary digit is written as its own 4-bit pattern. The number $93$ is 1001 0011 in BCD — not binary 93 ($01011101$). Each nibble uses only 0–9; patterns $1010$$1111$ are invalid.

    BCD reading: 0010 0111 0101 → 2, 7, 5 → 275.

    Use: calculators, digital clocks, and devices that show denary digits — each digit drives a 7-segment display 七段显示器. Currency code often uses BCD to avoid the rounding errors of converting fractions like 0.1 to binary.

    A "justify" answer must link the use to a property of BCD: each denary digit has its own 4 bits, so a digit can be sent straight to its display, or added digit by digit, with no conversion of the whole number; and a decimal fraction such as $0.10$ is stored exactly, which a binary fraction cannot do.

    A single-digit seven-segment LED display component, showing its seven separate bars
    A seven-segment display shows one denary digit, often driven by BCD
    Vocabulary Train
    English Chinese Pinyin
    BCD 二进码十进数 èr jìn mǎ shí jìn shù
    7-segment display 七段显示器 qī duàn xiǎn shì qì
    1.1

    Hexadecimal — practical uses

    Hex is a compact way to write binary (1 hex digit = 4 bits):

    A byte splits into two nibbles; each nibble is one hexadecimal digit
    A byte is two nibbles; each nibble is one hex digit
    • memory addresses 内存地址 in low-level programming — 0x7FFE.
    • colour values in HTML/CSS — #FF8800.
    • MAC addressesAC:DE:48:00:11:22.

    Hex does not change the stored data — it just makes binary easier for humans.

    Vocabulary Train
    English Chinese Pinyin
    memory address 内存地址 nèi cún dì zhǐ
    1.1

    Character codes

    Computers store text as numbers; each character has a numeric code point 码点 set by a character set 字符集.

    ASCII

    • ASCII uses 7 bits — 128 code points. Basic Latin letters, digits, punctuation, and control codes.
    • Extended ASCII uses 8 bits — 256 code points; the lower 128 match ASCII, the upper 128 vary by region.
    A small ASCII table: the character A is code 65 = 01000001, a is 97 = 01100001, the digit 0 is 48 = 00110000, and space is 32 = 00100000
    Each character is stored as a number — a few ASCII code points in denary and binary

    Unicode

    • Unicode is a universal character set covering almost every script, plus symbols and emoji.
    • common encodings 编码: UTF-8 (1–4 bytes, ASCII-compatible), UTF-16 (2 or 4 bytes), UTF-32 (fixed 4 bytes).

    Why Unicode beats ASCII

    • it represents far more characters (every script, emoji); ASCII covers only basic English.
    • files are portable with no code-page confusion, and allow multilingual text in one document.
    • trade-off: Unicode files are usually larger for English-only text.

    When a question asks for differences, give them in pairs with numbers: ASCII uses 7 bits (extended ASCII 8), so 128 (256) characters; Unicode uses up to 32 bits (UTF-8 uses 1 to 4 bytes), so more than a million code points. ASCII covers basic English only; Unicode covers every script, and its first 128 code points are the ASCII ones. In UTF-8 an English letter still takes 1 byte, so a 40-letter English file name is 40 bytes in ASCII and in UTF-8 alike, while a Chinese character takes 3 bytes.

    Explore

    A character is stored as a number

    Each character has a code number — 'A' is 65. Flip the bits to see that code in binary and hex, exactly how the computer holds it.

    Vocabulary Train
    English Chinese Pinyin
    code point 码点 mǎ diǎn
    character set 字符集 zì fú jí
    encoding 编码 biān mǎ
    1.2

    Bitmap images

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of how data for a bitmapped image are encoded Use and understand the terms: pixel, file header, image resolution, screen resolution, colour depth / bit depth
    Perform calculations to estimate the file size for a bitmap image
    Show understanding of the effects of changing elements of a bitmap image on the image quality and file size Use the terms: image resolution, colour depth / bit depth
    Show understanding of how data for a vector graphic are encoded Use the terms: drawing object, property, drawing list
    Justify the use of a bitmap image or a vector graphic for a given task
    Show understanding of how sound is represented and encoded Use the terms: sampling, sampling rate, sampling resolution, analogue and digital data
    Show understanding of the impact of changing the sampling rate and resolution Including the impact on file size and accuracy

    Source: Cambridge International syllabus

    A bitmap 位图 image (also called a bitmapped image) stores the colour of every pixel 像素 in a grid. At the start of the file a file header 文件头 records the image's metadata — its width, height and colour depth — so software knows how to read the pixel data that follows.

    • image resolution 图像分辨率: the bitmap's own size, width × height in pixels (e.g. 1920 × 1080).
    • screen resolution 屏幕分辨率: the width × height the display can show. If an image's resolution is larger than the screen it is scaled down to fit; a low-resolution image looks blocky when stretched onto a higher-resolution screen.
    • colour depth 颜色深度 (bit depth 位深度): bits per pixel. 1 bit → black/white; 8 bits → 256 colours; 24 bits → 16.7 million ("true colour").
    The same disc stored on three pixel grids, A to C, getting blockier as the pixels grow larger and fewer
    The same image stored at three resolutions, from high (A) to low (C): fewer, larger pixels mean less detail

    File size

    $$\text{size in bits} = \text{width} \times \text{height} \times \text{bit depth}.$$

    Divide by 8 for bytes, by 1024 for KiB, etc. Example: a $3000 \times 2000$ image at 24 bpp is $3000 \times 2000 \times 24 = 1.44 \times 10^{8}$ bits $\approx 17.2\ \text{MiB}$.

    A 6 by 4 grid of pixels with its width and height labelled; pixels = 6 times 4 = 24, and at 8 bits per pixel the size = 24 times 8 = 192 bits
    The same formula on small numbers: count the pixels, then multiply by the colour depth

    State the units you used. The mark scheme accepts $1\ \text{MB} = 10^{6}$ bytes (the SI prefix) or $1\ \text{MiB} = 1024 \times 1024$ bytes (the binary prefix), as long as your working shows which one; the same image is $18.0\ \text{MB}$ or $17.2\ \text{MiB}$. Add the size of the file header if the question gives one.

    A video is a sequence of bitmap images, each one a frame. Before compression its size is the size of one frame $\times$ the frame rate 帧率 (frames per second) $\times$ the duration in seconds: 30 frames per second of $1920 \times 1080$ pixels at 24 bits is $30 \times 1920 \times 1080 \times 24 \approx 1.5 \times 10^{9}$ bits, about $187\ \text{MB}$, for every second. That is why video is always compressed.

    Changing settings

    • lower resolution → smaller file, less detail (looks blocky when enlarged).
    • lower colour depth → smaller file, but smooth shades show banding.
    • higher of either → larger file, better quality.
    Vocabulary Train
    English Chinese Pinyin
    bitmap 位图 wèi tú
    pixel 像素 xiàng sù
    file header 文件头 wén jiàn tóu
    colour depth 颜色深度 yán sè shēn dù
    image resolution 图像分辨率 tú xiàng fēn biàn lǜ
    screen resolution 屏幕分辨率 píng mù fēn biàn lǜ
    bit depth 位深度 wèi shēn dù
    frame zhēn
    frame rate 帧率 zhēn lǜ
    Watch lesson Exercise sheet
    1.2

    Vector graphics

    A vector graphic 矢量图形 stores the instructions to draw the image as a drawing list 绘图列表 — an ordered list of drawing objects 绘图对象 (geometric primitives 图元: lines, curves, polygons, circles). Each drawing object has properties 属性 such as colour, fill, line width and position (coordinates). To show it, the program renders 渲染 the drawing list at any resolution needed.

    A simple house drawing made from a rectangle body, triangle roof, circle window, door rectangle and a line, each labelled with its shape type and attributes
    A vector image is built from labelled geometric shapes, each with attributes

    Bitmap vs vector

    Task Better choice Why
    Photograph Bitmap Complex pixel-level detail can't be described as shapes.
    Logo, icon, sign Vector Sharp edges; scales to any size without blur.
    Engineering drawing Vector Precise geometry and scaling.
    Painting, texture Bitmap Smooth tonal detail per area.

    Vector advantage: it scales without losing quality — a vector logo stays sharp at any size, while a bitmap blurs when enlarged. Vector disadvantage: it cannot describe arbitrary pixel detail (photographs).

    A "justify" answer links the choice to the task. "The logo must appear on a business card and on a billboard, so it should be a vector graphic: it is stored as drawing objects and is re-rendered sharply at any size, whereas a bitmap would show its pixels when enlarged." For a photograph the argument runs the other way: there are no shapes to describe, so every pixel's colour must be stored.

    Side by side, both enlarged: a bitmap diagonal is a jagged staircase of pixels, while a vector diagonal stays a smooth straight line
    Enlarged, a bitmap's pixels turn jagged; a vector stays smooth at any size
    Explore

    Computing concept lab

    Classify concrete examples by the computing idea they demonstrate.

    Vocabulary Train
    English Chinese Pinyin
    vector graphic 矢量图形 shǐ liàng tú xíng
    drawing list 绘图列表 huì tú liè biǎo
    drawing objects 绘图对象 huì tú duì xiàng
    primitives 图元 tú yuán
    primitive 图元 tú yuán
    properties 属性 shǔ xìng
    render 渲染 xuàn rǎn
    1.2

    Sound

    A continuous wave of analogue data 模拟数据 (the sound) is converted into digital data 数字数据 by sampling 采样:

    • sampling rate 采样率 — samples per second (Hz). CD quality is $44.1\ \text{kHz}$.
    • sampling resolution 采样分辨率 (bit depth) — bits per sample's amplitude 振幅. CD quality is 16 bits.
    A smooth analogue sound wave with vertical sample bars at regular time intervals, each bar reading the wave's amplitude
    Sampling a sound wave: its amplitude is read at each time interval

    File size

    $$\text{size in bits} = \text{sampling rate} \times \text{resolution} \times \text{duration} \times \text{channels}.$$

    A 10-second stereo CD clip: $44100 \times 16 \times 10 \times 2 = 14\,112\,000$ bits $\approx 1.68\ \text{MiB}$.

    Changing settings

    • higher sampling rate → captures higher pitches, larger file.
    • higher sample resolution → finer amplitude steps, less quantisation 量化 noise, larger file.
    • lower of either → smaller file, clear quality loss.

    (The sampling rate must be at least twice the highest frequency you want to keep.)

    A sound wave crossed by evenly spaced sample lines, one dot per sample, noted as sample rate = samples per second and Nyquist at least twice the highest frequency
    Sample rate is samples per second; the Nyquist rule is why it must be at least twice the highest frequency kept
    Explore

    Sound sampling

    y = a sin(bt + c)

    Sampling measures a sound wave at regular intervals — a higher rate copies it more truly.

    Vocabulary Train
    English Chinese Pinyin
    analogue data 模拟数据 mó nǐ shù jù
    digital data 数字数据 shù zì shù jù
    sampling 采样 cǎi yàng
    sampling rate 采样率 cǎi yàng lǜ
    sampling resolution 采样分辨率 cǎi yàng fēn biàn lǜ
    amplitude 振幅 zhèn fú
    sample resolution 采样分辨率 cǎi yàng fēn biàn lǜ
    quantisation 量化 liàng huà
    1.3

    Compression

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the need for and examples of the use of compression
    Show understanding of lossy and lossless compression and justify the use of a method in a given situation
    Show understanding of how a text file, bitmap image, vector graphic and sound file can be compressed Including the use of run-length encoding (RLE)

    Source: Cambridge International syllabus

    Compression 压缩 reduces file size, saving storage and transmission bandwidth 带宽. Two kinds:

    • lossless 无损 — the original data is recovered exactly (text, programs, ZIP/PNG).
    • lossy 有损 — some detail is dropped for much smaller files (JPEG, MP3, video).

    When to use which

    • lossless for documents, source code, medical images — anything needing exact data.
    • lossy for streaming media. Real-time video streaming uses lossy compression because it must send huge amounts of data in real time over limited bandwidth; lossless would not shrink it enough. Raw HD video is gigabytes per minute, so without compression the picture would keep freezing.

    A "justify" answer names the method, then the reason from the situation: "Lossless, because the spreadsheet must be restored exactly; a single changed value would make the accounts wrong." Or: "Lossy, because the photographs are viewed on a phone screen where the dropped detail is not visible, and the smaller files upload faster and use less storage."

    Lossless methods

    • run-length encoding 行程编码 (RLE): store "the next $n$ values are $x$" instead of repeating $x$. Great for flat areas; useless for noisy data.
    • dictionary methods 字典编码 (ZIP, PNG): replace repeated byte sequences with a short reference. Good for text and code.
    • Huffman coding 霍夫曼编码: give short codes to common symbols and long codes to rare ones, bringing the average code length near the data's entropy.

    How each kind of file is compressed:

    • text file: dictionary methods and Huffman coding turn repeated words and common characters into short codes. Text must stay lossless, because one changed character changes the meaning.
    • bitmap image: RLE for runs of identical pixels (icons, diagrams, black-and-white scans); lossy JPEG for photographs, or a lower colour depth or resolution.
    • vector graphic: the drawing list is already small; remove drawing objects that are not needed, store coordinates to fewer decimal places, or apply a lossless method such as ZIP to the file.
    • sound file: lossy MP3 or AAC removes what the ear cannot hear; a lower sampling rate or resolution is also lossy; lossless formats keep every sample and shrink the file much less.
    A 16-pixel row of 6 white, 4 black and 6 white cells; the three runs are bracketed and labelled 6W, 4B, 6W, so 16 pixels are stored as the 3 runs 6W 4B 6W
    Run-length encoding on a single row: 16 pixels become 3 runs
    An 8 by 8 black-and-white grid showing the letter F, with each row's binary pattern and its shorter run-length code listed beside it
    Run-length encoding of the letter F in an $8\times8$ black-and-white grid
    Dictionary coding worked through: the source ABC ABC ABC XYZ, a dictionary in which 1 stands for ABC and 2 stands for XYZ, and the encoded stream 1 1 1 2
    Dictionary coding: each repeated sequence is stored once, and every occurrence becomes a short index
    Huffman coding worked through on the word BANANA: the letter counts A 3, N 2 and B 1, the code tree built from them, and the resulting codes A = 0, B = 10, N = 11
    Huffman coding: the commonest symbol gets the shortest code, so BANANA needs 10 bits instead of 12

    Lossy methods

    • images (JPEG): drop fine detail and colour differences the eye barely sees.
    • sound (MP3, AAC): drop pitches we hear less well, and quiet sounds hidden by louder ones.
    • video combines spatial 空间 compression (within each frame, like JPEG) with temporal 时间 compression (most frames store only the differences from the previous frame).
    A tree classifying compression into lossless (RLE, dictionary/ZIP/PNG, Huffman) and lossy (JPEG images, MP3/AAC sound, video) with examples under each branch
    Compression methods: lossless versus lossy, with common examples
    Explore

    Run-length encoding

    Watch a run of repeated symbols get squashed into a count — simple lossless compression.

    Vocabulary Train
    English Chinese Pinyin
    compression 压缩 yā suō
    bandwidth 带宽 dài kuān
    lossless 无损 wú sǔn
    lossy 有损 yǒu sǔn
    run-length encoding 行程编码 xíng chéng biān mǎ
    dictionary methods 字典编码 zì diǎn biān mǎ
    Huffman coding 霍夫曼编码 huò fū màn biān mǎ
    entropy shāng
    spatial 空间 kōng jiān
    temporal 时间 shí jiān
    Watch lesson Exercise sheet
    1.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    bit a single binary digit, 0 or 1
    byte a group of 8 bits
    binary prefix a multiplier that is a power of 2 (kibi = 1024) rather than a power of 10 (kilo = 1000)
    two's complement a way of representing signed integers in which the most significant bit has a negative place value
    overflow the result of a calculation is too large to be represented in the number of bits available
    Binary Coded Decimal each denary digit is stored as its own 4-bit binary pattern
    character set the set of characters a computer can represent, each with its own binary code
    pixel the smallest element of a bitmap image, storing one colour value
    image resolution the number of pixels in an image, given as width by height
    screen resolution the number of pixels a display can show, given as width by height
    colour depth the number of bits used to store the colour of one pixel
    sampling rate the number of samples of the sound taken per second
    sampling resolution the number of bits used to store the amplitude of one sample
    lossless compression compression from which the original data can be recovered exactly
    lossy compression compression that permanently removes some data, so the original cannot be recovered
    run-length encoding replacing a run of repeated values with one value and a count
    1.3

    Exam tips

    • Show working for base conversions: denary → binary by place values, binary → hexadecimal in nibbles (groups of 4 bits).
    • For two's complement the MSB is negative; to negate, invert and add 1; watch for overflow when the sign bit flips wrongly.
    • Distinguish bitmap (pixels; file size $=$ width $\times$ height $\times$ colour depth) from vector (drawing commands; scales without loss).
    • Sound file size depends on sample rate $\times$ bit depth $\times$ time — more of each means better quality but a bigger file.
    • Compare lossless vs lossy compression and give a use for each.

    Common mistakes

    • Explaining an overflow with "the answer was greater than 255" or "it has 9 bits". State the word size the question gave, then say the result cannot be represented in it.
    • Making a negative number by setting the top bit to 1 and leaving the rest (sign and magnitude). Two's complement means invert every bit of the positive value, then add 1.
    • Forgetting to pad a converted number to the register width the question asks for.
    • Mixing bits and bytes in a file-size calculation. Work in bits, divide by 8 once, and say whether you used 1000 or 1024.
    • Answering "describe" in everyday words ("the picture gets worse"). Use the syllabus terms: fewer colours, banding, lower image resolution, larger pixels.
  • 2

    Communication

    2.1

    Networks: purpose and benefits

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the purpose and benefits of networking devices
    Show understanding of the characteristics of a LAN (local area network) and a WAN (wide area network)
    Explain the client-server and peer-to-peer models of networked computers Roles of the different computers within the network and subnetwork models Benefits and drawbacks of each model Justify the use of a model for a given situation
    Show understanding of thin-client and thick-client and the differences between them
    Show understanding of the bus, star, mesh and hybrid topologies Understand how packets are transmitted between two hosts for a given topology Justify the use of a topology for a given situation
    Show understanding of cloud computing Including the use of public and private clouds Benefits and drawbacks of cloud computing
    Show understanding of the differences between and implications of the use of wireless and wired networks Describe the characteristics of copper cable, fibre-optic cable, radio waves (including WiFi), microwaves, satellites
    Describe the hardware that is used to support a LAN Including switch, server, Network Interface Card (NIC), Wireless Network Interface Card (WNIC), Wireless Access Points (WAP), cables, bridge, repeater
    Describe the role and function of a router in a network
    Show understanding of Ethernet and how collisions are detected and avoided Including Carrier Sense Multiple Access/Collision Detection (CSMA/CD)
    Show understanding of bit streaming Methods of bit streaming, i.e. real-time and on-demand Importance of bit rates broadband speed on bit streaming
    Show understanding of the differences between the World Wide Web (WWW) and the internet
    Describe the hardware that is used to support the internet Including modems, PSTN (Public Switched Telephone Network), dedicated lines, cell phone network
    Explain the use of IP addresses in the transmission of data over the internet Including: • format of an IP address including IPv4 and IPv6 • use of subnetting in a network • how an IP address is associated with a device on a network • difference between a public IP address and a private IP address and the implications for security • difference between a static IP address and a dynamic IP address
    Explain how a Uniform Resource Locator (URL) is used to locate a resource on the World Wide Web (WWW) and the role of the Domain Name Service (DNS)

    Source: Cambridge International syllabus

    A network 网络 is a set of computing devices connected so they can communicate and share resources. Benefits:

    • sharing resources (printers, file servers, internet) — cheaper than equipping each computer.
    • sharing data — many users access the same files.
    • central management — install software, manage users and back up once on a server.
    • communication — email, video calls, messaging.
    • remote access — work from anywhere.
    Explore

    Network route lab

    Follow data from a device through network hardware and protocols.

    Vocabulary Train
    English Chinese Pinyin
    network 网络 wǎng luò
    Exercise sheet
    2.1

    LAN vs WAN

    A local area network 局域网 (LAN) covers a small area — a home, office or school, usually owned by the organisation, with high data rates and low latency 延迟.

    A wide area network 广域网 (WAN) covers a large area — a city, country, or the world (the internet is the largest WAN). It uses telecom-company infrastructure — often the Public Switched Telephone Network 公共交换电话网 (PSTN), leased lines or fibre — with lower data rates and higher latency. A WAN connects LANs together.

    For "give two characteristics of a LAN": it covers a small geographical area (one site or building); the hardware is owned by the organisation, not leased from a telecom company; it connects through its own switches, cables and access points. For "two ways a WAN is different": it covers a large geographical area; it uses third-party (leased or public) infrastructure; data rates are lower and latency higher; it usually joins several LANs. A school on one site is a LAN; a company with offices in two cities needs a WAN, with a leased line or the internet between the sites. Justify the choice with the area covered and who owns the links.

    Several LAN sites spread across a large area, each joined through a central carrier WAN cloud, with one direct leased line between two distant sites
    A wide-area network links many systems across a large area
    Vocabulary Train
    English Chinese Pinyin
    local area network 局域网 jú yù wǎng
    latency 延迟 yán chí
    wide area network 广域网 guǎng yù wǎng
    Public Switched Telephone Network 公共交换电话网 gōng gòng jiāo huàn diàn huà wǎng
    2.1

    Client-server and peer-to-peer

    Client-server

    • powerful machines act as servers 服务器, providing services (files, web pages, email).
    • other machines are clients 客户端 that request services.
    • central and easy to manage, but the server is a single point of failure unless backed up.
    A desktop, laptop and tablet client send requests through the internet to one central server, which sends responses back
    In a client-server network, clients request services from a central server

    Peer-to-peer (P2P)

    • all machines are equal peers; each can be both client and server (peer-to-peer 对等网络).
    • resources are spread across the peers — no central server. Robust to one failure, but harder to keep secure and consistent.

    Choosing a model. Client-server suits a school or a business: files are stored and backed up centrally, a user logs in with one account from any machine, software and security are managed once, and the server can be a powerful machine. The drawbacks are the cost of the server and of a technician, and that the server is a single point of failure. Peer-to-peer suits a few friends sharing files or a game: no server to buy, easy to set up, and each user keeps control of their own machine. The drawbacks the scheme lists: files are spread across many machines, so they are hard to back up and a file is unavailable when its owner's machine is off; each machine must be secured separately; and a peer that serves the others slows down. An online game played through a web browser with other users is the client-server model: the browser is the client, and the game and its shared virtual world run on the company's server, which keeps every player's view consistent.

    Six peer computers in a ring, each linked directly to every other peer, with no central server; every peer is both client and server
    In a peer-to-peer network, every node is both client and server
    Vocabulary Train
    English Chinese Pinyin
    server 服务器 fú wù qì
    client 客户端 kè hù duān
    peer-to-peer 对等网络 duì děng wǎng luò
    2.1

    Thin and thick clients

    A thin client 瘦客户端 does little processing locally and relies on a powerful server (web terminals, remote desktops). A thick client 胖客户端 has strong local processing and storage and runs full applications itself (a normal desktop PC).

    Feature Thin client Thick client
    Local processing minimal substantial
    Local storage minimal substantial
    Reliance on network high lower
    Server load high lower

    The roles: in a thin-client model the server does the processing and stores the data, and the client only sends input and shows the output. A cheap terminal is enough, and everything is backed up and updated on the server, but nothing works if the network or the server fails. In a thick-client model the client runs the software and stores files itself, so it can work with no network connection and puts less load on the server, at the cost of more powerful (and more expensive) clients that must each be updated and secured. A school computer room can run thin clients (cheap, centrally managed); a video editor needs a thick client.

    Vocabulary Train
    English Chinese Pinyin
    thick client 胖客户端 pàng kè hù duān
    thin client 瘦客户端 shòu kè hù duān
    2.1

    Network topologies

    The topology 拓扑 is how the nodes and links are arranged.

    • bus 总线 — all devices on one shared cable. Cheap; the whole LAN fails if the bus fails; performance drops as more devices share the bandwidth 带宽.
    • star 星形 — every device connects to a central switch. One device failing does not affect others; the switch failing brings all down. Most common today.
    • mesh 网状 — every device links directly to others, with many paths. Very fault-tolerant 容错 (traffic reroutes) but needs lots of cabling.
    • hybrid — a mix (a star in each office, mesh links between offices).
    Six computers each connected by a drop cable to one shared backbone cable, with a terminator block at each end
    Bus topology: all devices share one cable with a terminator at each end
    Five computers each connected by its own dedicated cable to a central hub or switch
    Star topology: every device connects to a central hub or switch
    Six computers in a ring with a direct cable between every pair of devices
    Mesh topology: every device links directly to the others
    Three star clusters, each a switch with its own computers, all joined by one shared bus backbone with a terminator at each end
    Hybrid topology: star clusters joined by a central bus

    How packets travel in each topology

    Bus: the sending device puts the packet on the shared cable; every device sees it, and only the one whose address matches accepts it. Only one device can transmit at a time, so collisions happen (CSMA/CD, below). Star: the sender passes the packet to the central switch, which reads the destination address and forwards it only down the cable to that device; two other devices can talk at the same time. Mesh: the packet is passed from node to node along one of several possible routes until it reaches the destination; if a link fails, another route is used.

    To justify a topology: a star for a classroom or an office (a failed cable affects one device; a device is easy to add; with a switch there are no collisions); a mesh where reliability matters most (a hospital, the internet's backbone); a bus only where cost matters and few devices share it. "Draw the star topology" means: the switch in the middle, one line from the switch to each computer, and the server (and the router, if there is one) on their own lines to the switch.

    Explore

    Compare the network topologies

    Tap through the four topologies. Each trades off cost, speed and how well it survives a failure — notice what breaks the whole network in each one.

    Vocabulary Train
    English Chinese Pinyin
    topology 拓扑 tuò pū
    bus 总线 zǒng xiàn
    bandwidth 带宽 dài kuān
    star 星形 xīng xíng
    mesh 网状 wǎng zhuàng
    fault-tolerant 容错 róng cuò
    2.1

    Cloud computing

    Cloud computing 云计算 delivers computing services (servers, storage, software) over the internet, hosted by a third party. Benefits: scalability 可扩展性 (pay for what you need), lower cost, access from anywhere, and reliable redundant data centres. Drawbacks: needs internet, your data is held by a third party, and possible vendor lock-in.

    For the one-mark definition: cloud computing is on-demand computing services (storage, processing, software) provided over the internet by a third party. A public cloud 公有云 is owned by a provider and shared by many customers over the internet; a private cloud 私有云 is dedicated to one organisation, on its own hardware or hosted for it alone. Benefits the scheme accepts: files are accessible from any device with an internet connection; storage scales up and down as needed; the provider handles the hardware, backups and security updates; there is no local server to buy or maintain. Drawbacks: no access without an internet connection; the data is on a third party's hardware, so security and privacy depend on the provider; an ongoing subscription cost; the provider could fail or be attacked; large files may be slow to transfer. A "why does the company use a public cloud" answer says that they need no hardware of their own, pay only for what they use, and their users can reach it from anywhere.

    Vocabulary Train
    English Chinese Pinyin
    cloud computing 云计算 yún jì suàn
    scalability 可扩展性 kě kuò zhǎn xìng
    public cloud 公有云 gōng yǒu yún
    private cloud 私有云 sī yǒu yún
    2.1

    Wired vs wireless

    • wired (Ethernet 以太网 over twisted-pair 双绞线 or fibre-optic 光纤): higher speed, lower latency, fewer errors, more secure.
    • wireless (Wi-Fi, Bluetooth, cellular): no cables, devices can move, but slower, prone to interference and eavesdropping.

    For the same generation, wired wins on speed and reliability; wireless wins on convenience.

    Transmission media

    Medium Characteristics
    copper cable (twisted pair, coaxial) cheap and easy to install; carries an electrical signal; affected by electromagnetic interference; the signal weakens with distance, so repeaters are needed; lower bandwidth than fibre
    fibre-optic cable light pulses in a glass core; very high bandwidth; long distances without repeaters; immune to interference; hard to tap, so secure; expensive and needs skilled installation
    radio waves (including WiFi) no cable, so devices can move; a range of tens of metres, weakened by walls; a shared frequency, so interference and lower speed; can be intercepted, so needs encryption
    microwaves higher-frequency radio for point-to-point links; needs a line of sight; affected by rain and buildings; high bandwidth
    satellites reach remote areas and the whole globe; a long delay (latency), because the signal travels to orbit and back; affected by weather; expensive

    The exam asks for the comparison in both directions. Wired beats wireless on speed, reliability (no interference), security (a cable must be physically tapped) and consistency; wireless beats wired on mobility, the cost of installation, and adding a device without cabling. Allowing both lets students move around with laptops and phones while the fixed desktops keep the faster, more secure connection, and a device with no network port can still connect. Satellite instead of copper reaches places no cable can, but with more delay, weather interference and higher cost.

    Vocabulary Train
    English Chinese Pinyin
    ethernet 以太网 yǐ tài wǎng
    twisted-pair 双绞线 shuāng jiǎo xiàn
    fibre-optic 光纤 guāng xiān
    2.1

    LAN hardware

    • network interface card 网络接口卡 (NIC) — lets a device send and receive on the network; has a unique MAC address MAC地址 (a 48-bit hardware address). A wireless device uses a wireless network interface card 无线网络接口卡 (WNIC).
    • switch 交换机 — forwards Ethernet frames only to the port for the destination MAC address.
    • hub 集线器 — a simpler device that copies traffic to all ports (now obsolete).
    • wireless access point 无线接入点 (WAP) — lets wireless clients join a wired LAN.
    • cabling — twisted-pair for short runs; fibre-optic for longer, faster runs.
    • server — a computer that provides a service to the other devices: files, printing, web pages, email storage.
    • bridge 网桥 — joins two LAN segments into one network, passing traffic between them.
    • repeater 中继器 — receives a weakened signal and retransmits it at full strength, to extend a cable's reach.

    A WNIC's functions, for a four-mark describe: it converts the data into radio signals and back; it carries the device's unique MAC address; it connects the device to a wireless access point and follows the wireless protocol (which channel and frequency to use); and it decodes the incoming signals for the device. Two devices that can physically connect thirty computers with NICs: a switch, or a hub.

    A 5-port gigabit Ethernet switch on a white background, with five numbered RJ-45 ports along the front and a power light
    A network switch: each device's cable plugs into one of its ports
    A black Ethernet patch cable on a white background, with an RJ-45 plug at each end showing the gold metal contacts and the locking clip
    An RJ-45 plug on a twisted-pair Ethernet cable
    A frame addressed to computer C arrives at a switch, which forwards it out only the port for C, leaving the cables to A, B and D unused
    A switch sends each frame only to the port for its destination
    Vocabulary Train
    English Chinese Pinyin
    switch 交换机 jiāo huàn jī
    hub 集线器 jí xiàn qì
    repeater 中继器 zhōng jì qì
    network interface card 网络接口卡 wǎng luò jiē kǒu kǎ
    MAC address MAC地址 MAC dì zhǐ
    wireless network interface card 无线网络接口卡 wú xiàn wǎng luò jiē kǒu kǎ
    wireless access point 无线接入点 wú xiàn jiē rù diǎn
    bridge 网桥 wǎng qiáo
    2.1

    Routers

    A router 路由器 connects different networks and forwards data between them — usually at the boundary of a LAN and the internet. It does:

    • forwarding — reads each packet 数据包's destination IP address IP地址 and sends it out the right port, using a routing table 路由表.
    • network address translation 网络地址转换 (NAT) — lets many private LAN addresses share one public IP.
    • DHCP 动态主机配置协议 — hands out private IP addresses to LAN devices.
    • firewall 防火墙 — blocks unwanted incoming traffic.

    In packet switching 分组交换 a message is split into packets that are sent independently. Each router reads a packet's destination IP address, looks up the next hop in its routing table and forwards it, so the packets of one message may take different routes and are reassembled in order at the destination. A router does receive packets, forward them between networks and hand out IP addresses; it does not find the IP address for a URL (DNS does that) and it does not store web pages. A home router also contains the modem and the wireless access point, so one box connects the LAN to the internet.

    A LAN of three computers and a server joined to a switch, which connects through a router to both the internet and another LAN or WAN
    A router connects a LAN to the internet or another network
    Vocabulary Train
    English Chinese Pinyin
    packet 数据包 shù jù bāo
    router 路由器 lù yóu qì
    IP address IP地址 IP dì zhǐ
    routing table 路由表 lù yóu biǎo
    network address translation 网络地址转换 wǎng luò dì zhǐ zhuǎn huàn
    DHCP 动态主机配置协议 dòng tài zhǔ jī pèi zhì xié yì
    firewall 防火墙 fáng huǒ qiáng
    packet switching 分组交换 fēn zǔ jiāo huàn
    2.1

    Ethernet and CSMA/CD

    Ethernet is the standard (protocol) for wired LANs: devices are joined by twisted-pair or fibre cable, data is sent in frames that carry the source and destination MAC addresses, and a shared medium uses CSMA/CD to deal with collisions. On shared media a collision 冲突 can happen when two devices send at once. The protocol is CSMA/CD 载波侦听多路访问/冲突检测 (Carrier Sense Multiple Access with Collision Detection):

    1. carrier sense — listen before sending; wait if the cable is busy.
    2. multiple access — many devices share the medium.
    3. collision detection — keep listening while sending; a clash is a collision.
    4. on a collision, both stop, send a brief "jam" signal, then wait a random backoff time before retrying.

    The three tasks, in the scheme's words: the device listens (senses the carrier) before transmitting; it keeps checking for a collision while it transmits; on a collision it stops, sends a jam signal, waits a random time and retransmits.

    Modern switched Ethernet uses full-duplex 全双工 point-to-point links, so collisions no longer happen.

    A flowchart of the CSMA/CD process: assemble frame, check the line is idle, send, detect collisions, send a jam signal, back off and retry up to a maximum count
    The CSMA/CD process for handling collisions on shared media
    Vocabulary Train
    English Chinese Pinyin
    collision 冲突 chōng tū
    CSMA/CD 载波侦听多路访问/冲突检测 zài bō zhēn tīng duō lù fǎng wèn / chōng tū jiǎn cè
    full-duplex 全双工 quán shuāng gōng
    2.1

    Bit streaming

    Bit streaming 流式传输 sends multimedia as a continuous stream that the receiver plays as it arrives, instead of downloading the whole file first.

    • real-time (live): captured and streamed as it happens (live sport, video calls). You cannot rewind; low latency is vital.
    • on-demand: pre-recorded on a server (YouTube, Netflix). You can pause and rewind; the server can buffer 缓冲 ahead.

    Real-time streaming works as a short pipeline:

    1. capture and sample the source (a camera or microphone).
    2. encode it, using compression 压缩 to shrink the data.
    3. send it across the network as packets.
    4. the receiver buffers a little, then plays it live — dropping any packet that arrives late, because a live stream cannot wait for it.

    Lossy 有损 compression is used here: moving pictures hide small losses, and the stream must be small enough to fit the bandwidth.

    Why a video is compressed before real-time streaming: the uncompressed stream would need more bandwidth than the connection has, so frames would arrive late and the playback would stall. Compression cuts the number of bits, so the bit rate 比特率 stays below the broadband speed, the delay stays small, and less storage and cost are needed at both ends. The bit rate must be lower than the connection's speed: a higher bit rate gives better quality but needs a faster connection, and if the data arrives more slowly than it is played, the buffer empties and the video freezes. On-demand streaming can buffer more of the file ahead, so it copes with a slower connection; real-time streaming cannot.

    Data flows from the source server into a buffer that fills between a low and a high mark, and the media player reads from the buffer
    Data streams from the server into a buffer before the media player reads it
    Vocabulary Train
    English Chinese Pinyin
    bit streaming 流式传输 liú shì chuán shū
    buffer 缓冲 huǎn chōng
    compression 压缩 yā suō
    lossy 有损 yǒu sǔn
    bit rate 比特率 bǐ tè lǜ
    2.1

    The internet and the World Wide Web

    The internet 互联网 is a global network of networks using a common protocol 协议 suite (TCP/IP). The World Wide Web 万维网 (WWW) is a service that runs over it: hyperlinked documents identified by URLs, viewed in browsers via HTTP/HTTPS. Email and file transfer are other internet services that are not part of the WWW.

    Webmail uses both: the WWW, because the mailbox is a web page reached through a URL in a browser over HTTP; and the internet, because the email itself travels across the network of networks (email is a separate internet service from the web).

    The World Wide Web is one service running on top of the Internet
    The Web is one service running on top of the Internet

    Hardware that supports the internet

    • modem 调制解调器 — converts the computer's digital signal into an analogue signal for a telephone line, and back again at the other end (modulation and demodulation).
    • PSTN — the public telephone network of exchanges and lines; a dial-up or DSL connection carries internet data over it.
    • dedicated line 专线 — a leased line between an organisation and its ISP: always on, with a fixed bandwidth that is not shared, so faster and more reliable, but expensive.
    • cell phone network 蜂窝网络 — the phone sends data by radio to the nearest cell tower (base station); the towers are linked to the phone company's network, which routes the data to the internet; as the phone moves, it is handed over from one cell to the next.
    Three lanes, one per way of reaching the internet: a home computer through a modem and the public switched telephone network; an office LAN over a dedicated leased line; a smartphone by radio to a cell tower and on through the cell phone network; all three end at the ISP
    Three ways to reach the internet: a modem and the PSTN, a dedicated line, and the cell phone network
    Vocabulary Train
    English Chinese Pinyin
    internet 互联网 hù lián wǎng
    protocol 协议 xié yì
    modem 调制解调器 tiáo zhì jiě tiáo qì
    World Wide Web 万维网 wàn wéi wǎng
    dedicated line 专线 zhuān xiàn
    cell phone network 蜂窝网络 fēng wō wǎng luò
    2.1

    IP addresses

    An IP address uniquely identifies a device.

    • IPv4 — 32-bit, four denary numbers 0–255 (192.168.1.10); about $4.3 \times 10^{9}$ addresses (now exhausted).
    • IPv6 — 128-bit, eight groups of four hex digits; about $3.4 \times 10^{38}$ addresses.

    IPv4 is written as four groups of denary numbers separated by dots; each group is an 8-bit number, so it runs from 0 to 255. IPv6 is written as eight groups of four hexadecimal digits separated by colons, 2001:0db8:0000:0000:0000:ff00:0042:8329, and a run of zero groups can be shortened to ::. So 192.168.3.2 is not IPv6: it has four groups, not eight, separated by dots rather than colons, and its groups are denary, not hexadecimal. 256.0.0.A is not a valid address of either kind: an IPv4 group cannot exceed 255 and cannot be a letter, and IPv6 would need colons and eight groups.

    Subnetting

    A network can be split into subnets 子网. The IP address splits into a network part and a host part, given by a subnet mask 子网掩码 (e.g. 255.255.255.0 = first 24 bits are network). Subnetting improves management, cuts broadcast traffic, and improves security.

    The two parts of an address in a subnetwork: the network ID (the first bits, the same for every device in that subnet, given by the ones in the mask) and the host ID (the remaining bits, unique to each device). Benefits of subnetting, for "describe two benefits": less traffic on each part, because broadcasts stay inside their subnet; better security, because one department's traffic is kept from the others; easier management and fault-finding; more efficient use of the addresses. Two devices with the mask 255.255.255.0 are in different subnets when their first three groups differ.

    Six department subnets, each with its own /24 netID, all connected through one central router that also reaches the internet
    Splitting a network into subnets, one netID per department

    Public vs private addresses

    • private addresses are used within a LAN and are not routable on the internet (e.g. 192.168.0.0/16).
    • a public IP address is globally unique and routable, assigned by an ISP 互联网服务提供商.

    Devices behind NAT with private addresses are not directly reachable from the internet, giving some protection.

    The descriptions the tables want: a public address is visible on the internet and unique across it, allocated by the ISP; a private address is visible only inside the LAN, is reused by many LANs, and needs NAT to reach the internet. A static address never changes (set by hand or reserved, as a server needs); a dynamic address is allocated by DHCP each time the device connects and may change.

    Static vs dynamic

    • a static IP address is fixed; used for servers that must be found at a known address.
    • a dynamic IP address is assigned by DHCP and may change; easier for client devices and uses a limited address pool efficiently.

    Worked example. A host has IP address 192.168.10.130 with subnet mask 255.255.255.192. Which network is it on, and is 192.168.10.200 on the same one? The mask's last octet, 192, is 11000000 in binary, so the first 26 bits are the network part and the last 6 bits address the host. That makes the subnets step in blocks of $256 - 192 = 64$: .0, .64, .128, .192. The address 130 falls in the block starting at .128, so the host is on network 192.168.10.128/26, whose usable hosts run .129 to .190 (.191 is the broadcast address). 200 falls in the next block (.192), so it is on a different subnet and traffic between the two must pass through a router. Get the block size from the mask first ($256$ minus the mask octet) - guessing from the first three octets is what makes these go wrong.

    Vocabulary Train
    English Chinese Pinyin
    ISP 互联网服务提供商 hù lián wǎng fú wù tí gōng shāng
    subnets 子网 zi wǎng
    subnet mask 子网掩码 zi wǎng yǎn mǎ
    2.1

    URL and DNS

    A URL 统一资源定位符 (Uniform Resource Locator) locates a resource on the WWW:

    https://www.example.com/about/contact.html
    protocol     domain name        path
    
    • protocol: http, https, etc.
    • domain name 域名: a readable server address.
    • path: the resource on that server.

    The Domain Name System 域名系统 (DNS, also called the Domain Name Service) is a distributed set of servers that turns domain names into IP addresses. When you type a URL, the browser asks a DNS resolver for the IP, which queries DNS servers (root → top-level → authoritative) until it finds it; the browser then connects to that IP and requests the path. DNS saves humans from memorising IP addresses and lets a site change server without changing its name.

    For "explain how the browser uses the URL": the browser splits the URL into the protocol, the domain name and the path; it sends the domain name to a DNS server, which returns the matching IP address (a cache on the computer or at the ISP may answer first); it opens a connection to that IP address using the protocol (HTTPS on port 443); it sends a request for the path; and the web server returns the page, which the browser renders. If the DNS lookup fails, the browser reports that the server cannot be found.

    Numbered one to five: the computer asks a DNS resolver for the IP, the resolver queries another DNS server, the IP is returned to the resolver and then the computer, and the browser connects to the website server
    How DNS finds a website's IP address before the browser connects
    Explore

    How DNS finds a website

    Step through a DNS lookup. The network routes by IP, not by name — so before anything loads, DNS must turn the domain name into an IP address.

    Vocabulary Train
    English Chinese Pinyin
    URL 统一资源定位符 tǒng yī zī yuán dìng wèi fú
    domain name 域名 yù míng
    Domain Name System 域名系统 yù míng xì tǒng
    2.1

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly.

    Term Definition
    LAN a network covering a small geographical area, usually one site, whose hardware is owned by the organisation
    WAN a network covering a large geographical area, joining LANs through third-party (leased or public) links
    client-server a model in which client computers request services from a central, more powerful server that provides them
    peer-to-peer a model in which every computer is equal and can act as both client and server, with no central server
    thin client a client that does little processing or storage itself and depends on the server for both
    thick client a client that does its own processing and storage and can work without the server
    mesh topology a topology in which each device is connected directly to many others, giving more than one route between two devices
    cloud computing on-demand computing services (storage, processing, software) provided over the internet by a third party
    Ethernet the standard protocol for wired LANs, sending data in frames and using CSMA/CD on a shared medium
    switch a device that forwards each frame only to the port of its destination MAC address, within a LAN
    router a device that connects networks and forwards packets between them by their destination IP address
    bit streaming sending a continuous stream of bits so that the receiver plays the media as it arrives, without downloading the whole file first
    internet the global network of networks that uses the TCP/IP protocols
    World Wide Web the collection of hyperlinked web pages, identified by URLs and accessed over the internet through a browser
    URL the address that locates a resource on the web: protocol, domain name and path
    DNS the service that translates a domain name into the IP address of the server that holds the resource
    2.1

    Exam tips

    • Distinguish LAN vs WAN and client-server vs peer-to-peer by who stores and controls the resources.
    • Match each topology (bus, star, mesh) to its advantages and drawbacks (cost, reliability, collisions).
    • Know the job of each device: a switch directs within a LAN by MAC address, a router routes between networks by IP.
    • Explain bit streaming and why buffering is needed (data arrives at a different rate from playback).
    • Distinguish IPv4 vs IPv6 and public vs private addresses; DNS turns a URL into an IP address.

    Common mistakes

    • Saying a switch works by IP address. A switch forwards by MAC address inside the LAN; the router forwards by IP address between networks.
    • Treating the internet and the World Wide Web as the same thing. The web is one service that runs over the internet; email and file transfer are others.
    • Giving "faster" as the whole comparison of wired and wireless. Say faster and more reliable and more secure, and give the wireless side (mobility, no cabling) when the question asks for a comparison.
    • Writing that a router finds the IP address for a URL. DNS does that; the router forwards packets to it.
    • Describing IPv6 with dots and denary groups. Eight groups of four hexadecimal digits, separated by colons.
    • Drawing a star topology as a ring or a chain. Every device has its own line to the switch in the middle.
  • 3

    Hardware

    3.1

    Computers and their components

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the need for input, output, primary memory and secondary (including removable) storage
    Show understanding of embedded systems Including: benefits and drawbacks of embedded systems
    Describe the principal operations of hardware devices Including: Laser printer, 3D printer, microphone, speakers, magnetic hard disk, solid state (flash) memory, optical disc reader/writer, touchscreen, virtual reality headset
    Show understanding of the use of buffers
    Explain the differences between Random Access Memory (RAM) and Read Only Memory (ROM) Including their use in a range of devices and systems
    Explain the differences between Static RAM (SRAM) and Dynamic RAM (DRAM) Including the use of SRAM and DRAM in a range of devices and systems and the reasons for using one instead of the other depending on the device and its use
    Explain the difference between Programmable ROM (PROM), Erasable Programmable ROM (EPROM) and Electrically Erasable Programmable ROM (EEPROM)
    Show an understanding of monitoring and control systems Including: • difference between monitoring and control • use of sensors (including temperature, pressure, infra-red, sound) and actuators • importance of feedback

    Source: Cambridge International syllabus

    A general-purpose computer has four building blocks:

    • input devices 输入设备 — get data in (keyboard, mouse, microphone, scanner, sensors).
    • output devices 输出设备 — give results out (monitor, speakers, printer, actuators).
    • primary memory 主存储器 — fast memory the processor 处理器 (CPU) reaches directly (RAM and ROM). Holds the running program and its data.
    • secondary storage 辅助存储器 — slower, larger, keeps programs and data when not in use (hard disk, SSD, optical disc, USB stick).

    The syllabus asks why each is needed. Input devices are needed because the computer can only work on data and instructions that have been entered. Output devices are needed to present the results in a form people can use. Primary memory is needed because the processor can only execute instructions and use data that are held in memory it can address directly, and it must reach them fast. Secondary storage is needed because primary memory is volatile and small: programs and data must survive the power being switched off, in a larger and cheaper store, and removable storage lets data be moved between computers or kept as a backup.

    A full-size white wireless QWERTY computer keyboard on a white background
    A keyboard: a common input device for typing text and commands
    A modern wireless computer mouse on a white background, with two buttons and a scroll wheel
    A mouse: a pointing input device
    A flatbed scanner on a white background, with a photo coming out of the front after scanning
    A flatbed scanner: an input device that turns a paper page into a digital image
    A silver flat-screen computer monitor on a round stand, with a dark screen
    A monitor: a common output device that displays the screen image
    Explore

    Tap the blocks of a computer system

    Explore the four blocks plus the CPU. Data flows input → processing → output, while primary memory holds the running program and secondary storage keeps it for later.

    Explore

    Network route lab

    Follow data from a device through network hardware and protocols.

    Vocabulary Train
    English Chinese Pinyin
    input devices 输入设备 shū rù shè bèi
    output devices 输出设备 shū chū shè bèi
    primary memory 主存储器 zhǔ cún chǔ qì
    processor 处理器 chǔ lǐ qì
    secondary storage 辅助存储器 fǔ zhù cún chǔ qì
    Exercise sheet
    3.1

    Embedded systems

    An embedded system 嵌入式系统 is a computer built into another device to do one fixed job (washing machine, microwave, car engine unit, thermostat).

    • benefits: optimised for one task, so it is small, uses little power and is cheap to make in volume; reliable, because it runs one fixed program with few chances to go wrong; starts quickly and needs no user set-up; easy to use through a simple interface.
    • drawbacks: limited to its one task, so it cannot be upgraded to do more; hard to update (its firmware 固件 may need special tools or cannot be changed at all); difficult to troubleshoot, and usually the whole device must be replaced when it fails; if it is connected to a network it can be a security weakness, because its software is rarely patched.

    A "describe the drawbacks" question wants each drawback as a full point: what the limitation is and what it means for the user, for example "the firmware cannot be updated, so a security fault found later cannot be fixed".

    Vocabulary Train
    English Chinese Pinyin
    embedded system 嵌入式系统 qiàn rù shì xì tǒng
    firmware 固件 gù jiàn
    3.1

    Principal hardware devices

    Laser printer

    A laser printer 激光打印机 scans the page image onto a charged photosensitive drum 感光鼓. Toner 墨粉 sticks to the charged areas, transfers to the paper, and is melted on by a fuser. Fast, sharp, high-volume.

    A black desktop laser printer on a white background, with a printed page coming out of the top
    A laser printer: fast, sharp printing using a charged drum and toner

    How it works, in the steps the mark scheme lists:

    1. The data for the page is sent to the printer's buffer.
    2. The drum is given a uniform electrostatic charge.
    3. A laser, reflected off a rotating mirror, scans the page image onto the drum, removing the charge where it strikes, so the charge left on the drum matches the image.
    4. Toner, a charged powder, is attracted to the charged parts of the drum only.
    5. The paper is given the opposite charge and rolled against the drum, so the toner transfers onto it.
    6. The fuser 定影器, a pair of heated rollers, melts the toner into the paper. The drum is then discharged and cleaned for the next page.

    3D printer

    A 3D printer 3D打印机 builds an object layer by layer: FDM melts plastic filament through a nozzle; stereolithography cures liquid resin with a UV laser. Used for prototypes and custom medical parts.

    A black enclosed desktop FDM 3D printer with a glass front panel, a part being printed inside, on a white background
    An FDM 3D printer builds an object layer by layer by melting plastic filament

    How it works:

    1. A model of the object is designed in CAD software (or scanned).
    2. Slicing software divides the model into thin horizontal layers and produces the instructions for each one.
    3. The printer builds the object one layer at a time: an FDM printer melts plastic filament 塑料丝 and lays it down through a moving nozzle; a resin printer cures liquid resin with a laser or UV light; a powder printer fuses powder with a laser.
    4. Each layer bonds to the layer below, and the platform (or nozzle) moves by one layer's thickness.
    5. When the last layer is done, any support material is removed. Uses include prototypes, custom medical parts such as prosthetics, and spare parts printed on demand.

    Microphone and speakers

    A microphone 麦克风 turns sound into an electrical signal (a diaphragm vibrates, changing capacitor 电容器 charge or coil position); the signal is digitised by an analogue-to-digital converter 模数转换器 (ADC). A speaker does the reverse — a varying signal drives a coil in a magnetic field, moving a cone to make sound.

    A black USB desktop microphone standing on its base, on a white background
    A microphone turns sound into an electrical signal
    Cutaway of a microphone: sound waves hit a diaphragm linked to a coil around a permanent magnet, giving an output current
    Inside a microphone: sound vibrates the diaphragm and coil to produce a current
    Cutaway of a loudspeaker: current in a coil around an iron core near a permanent magnet moves a paper cone to produce sound waves
    Inside a loudspeaker: a varying current in the coil moves the cone to make sound

    How a microphone works: sound waves make a diaphragm 膜片 vibrate; in a dynamic microphone a coil attached to the diaphragm moves in a magnetic field, so a varying current is induced in it, and in a condenser microphone the diaphragm is one plate of a capacitor whose capacitance changes as it moves; the varying analogue signal is then sampled by an ADC and stored as digital data. A speaker runs the chain backwards: a digital-to-analogue converter 数模转换器 (DAC) produces a varying current, the current in the coil creates a changing magnetic field that pushes against the permanent magnet, the coil and cone move in and out, and the cone's movement makes pressure waves in the air.

    Magnetic hard disk (HDD)

    A hard disk 硬盘 stores data on spinning platters coated with magnetic material. Each platter has tracks 磁道 divided into sectors 扇区. A read/write head 读写头 floats just above and magnetises tiny regions (write) or senses them (read). Cheap per gigabyte, but slower than SSDs and has moving parts.

    An opened 3.5-inch hard disk drive: a shiny circular platter with the actuator arm and read/write head resting over it
    An opened hard disk: the actuator arm carries the read/write head over a platter
    A hard disk platter drawn as concentric track circles, one track highlighted, divided into sectors
    Tracks and sectors on a hard disk platter

    How it works: the platters spin at high speed (thousands of revolutions per minute); each surface is divided into concentric tracks and each track into sectors; read/write heads on actuator arms 磁头臂 move across the platters to the right track; to write, the head magnetises a tiny region with one of two polarities, representing 0 or 1; to read, it detects the polarity as the region passes beneath it. The delays, waiting for the arm to reach the track and for the sector to spin round, are why a hard disk is slower than an SSD.

    Solid-state (flash) memory

    A solid-state drive 固态硬盘 stores data as charge in transistors 晶体管, with no moving parts. Faster random access than HDDs, tougher, lower power, but dearer per gigabyte; each cell wears out after many writes.

    The opened circuit board of a solid-state drive on a white background: a large black flash-memory chip on the left, a smaller controller chip, many tiny components, and a flat SATA connector along the bottom edge — no platters or moving parts
    Inside an SSD: data is stored in flash memory chips, with no moving parts (compare the hard disk above)

    How it works: each cell is a floating-gate transistor 浮栅晶体管; a charge trapped on the floating gate represents a bit and stays there when the power is off; a controller chip maps each address to a cell and spreads writes across the cells, because a cell survives only a limited number of writes.

    Magnetic hard disk Solid-state drive
    Moving parts platters and heads none
    Speed slower: seek and rotation delays much faster random access
    Cost per gigabyte lower higher
    Robustness damaged by knocks; noisy; more power shock-resistant; silent; less power
    Lifetime many rewrites; wears mechanically limited write cycles per cell

    A "why a server uses hard disks rather than SSDs" question wants the left column: cheaper per gigabyte for very large capacities, a long life under constant rewriting, and easier data recovery.

    Optical disc

    A laser detects reflections from tiny pits on an optical disc 光盘 (CD, DVD, Blu-ray). The drive is an optical disc reader/writer: writing uses a stronger laser to change the surface's reflectivity.

    An external optical disc drive on a white background, its tray open with a rainbow-coloured disc loaded
    An optical disc drive: a laser reads tiny pits on a CD, DVD or Blu-ray disc

    How it works: the disc carries one long spiral track of pits 凹坑 and lands 平台 (the flat areas between them); the disc spins and a laser is focused on the track; light reflected from a land differs from light reflected at the edge of a pit, and a light sensor reads each change as a 1 and no change as a 0. Writing uses a stronger laser to change the reflectivity of a dye or alloy layer. A Blu-ray uses a blue laser with a shorter wavelength, so its pits are smaller and closer together, which is why it holds more data than a DVD.

    Touchscreen

    A touchscreen 触摸屏 senses contact. Resistive 电阻式: two conductive layers pressed together; works with anything but is less accurate. Capacitive 电容式: a finger disturbs a charge field; accurate, multi-touch, used in phones.

    People using a tablet touchscreen and a laptop
    A touchscreen senses where a finger touches the glass

    How it works: a resistive screen has two thin conductive layers separated by spacers; pressing pushes the top layer onto the bottom one, closing a circuit at that point, and the controller reads the voltage to find the coordinates. A capacitive screen has a glass layer coated with a transparent conductor that holds a charge; a finger touching it draws a tiny current, the current is measured at each corner, and the controller works out the touch position from the differences. Capacitive screens respond to a light touch and to several fingers at once, but not to a gloved finger or an ordinary stylus.

    Virtual reality headset

    A virtual reality 虚拟现实 (VR) headset has two small displays (one per eye) and motion sensors (accelerometer 加速度计, gyroscope 陀螺仪) that track head movement so the scene shifts as you look around.

    A white virtual reality headset with its head strap and front cameras, on a white background
    A virtual reality headset: two small displays and motion sensors track the head

    How it works: each eye sees its own display through a lens, and the two images differ slightly, so the brain sees depth; sensors (accelerometer, gyroscope, sometimes cameras) report where the head is and which way it points; the computer re-renders the scene from that viewpoint many times a second, so turning the head turns the view; headphones give sound that matches the direction. Used for games, for training such as flight or surgery simulators, and for viewing designs before they are built.

    Vocabulary Train
    English Chinese Pinyin
    microphone 麦克风 mài kè fēng
    hard disk 硬盘 yìng pán
    optical disc 光盘 guāng pán
    laser printer 激光打印机 jī guāng dǎ yìn jī
    drum 感光鼓 gǎn guāng gǔ
    toner 墨粉 mò fěn
    fuser 定影器 dìng yǐng qì
    3D printer 3D打印机 3D dǎ yìn jī
    filament 塑料丝 sù liào sī
    diaphragm 膜片 mó piàn
    capacitor 电容器 diàn róng qì
    analogue-to-digital converter 模数转换器 mó shù zhuǎn huàn qì
    digital-to-analogue converter 数模转换器 shù mó zhuǎn huàn qì
    tracks 磁道 cí dào
    sectors 扇区 shàn qū
    read/write head 读写头 dú xiě tóu
    actuator arms 磁头臂 cí tóu bì
    solid-state drive 固态硬盘 gù tài yìng pán
    transistors 晶体管 jīng tǐ guǎn
    floating-gate transistor 浮栅晶体管 fú zhà jīng tǐ guǎn
    pits 凹坑 āo kēng
    lands 平台 píng tái
    touchscreen 触摸屏 chù mō píng
    resistive 电阻式 diàn zǔ shì
    capacitive 电容式 diàn róng shì
    virtual reality 虚拟现实 xū nǐ xiàn shí
    accelerometer 加速度计 jiā sù dù jì
    gyroscope 陀螺仪 tuó luó yí
    3.1

    Buffers

    A buffer 缓冲 is memory that holds data temporarily while it moves between devices of different speeds. Example: the CPU writes a document to a printer buffer quickly, then is free to do other work while the printer prints from the buffer at its own pace. Buffers stop the fast device waiting for the slow one (also used in streaming, the keyboard, and disk access).

    "State why a 3D printer needs a buffer": the computer sends the print data much faster than the printer can build the layers, so the data is held in the buffer until the printer is ready for it, and the processor is freed to do other work. When the buffer runs low the printer sends an interrupt 中断 to ask for more (topic 4). A video stream works the same way: the buffer fills ahead of playback so a short drop in the network speed does not stop the picture.

    Vocabulary Train
    English Chinese Pinyin
    buffer 缓冲 huǎn chōng
    interrupt 中断 zhōng duàn
    3.1

    RAM and ROM

    • RAM 随机存取存储器 (Random Access Memory) — volatile 易失性 (loses data without power). Holds the OS, running programs and their data; read and written constantly.
    • ROM 只读存储器 (Read-Only Memory) — non-volatile 非易失性 (keeps data without power). Usually written once; holds firmware needed at start-up (the BIOS / boot loader).
    RAM is volatile and read/write; ROM is non-volatile and read-only
    RAM is volatile and read/write; ROM is non-volatile and read-only

    ROM starts the system; RAM then holds the active work.

    RAM ROM
    Volatile? yes: contents lost when the power is off no: contents kept without power
    Read/write? read and written constantly read only in normal use
    Holds the operating system, running programs and their data the firmware and bootstrap program that start the computer
    Size large, and can usually be increased small and fixed
    Typical use the main memory of a computer or phone the start-up code of a PC; the whole program of an embedded system such as a washing machine

    More RAM lets a computer hold more programs and data at once, so it swaps less between memory and disk and runs faster; that is the answer to "explain why the computer with more RAM performs better".

    A RAM module (DIMM): a circuit-board stick with a black heat-spreader over the memory chips and a gold-edged connector that plugs into a slot on the motherboard
    A RAM module (DIMM) plugs into the motherboard as the computer's fast main memory
    Explore

    Device and storage lab

    Classify computing examples by what job they do in a system.

    Vocabulary Train
    English Chinese Pinyin
    RAM 随机存取存储器 suí jī cún qǔ cún chǔ qì
    ROM 只读存储器 zhī dú cún chǔ qì
    volatile 易失性 yì shī xìng
    non-volatile 非易失性 fēi yì shī xìng
    3.1

    SRAM vs DRAM

    • SRAM 静态RAM (Static RAM) stores each bit in a flip-flop 触发器 of several transistors. Fast, but expensive and not dense. Used for CPU cache 高速缓存.
    • DRAM 动态RAM (Dynamic RAM) stores each bit as charge on a tiny capacitor. Cheaper and denser but slower, and must be refreshed 刷新 (rewritten) thousands of times a second. Used for main memory.

    Use SRAM for small fast memory (cache); DRAM for large main memory.

    SRAM DRAM
    Each bit stored in a flip-flop of several transistors one capacitor and one transistor
    Needs refreshing? no yes, thousands of times a second
    Speed faster slower
    Density and cost fewer bits per chip, more expensive more bits per chip, cheaper
    Power uses less power when idle uses more, because of the refresh
    Used for processor cache main memory, including in embedded systems

    "Explain why the embedded system uses DRAM": it needs a large amount of memory at low cost in a small space, and its speed requirement is modest, so the cheaper, denser DRAM is the right choice; SRAM is kept for the small cache where speed matters most.

    Vocabulary Train
    English Chinese Pinyin
    SRAM 静态 jìng tài
    DRAM 动态 dòng tài
    flip-flop 触发器 chù fā qì
    cache 高速缓存 gāo sù huǎn cún
    refreshed 刷新 shuā xīn
    3.1

    PROM, EPROM and EEPROM

    ROM variants you can program after manufacture:

    • PROM (Programmable ROM) — written once (fuses burned by a programmer); cannot be changed.
    • EPROM (Erasable Programmable ROM) — erased by strong UV light through a window, then rewritten (whole chip at once).
    • EEPROM (Electrically Erasable Programmable ROM) — erased and rewritten electrically, a byte at a time, in circuit. Flash memory is a derivative optimised for block erase.
    PROM EPROM EEPROM
    Written once, by the user with a programmer many times many times
    Erased by cannot be erased ultraviolet light through a quartz window an electrical signal
    Erases nothing the whole chip at once a byte or block at a time
    Must be removed from the circuit to reprogram? not applicable yes no

    "Give two differences between EPROM and EEPROM" wants two rows of this table, each stated for both types.

    3.1

    Monitoring and control systems

    Both read sensors; the difference is what they do next.

    • monitoring 监控 — collects and reports data but takes no action (a weather station logging readings).
    • control system 控制系统 — uses sensor data to decide and act through actuators, usually in a feedback loop (a thermostat turning a boiler on/off).

    The three-mark "describe the differences" answer: a monitoring system only measures, records or displays the readings, and at most raises a warning; a control system compares each reading with a preset value 预设值 and, if it is outside the range, sends signals to actuators that change the physical process; the change is then measured again, so a control system contains feedback and a monitoring system does not. Whether a given system is one or the other is decided by that test: a bridge system that measures a vehicle's height and switches on a warning sign is monitoring, because nothing it does changes the vehicle; a system that lowers a barrier is control.

    Worked example. Describe how an automated system opens a door when a person is within 2 metres and closes it when nobody is.

    An infra-red or ultrasonic sensor measures the distance to anything in front of the door; the analogue reading is converted to digital by an ADC and sent to the processor; the processor compares the distance with the preset 2 metres; if it is less, the processor sends a signal to the actuator (a motor) to open the door; the sensor keeps measuring, and when no reading below 2 metres is received the processor signals the motor to close the door. The repeated measuring after each action is the feedback that stops the door opening and closing at the wrong times.

    Flowchart: sensors send signals through an ADC to the processor, which either reports a warning for monitoring or sends signals to actuators in a feedback loop for control
    Monitoring reports data; a control system acts through a feedback loop

    Sensors and actuators

    A sensor 传感器 turns a physical quantity into a signal: temperature (a thermistor 热敏电阻 or thermocouple), pressure (strain gauge), infra-red, sound. Analogue signals need an ADC first. An actuator 执行器 does the reverse — turns a signal into an action (a motor, valve, heater, buzzer).

    Small bead thermistors with two wire legs each, on a white background
    A thermistor: a temperature sensor whose resistance changes with heat
    A small metal stepper motor with a central shaft and coloured wires, on a dark studio background
    A small electric motor: an actuator that turns a signal into movement

    Feedback

    In a control system the actuator changes the environment, which the sensors then re-measure — a feedback 反馈 loop. Without feedback the system cannot correct itself or know when to stop (a thermostat with no temperature feedback would heat forever).

    Explore

    The control feedback loop

    Tap round the loop a thermostat or autopilot repeats. A control system doesn't just read the world — it acts, then re-measures, correcting itself again and again.

    Vocabulary Train
    English Chinese Pinyin
    sensor 传感器 chuán gǎn qì
    actuator 执行器 zhí xíng qì
    monitoring 监控 jiān kòng
    control system 控制系统 kòng zhì xì tǒng
    feedback 反馈 fǎn kuì
    preset value 预设值 yù shè zhí
    thermistor 热敏电阻 rè mǐn diàn zǔ
    3.2

    Logic gates

    Syllabus
    Candidates should be able to: Notes and guidance
    Use the following logic gate symbols: [NOT, AND, OR, NAND, NOR, XOR]
    Understand and define the functions of: NOT, AND, OR, NAND, NOR and XOR (EOR) gates All gates except the NOT gate will have two inputs only.
    Construct the truth table for each of the logic gates above
    Construct a logic circuit From: • a problem statement • a logic expression • a truth table
    Construct a truth table From: • a problem statement • a logic circuit • a logic expression
    Construct a logic expression From: • a problem statement • a logic circuit • a truth table

    Source: Cambridge International syllabus

    The half adder: XOR + AND add two bits

    A logic gate 逻辑门 is a small circuit that does one Boolean 布尔 operation. Inputs and outputs are 0 (false, low) or 1 (true, high). Know the symbol, function and truth table 真值表 for each gate.

    The circuit symbols for NOT, AND, OR, NAND, NOR and XOR gates in a two-by-three grid
    The symbols for the six logic gates

    NOT (inverter)

    A NOT A
    0 1
    1 0

    AND — output 1 only if all inputs are 1

    A B A AND B
    0 0 0
    0 1 0
    1 0 0
    1 1 1

    OR — output 1 if at least one input is 1

    A B A OR B
    0 0 0
    0 1 1
    1 0 1
    1 1 1

    NAND (NOT AND) — output 0 only when all inputs are 1

    A B A NAND B
    0 0 1
    0 1 1
    1 0 1
    1 1 0

    NOR (NOT OR) — output 1 only when all inputs are 0

    A B A NOR B
    0 0 1
    0 1 0
    1 0 0
    1 1 0

    XOR (Exclusive OR, also called EOR) — output 1 if the inputs are different

    A B A XOR B
    0 0 0
    0 1 1
    1 0 1
    1 1 0
    Explore

    Logic gates

    Switch the inputs and pick a gate. Each gate has its own rule — the building blocks of every digital circuit.

    Vocabulary Train
    English Chinese Pinyin
    logic gate 逻辑门 luó jí mén
    Boolean 布尔 bù ěr
    truth table 真值表 zhēn zhí biǎo
    Exercise sheet
    3.2

    Logic circuits

    A logic circuit 逻辑电路 is a network of gates that carries out a Boolean expression. You should be able to move between a problem statement, a logic expression, a truth table, and a circuit diagram.

    The paper writes expressions in words, X = (A AND NOT B) OR (B AND C), and accepts the algebraic form $X = A\overline{B} + BC$ where a dot (or nothing) is AND, a plus is OR, and a bar is NOT. Use whichever the question uses.

    From expression to circuit

    Draw one gate per operator and wire them up. For $X = (A \text{ AND } B) \text{ OR } (\text{NOT } C)$: a NOT gate on $C$, an AND gate on $A$ and $B$, then an OR gate on the two results.

    A logic circuit: an AND gate on inputs A and B, a NOT gate on input C, both feeding an OR gate that gives output X
    Gates wired together to carry out a Boolean expression

    From circuit to expression

    Work forwards from the inputs, labelling each gate's output, until you reach the final output.

    Worked example. Write the expression for the circuit below, then complete its truth table.

    A logic circuit with inputs A, B and C. B passes through a NOT gate; A and NOT B feed an AND gate whose output is labelled P; B and C feed a second AND gate whose output is labelled Q; P and Q feed an OR gate whose output is X
    Label every intermediate output: here P is A AND NOT B and Q is B AND C, so X is P OR Q

    Label the gate outputs: $P = A \text{ AND NOT } B$, $Q = B \text{ AND } C$, so $X = P \text{ OR } Q = (A \text{ AND NOT } B) \text{ OR } (B \text{ AND } C)$. Then give the truth table a column for each intermediate output, so every row can be checked one gate at a time:

    A B C NOT B P Q X
    0 0 0 1 0 0 0
    0 0 1 1 0 0 0
    0 1 0 0 0 0 0
    0 1 1 0 0 1 1
    1 0 0 1 1 0 1
    1 0 1 1 1 0 1
    1 1 0 0 0 0 0
    1 1 1 0 0 1 1

    Drawing a circuit from an expression is the same walk in reverse: start from the innermost brackets, draw one gate per operator, draw a NOT gate on the wire of any input that appears with NOT, keep the inputs on the left and the single output on the right, and label the output with its letter. Every line must end at a gate input or the output; a line that goes nowhere loses the mark.

    From circuit to truth table

    For $n$ inputs there are $2^{n}$ rows. List every input combination; for each, work out the internal gates then the output.

    From truth table to expression (sum of products)

    For each row that outputs 1, write an AND of the inputs (with NOT on any input that is 0 in that row); OR these together. Example: a table that is 1 only on $(A=0,B=1)$ and $(A=1,B=0)$ gives $\overline{A}B + A\overline{B}$, which is $A \text{ XOR } B$.

    From a problem statement

    Turn the English into a Boolean expression first: "A and B" → A AND B; "A or B or both" → A OR B; "exactly one of A and B" → A XOR B; "neither A nor B" → A NOR B; "not both" → A NAND B.

    Worked example. A machine's alarm $X$ sounds when the guard is open ($A=1$) and either the motor is running ($B=1$) or the temperature is high ($C=1$). Write the Boolean expression, and give the rows where $X=1$. Turn the English into logic one clause at a time: "either B or C" is $B + C$, and "A and that" is $X = A\cdot(B + C)$. For the rows, $X=1$ needs $A=1$ and at least one of $B$, $C$ equal to 1 - so $(A,B,C) = (1,0,1)$, $(1,1,0)$ and $(1,1,1)$, three rows out of eight. Notice $A=0$ can never sound the alarm, whatever $B$ and $C$ do. Bracket the OR before ANDing it: $X = A\cdot B + C$ is a different circuit altogether, one that would sound the alarm on a high temperature even with the guard closed.

    Explore

    Half adder

    Wire XOR and AND to the same two inputs: XOR gives the sum bit, AND gives the carry. Click A and B.

    Explore

    Logic circuits

    gates combine into circuits

    Each gate has a fixed rule; chaining them builds every circuit — start with one gate.

    Vocabulary Train
    English Chinese Pinyin
    logic circuit 逻辑电路 luó jí diàn lù
    3.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    embedded system a computer system with a dedicated function built into a larger device
    buffer an area of memory that temporarily stores data while it is transferred between devices working at different speeds
    RAM volatile memory that can be read from and written to, holding the programs and data in use
    ROM non-volatile memory whose contents cannot be changed in normal use, holding the start-up instructions
    SRAM static RAM that stores each bit in a flip-flop and needs no refreshing
    DRAM dynamic RAM that stores each bit as a charge on a capacitor and must be refreshed continually
    monitoring system a system that uses sensors to measure and report on a physical process without changing it
    control system a system that uses sensor readings to decide on and carry out actions, through actuators, that change a physical process
    sensor a device that measures a physical quantity and converts it into a signal for the computer
    actuator a device that converts a signal from the computer into a physical action
    feedback the output of a control system being measured and fed back as input so that the system can correct itself
    logic gate an electronic circuit that performs a Boolean operation on one or more binary inputs to give one binary output
    truth table a table listing every combination of inputs to a logic circuit with the output for each
    3.2

    Exam tips

    • Distinguish RAM (volatile, read/write) from ROM (non-volatile, holds the bootstrap); SRAM (cache, faster) from DRAM (main memory, needs refreshing).
    • For a logic circuit, build the Boolean expression gate by gate, then a truth table covering every input combination.
    • Learn the symbol, expression and truth table for each gate (AND, OR, NOT, NAND, NOR, XOR).
    • Explain a buffer (a temporary store bridging two different speeds) and the role of an interrupt.

    Common mistakes

    • Naming the device instead of describing its operation. "It uses a laser" earns nothing; the steps (charge the drum, laser removes charge, toner attracted, transferred, fused) earn the marks.
    • Saying a monitoring system "controls" something. If nothing changes the physical process, it is monitoring; add the actuator and the feedback and it becomes control.
    • Writing that RAM "stores files permanently" or that ROM "stores the user's data". RAM is volatile working memory; ROM holds the fixed start-up instructions.
    • A truth table with fewer than $2^{n}$ rows, or rows in a random order. Count in binary from 000 to 111 so no combination is missed.
    • Drawing two lines from one output of a gate to be safe, or leaving a wire that ends nowhere. Draw exactly the connections the expression needs.
  • 4

    Processor Fundamentals

    4.1

    Von Neumann architecture

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the basic Von Neumann model for a computer system and the stored program concept
    Show understanding of the purpose and role of registers, including the difference between general purpose and special purpose registers Special purpose registers including: • Program Counter (PC) • Memory Data Register (MDR) • Memory Address Register (MAR) • The Accumulator (ACC) • Index Register (IX) • Current Instruction Register (CIR) • Status Register
    Show understanding of the purpose and roles of the Arithmetic and Logic Unit (ALU), Control Unit (CU) and system clock, Immediate Access Store (IAS)
    Show understanding of how data are transferred between various components of the computer system using the address bus, data bus and control bus
    Show understanding of how factors contribute to the performance of the computer system Including: • processor type and number of cores • the bus widthclock speedcache memory
    Understand how different ports provide connection to peripheral devices Including connection to: • Universal Serial Bus (USB) • High Definition Multimedia Interface (HDMI) • Video Graphics Array (VGA)
    Describe the stages of the Fetch-Execute (F-E) cycle Describe and use 'register transfer' notation to describe the F-E cycle
    Show understanding of the purpose of interrupts Including: • possible causes of interrupts • applications of interrupts • use of an Interrupt Service Routine (ISR) • when interrupts are detected during the fetch-execute cycle • how interrupts are handled

    Source: Cambridge International syllabus

    The fetch-decode-execute cycle

    The Von Neumann architecture·诺依曼体系结构 underlies almost every general-purpose computer:

    • a single memory — the Immediate Access Store 立即存取存储器 (IAS) — holds both program instructions and data (the stored program 存储程序 concept).
    • a processor 处理器 (CPU) fetches instructions from memory and runs them one at a time.
    • instructions run in order unless a branch changes the flow.

    The stored-program idea is what makes a computer flexible: change the program and you change what it does, with no rewiring.

    Explore

    Tap the parts of a Von Neumann computer

    Explore each block. The CPU (control unit, ALU, registers) talks to a single main memory over the buses — and that one shared memory for instructions AND data is the Von Neumann idea.

    Vocabulary Train
    English Chinese Pinyin
    Von Neumann architecture 冯·诺依曼体系结构 féng · nuò yī màn tǐ xì jié gòu
    Immediate Access Store 立即存取存储器 lì jí cún qǔ cún chǔ qì
    stored program 存储程序 cún chǔ chéng xù
    processor 处理器 chǔ lǐ qì
    RAM 随机存取存储器 suí jī cún qǔ cún chǔ qì
    Exercise sheet
    4.1

    The CPU's main parts

    All of these parts sit inside one small chip. The diagram later in this section shows how they connect; the photo below shows the real thing.

    The underside of an Intel CPU chip on a white background, a flat square covered in a grid of hundreds of small gold contact pads that press onto the motherboard socket
    A modern CPU: the whole processor is one small chip (here seen from below, showing the contacts)
    A square CPU socket on a motherboard, with a grid of tiny pins and a metal retention lever, surrounded by circuit tracks
    The matching CPU socket on the motherboard: the chip's contacts press onto these pins

    Arithmetic and Logic Unit (ALU)

    The ALU 算术逻辑单元 does the arithmetic (add, subtract, …) and logic (AND, OR, comparisons). It takes operands from registers 寄存器 and puts results back in a register.

    Control Unit (CU)

    The control unit 控制单元 decodes each instruction and sends the control signals to carry it out — opening data paths, telling the ALU what to do, and controlling memory reads and writes.

    System clock

    The clock sends a steady stream of pulses that keep the CPU in step. Each instruction takes a fixed number of cycles, and the clock speed 时钟频率 (e.g. 3.8 GHz) is one factor in performance.

    "Explain how the CU and the system clock work together": the clock emits pulses at a fixed frequency; the control unit uses each pulse to move the fetch-execute cycle on by one step, sending its control signals in time with the pulses, so every part of the processor changes state together. A faster clock means more steps per second, up to the point where the circuits cannot settle between pulses.

    Registers

    Registers are tiny, very fast stores inside the CPU. The special purpose registers 专用寄存器 each have a fixed job in the cycle:

    • Program Counter 程序计数器 (PC) — the address of the next instruction.
    • Memory Address Register 内存地址寄存器 (MAR) — the address being read or written.
    • Memory Data Register 内存数据寄存器 (MDR) — the data going to or from memory.
    • Current Instruction Register 当前指令寄存器 (CIR) — the instruction being decoded.
    • Accumulator 累加器 (ACC) — the value the ALU is working on.
    • Status Register 状态寄存器 — holds flags 标志 (carry, zero, negative, overflow) used by branches. Each flag is one bit, set or cleared by the ALU after an operation: the zero flag after a comparison that matched, the carry flag when an addition overflowed the register, the negative flag when a result is negative. A conditional jump reads the flags to decide whether to branch, and an overflow flag can raise an interrupt.
    • Index Register 变址寄存器 — an offset added to an address in indexed addressing; incrementing it steps through an array one element at a time.

    The "complete the table describing the role of each register" question wants one precise sentence per register in these terms: the PC holds the address of the next instruction to be fetched; the MAR holds the address of the location being read from or written to; the MDR holds the data or instruction just read from, or about to be written to, that location; the CIR holds the instruction currently being decoded and executed; the ACC holds the result of the last arithmetic or logic operation.

    General-purpose registers 通用寄存器 are used by the programmer for temporary values during a calculation. Movements of data between registers and memory are written in register transfer 寄存器传送 notation — e.g. MAR ← [PC] ("copy the contents of PC into MAR").

    Block diagram of the Von Neumann CPU showing PC, MAR, MDR, CIR, ACC, status register, control unit, ALU and system clock, linked to main memory and input/output by the address, data and control buses
    The Von Neumann CPU: registers, control unit and ALU linked by buses
    Vocabulary Train
    English Chinese Pinyin
    arithmetic and logic unit 算术逻辑单元 suàn shù luó jí dān yuán
    ALU 算术逻辑单元 suàn shù luó jí dān yuán
    register 寄存器 jì cún qì
    control unit 控制单元 kòng zhì dān yuán
    clock speed 时钟频率 shí zhōng pín lǜ
    special purpose registers 专用寄存器 zhuān yòng jì cún qì
    Program Counter 程序计数器 chéng xù jì shù qì
    Memory Address Register 内存地址寄存器 nèi cún dì zhǐ jì cún qì
    Memory Data Register 内存数据寄存器 nèi cún shù jù jì cún qì
    Current Instruction Register 当前指令寄存器 dāng qián zhǐ lìng jì cún qì
    accumulator 累加器 lěi jiā qì
    Status Register 状态寄存器 zhuàng tài jì cún qì
    flags 标志 biāo zhì
    Index Register 变址寄存器 biàn zhǐ jì cún qì
    general-purpose registers 通用寄存器 tōng yòng jì cún qì
    register transfer 寄存器传送 jì cún qì chuán sòng
    4.1

    Buses

    Three internal buses 总线 (sets of parallel wires) connect the parts:

    • address bus 地址总线 — carries the memory address. One-way (CPU → memory).
    • data bus 数据总线 — carries the data. Two-way.
    • control bus 控制总线 — carries control signals (read, write, interrupt). Two-way.

    An $n$-bit address bus can reach $2^{n}$ memory locations. The data-bus width sets how many bits move per access (often the word size).

    CPU, memory and input/output each tapping the address bus (one-way), data bus and control bus inside the system bus
    The three system buses connecting the CPU, memory and input/output
    A motherboard seen from above: the CPU socket, memory slots and expansion slots joined by dense printed tracks
    A motherboard: the CPU, memory and I/O all sit on one set of buses — the printed tracks running between them
    Vocabulary Train
    English Chinese Pinyin
    control bus 控制总线 kòng zhì zǒng xiàn
    buses 总线 zǒng xiàn
    address bus 地址总线 dì zhǐ zǒng xiàn
    data bus 数据总线 shù jù zǒng xiàn
    4.1

    What affects performance

    • clock speed — more cycles per second.
    • number of cores 核心 — a multi-core CPU runs several threads at once.
    • word size 字长 — a 64-bit CPU handles 64-bit chunks per cycle and can address far more memory than a 32-bit one.
    • amount of RAM 随机存取存储器 — more RAM holds more of the working set; too little forces the OS to page to disk.
    • cache memory 高速缓存 size — more cache cuts average memory access time.
    • secondary storage 辅助存储器 type — an SSD loads programs far faster than an HDD.
    • bus width and speed — wider/faster buses move data more quickly.

    Match the specs to the workload: a quad-core beats a dual-core on parallel work, but higher per-core speed wins on single-threaded work.

    Each factor is a two-mark answer with a reason attached:

    • More cores: each core can fetch and execute its own instruction at the same time, so several programs, or the threads of one program, run in parallel. But a program must be written to use more than one core, so doubling the cores does not double the speed.
    • Higher clock speed: more fetch-execute cycles per second, so more instructions per second; the limit is the heat produced.
    • Wider bus: a wider data bus moves more bits in each transfer, so fewer transfers are needed for the same data; a wider address bus can address more memory locations.
    • Cache memory: a small, fast memory inside or next to the processor that keeps the instructions and data used most recently or most often. Reading them from cache is much faster than from RAM, so the processor spends less time waiting.

    "Explain why the new computer performs better" is answered by comparing the two specifications line by line: a higher clock speed executes more instructions per second, more cores run more tasks at once, more cache means fewer slow accesses to RAM, and more RAM means fewer transfers to disk.

    Vocabulary Train
    English Chinese Pinyin
    word size 字长 zì cháng
    number of cores 核心 hé xīn
    cores 核心 hé xīn
    amount of RAM 随机存取存储器 suí jī cún qǔ cún chǔ qì
    page
    cache memory 高速缓存 gāo sù huǎn cún
    cache 高速缓存 gāo sù huǎn cún
    secondary storage 辅助存储器 fǔ zhù cún chǔ qì
    4.1

    Ports

    A port 端口 is a physical socket for connecting a peripheral 外围设备:

    • USB (Universal Serial Bus) — general-purpose (keyboards, drives, phones).
    • HDMI (High Definition Multimedia Interface) — digital video and audio to a screen.
    • VGA (Video Graphics Array) — older analogue video output to a monitor.
    • Ethernet (RJ-45) — wired LAN. Audio jacks — headphones/microphone.

    Different ports use different signals, so an HDMI cable will not fit a USB socket. USB-C is unusual in carrying video, data and power.

    "Explain how the computer connects to the monitor through HDMI": the HDMI port sends the video and the audio as one digital signal down a single cable, so no conversion to analogue is needed and the picture is not degraded; the cable carries high-definition resolutions and the monitor's own port decodes the signal. A USB device is plug-and-play: when it is connected the computer detects it, identifies it, loads or installs the driver it needs, and can supply it with power, all without a restart.

    Vocabulary Train
    English Chinese Pinyin
    port 端口 duān kǒu
    peripheral 外围设备 wài wéi shè bèi
    4.1

    Fetch-Execute cycle

    The CPU repeats the fetch-execute cycle 取指-执行周期, one run per machine instruction.

    Fetch

    1. the PC's address is copied to the MAR.
    2. the PC is incremented to point to the next instruction.
    3. a read signal goes over the control bus.
    4. memory puts the instruction on the data bus.
    5. it is copied into the MDR, then into the CIR.

    The exam asks for these steps in register transfer notation 寄存器传送记法, where [X] means the contents of register X and [[MAR]] means the contents of the memory location whose address is in the MAR:

    MAR ← [PC]          the address of the next instruction goes to the MAR
    PC  ← [PC] + 1      the PC now points to the following instruction
    MDR ← [[MAR]]       the instruction at that address is read into the MDR
    CIR ← [MDR]         the instruction is copied into the CIR for decoding
    

    The order matters: the PC is incremented straight after its address has been copied, so that a jump executed later can still overwrite it. During execution the same notation describes each instruction; for LDD 200, for example, MAR ← 200, MDR ← [[MAR]], ACC ← [MDR].

    The fetch register transfers in order: 1 the PC's address goes to the MAR; 2 the MAR sends the address to memory; 3 the instruction returns to the MDR; 4 the MDR copies it to the CIR; meanwhile the PC is incremented
    The register transfers in a fetch: PC → MAR → memory → MDR → CIR, with the PC incremented

    Decode

    The CU decodes the instruction in the CIR — what operation, and which operands or addresses.

    Execute

    The CU carries it out: arithmetic/logic goes to the ALU (result to the ACC); a load/store moves data between memory and a register; a branch changes the PC. Then the cycle repeats.

    Flowchart of the fetch-execute cycle from START: the fetch stage (PC to MAR, increment PC, read signal, memory to data bus to MDR to CIR), the decode stage, the execute stage, then a check for interrupts that loops back to START
    The fetch-execute cycle, with a check for interrupts each time
    Explore

    The fetch-execute cycle

    Tap round the loop the CPU repeats billions of times a second. Watch how fetch uses the PC/MAR/MDR/CIR registers, then decode and execute act on what was fetched.

    Explore

    The fetch–execute cycle

    Step through how the CPU runs one instruction — fetch it from memory, decode it, then execute it, over and over.

    Vocabulary Train
    English Chinese Pinyin
    fetch-execute cycle 取指-执行周期 qǔ zhǐ - zhí xíng zhōu qī
    register transfer notation 寄存器传送记法 jì cún qì chuán sòng jì fǎ
    4.1

    Interrupts

    An interrupt 中断 is a signal that pauses the normal cycle so the CPU can handle an urgent event (a key press, a packet arriving, a hardware fault, division by zero, the OS timer).

    Handling one:

    1. finish the current instruction.
    2. save the state (PC and registers).
    3. load the address of the interrupt service routine 中断服务程序 (ISR) into the PC and run it.
    4. the ISR handles the event.
    5. restore the saved state and carry on.

    Interrupts let the system respond promptly without the CPU constantly checking devices, and are how the OS multitasks.

    "Explain how an interrupt from an input device is detected and handled in the F-E cycle" is a four-mark answer with these points: the device sends an interrupt signal that sets the interrupt flag in the interrupt register 中断寄存器; the processor checks that register at the end of every fetch-execute cycle, after the current instruction has finished executing; if a flag is set and the interrupt has a higher priority than the current task, the contents of the PC and the other registers are saved onto the stack; the address of the interrupt service routine is loaded into the PC and the routine runs; when it finishes, the saved values are restored from the stack and the interrupted program continues from where it stopped.

    Causes worth naming: a hardware interrupt from a device (a key pressed, a printer buffer empty, a network packet arriving), a software interrupt from a fault (division by zero, an illegal instruction, arithmetic overflow), a timer interrupt from the operating system marking the end of a time slice, and a power failure warning.

    Flowchart of interrupt handling: the running program is interrupted, the CPU finishes the current instruction, saves its state (PC and registers) on the stack, runs the interrupt service routine, restores the state and resumes
    How an interrupt fits into the fetch-execute cycle
    Vocabulary Train
    English Chinese Pinyin
    interrupt 中断 zhōng duàn
    interrupt service routine 中断服务程序 zhōng duàn fú wù chéng xù
    interrupt register 中断寄存器 zhōng duàn jì cún qì
    stack zhàn
    4.2

    Assembly language and machine code

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the relationship between assembly language and machine code
    Describe the different stages of the assembly process for a two-pass assembler Apply the two-pass assembler process to a given simple assembly language program
    Trace a given simple assembly language program
    Show understanding that a set of instructions are grouped Including the following groups: • Data movement • Input and output of data • Arithmetic operations • Unconditional and conditional instructions • Compare instructions
    Show understanding of and be able to use different modes of addressing Including immediate, direct, indirect, indexed, relative

    Source: Cambridge International syllabus

    The CPU actually runs machine code 机器码 — bit patterns, specific to one architecture. Assembly language 汇编语言 is a readable form, with one instruction per machine instruction, written using mnemonics 助记符 like LDD, ADD, JMP. An assembler 汇编器 translates it to machine code.

    An assembler translates assembly mnemonics into machine-code bit patterns
    An assembler turns mnemonics into machine-code bit patterns

    Two-pass assembler

    A two-pass assembler reads the source twice:

    • pass 1 builds a symbol table 符号表: each time a label 标签 (like LOOP:) appears, record its address; no code yet.
    • pass 2 generates code: translate each instruction, and when one refers to a label (like JMP LOOP), look up its address in the symbol table.

    Two passes handle forward references 前向引用 (a jump to a label defined later).

    Worked example. Apply the two-pass process to this program, whose first instruction is stored at address 100.

            LDD  COUNT
    LOOP:   DEC  ACC
            CMP  #0
            JPN  LOOP
            END
    COUNT:  5
    

    Pass 1 reads each line, counts the address it will occupy, and records every label in the symbol table: LOOP = 101 (the DEC line) and COUNT = 105 (the data line). No code is produced. Pass 2 reads the program again and translates each line into machine code, replacing each mnemonic by its opcode 操作码 and each symbolic address by the number from the symbol table: LDD COUNT becomes the opcode for LDD with operand 操作数 105, and JPN LOOP becomes the opcode for JPN with operand 101. The jump back to LOOP could have been resolved in one pass, but a jump forward to a label not yet seen could not, which is why the assembler makes two.

    Example instruction set

    Cambridge uses a small generic set, printed in the paper's reference table, with one general-purpose register, the accumulator (ACC), and an index register (IX). An operand written #n is a denary number, Bn a binary number and &n a hexadecimal number; <address> is a location number or a label.

    Group Instruction What it does
    Data movement LDM #n load the number n into ACC (immediate)
    LDD <address> load the contents of the address into ACC (direct)
    LDI <address> the address holds another address; load the contents of that one into ACC (indirect)
    LDX <address> add IX to the address and load the contents of the result into ACC (indexed)
    LDR #n load the number n into IX
    MOV <register> copy ACC into the named register (IX)
    STO <address> store the contents of ACC at the address
    Input and output IN read a key press and put its ASCII code in ACC
    OUT output the character whose ASCII code is in ACC
    Arithmetic ADD <address> / ADD #n add the contents of the address, or the number, to ACC
    SUB <address> / SUB #n subtract from ACC
    INC <register> / DEC <register> add 1 to, or subtract 1 from, ACC or IX
    Compare CMP <address> / CMP #n compare ACC with the contents of the address, or with n, and set the flag
    CMI <address> compare ACC with the contents of the address held at the address (indirect)
    Jump JMP <address> jump to the address unconditionally
    JPE <address> / JPN <address> jump if the last compare was equal / not equal
    Bit manipulation AND, OR, XOR with #n, Bn, &n or <address> bitwise operation on ACC
    LSL #n / LSR #n shift ACC logically n places left or right
    END end the program

    The "assembly language instructions are grouped" question wants the group names, and an instruction from each: data movement, input and output, arithmetic, unconditional and conditional jumps, compare, and bit manipulation.

    Explore

    How a two-pass assembler works

    Step through it. The assembler reads your code twice: pass 1 just finds where every label lives, so pass 2 can fill in the addresses — that is how a jump to a label defined later still works.

    Vocabulary Train
    English Chinese Pinyin
    operand 操作数 cāo zuò shù
    assembly language 汇编语言 huì biān yǔ yán
    machine code 机器码 jī qì mǎ
    mnemonics 助记符 zhù jì fú
    assembler 汇编器 huì biān qì
    symbol table 符号表 fú hào biǎo
    label 标签 biāo qiān
    forward references 前向引用 qián xiàng yǐn yòng
    opcode 操作码 cāo zuò mǎ
    Exercise sheet
    4.2

    Addressing modes

    The addressing mode 寻址方式 (the modes of addressing) says how the CPU finds the operand:

    • immediate addressing 立即寻址 — the operand is the value in the instruction. LDM #10 loads 10.
    • direct addressing 直接寻址 — the instruction holds an address; the operand is the value there. LDD 200.
    • indirect addressing 间接寻址 — the instruction holds an address that holds another address, which is the data. LDI 200.
    • indexed addressing 变址寻址 — effective address is address + index register; used for arrays. LDX 100 with IR = 5 reads address 105.

    (Relative addressing 相对寻址 gives the address as an offset from the PC — used for jumps.)

    Four addressing modes reaching their operand. Immediate: LDM #10 gives 10 directly. Direct: LDD 200 reads memory location 200 (=42). Indirect: LDI 200 reads location 200 (=250) then location 250 (=99). Indexed: LDX 100 with index register 5 reads location 105 (=7)
    How each addressing mode reaches its operand — immediate, direct, indirect and indexed

    Worked example. Memory holds: location 200 = 250, location 250 = 99, location 105 = 7. The index register holds 5. What is in the accumulator after each of LDM #200, LDD 200, LDI 200 and LDX 100? Follow how far each mode has to look. LDM #200 is immediate - the operand is the number written in the instruction, so the accumulator holds 200. LDD 200 is direct - go to location 200 and take what is there: 250. LDI 200 is indirect - location 200 holds 250, which is another address, so go on to location 250: 99. LDX 100 is indexed - add the index register to the address, $100 + 5 = 105$, and read location 105: 7. Count the hops to keep them apart: immediate 0, direct 1, indirect 2, indexed 1 (once the index has been added).

    Vocabulary Train
    English Chinese Pinyin
    indexed addressing 变址寻址 biàn zhǐ xún zhǐ
    addressing mode 寻址方式 xún zhǐ fāng shì
    immediate addressing 立即寻址 lì jí xún zhǐ
    direct addressing 直接寻址 zhí jiē xún zhǐ
    indirect addressing 间接寻址 jiàn jiē xún zhǐ
    relative addressing 相对寻址 xiāng duì xún zhǐ
    4.2

    Tracing an assembly program

    To trace it: make a table with columns for the PC, ACC, index register, each variable and any flags. Step through the instructions, updating the table after each; follow branches when they change the PC; stop at END. A common pattern is a loop over an array using indexed addressing.

    Worked example. Trace this program. Address 200 holds 5 and address 201 holds 0.

    100   LDD  200
    101   CMP  #0
    102   JPE  108
    103   OUT
    104   DEC  ACC
    105   STO  200
    106   LDD  201
    107   JMP  100
    108   END
    

    Write one row for each instruction executed, filling in only the columns that change:

    Instruction ACC 200 201 Output
    start 5 0
    LDD 200 5
    CMP #0
    JPE 108 not taken
    OUT character with code 5
    DEC ACC 4
    STO 200 4
    LDD 201 0
    JMP 100
    LDD 200 4

    and so on, until LDD 200 loads 0, the compare sets the equal flag, JPE 108 is taken and the program ends. Three things the examiner checks: a CMP changes no register, only a flag; a jump not taken still counts as executed; and OUT outputs a character, so it goes in the output column, not the ACC column. "State the effect of changing LDD 10 to LDM #10": the ACC would hold the number 10 instead of the contents of address 10.

    4.3

    Binary shifts

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of and perform binary shifts Logical, arithmetic and cyclic Left shift, right shift
    Show understanding of how bit manipulation can be used to monitor/control a device Carry out bit manipulation operations Test and set a bit (using bit masking)
    Instruction Label | Opcode | Operand Explanation
    AND #n / Bn / &n Bitwise AND operation of the contents of ACC with the operand
    AND
    Bitwise AND operation of the contents of ACC with the contents of
    XOR #n / Bn / &n Bitwise XOR operation of the contents of ACC with the operand
    XOR
    Bitwise XOR operation of the contents of ACC with the contents of
    OR #n / Bn / &n Bitwise OR operation of the contents of ACC with the operand
    OR
    Bitwise OR operation of the contents of ACC with the contents of
    LSL #n Bits in ACC are shifted logically n places to the left. Zeros are introduced on the right hand end
    LSR #n Bits in ACC are shifted logically n places to the right. Zeros are introduced on the left hand end
    Labels an instruction
    Gives a symbolic address
    All questions will assume there is only one general purpose register available (Accumulator) ACC denotes Accumulator IX denotes Index Register
    can be an absolute or symbolic address # denotes a denary number, e.g. #123 B denotes a binary number, e.g. B01001010 & denotes a hexadecimal number, e.g. &4A

    Source: Cambridge International syllabus

    A logical shift 逻辑移位 moves all the bits left or right by some places, filling new positions with 0.

    • left shift by 1 (LSL #1) — bits move left, a 0 enters on the right; for an unsigned number this is × 2.
    • right shift by 1 (LSR #1) — bits move right, a 0 enters on the left; for an unsigned number this is integer ÷ 2.

    Shifting by $n$ places multiplies or divides by $2^{n}$. Example: 00001011 (11) LSL #100010110 (22).

    Bits shifted off the end are lost, so the multiplication is only correct while they were zeros. LSL #2 on the two's-complement integer 11001010 gives 00101000: the two 1s that fell off the left are gone, the sign bit has changed, and the result is no longer four times the original.

    An arithmetic right shift keeps the sign bit so a negative signed number stays negative. A cyclic shift 循环移位 (rotate) feeds the bit that drops off one end back in at the other end, so no bits are lost.

    "Show the result of an arithmetic right shift of 3 places on 10011110": copy the sign bit into each vacated place, 11110011. The same shift on 01011100 gives 00001011. A cyclic left shift of 1 on 10000110 gives 00001101: the leading 1 reappears on the right.

    Three 8-bit shifts: LSL #1 turns 00001011 into 00010110 (times 2, a 0 enters on the right); LSR #1 turns it into 00000101 (integer divide by 2, a 0 enters on the left); ASR #1 turns 10110100 into 11011010, copying the sign bit
    Logical left ($\times 2$), logical right ($\div 2$) and arithmetic right (keeps the sign bit)

    The difference between the two right shifts is a single bit. Take 11110000, which is 240 read as unsigned and $-16$ read as signed. LSR #1 brings in a 0 and gives 01111000 $= 120$, which is the correct half of 240. ASR #1 copies the sign bit instead and gives 11111000 $= -8$, which is the correct half of $-16$. Neither is wrong — each halves the value under one reading.

    The byte 11110000 shifted right twice over: LSR brings a 0 in on the left giving 01111000 which is 120, while ASR copies the sign bit giving 11111000 which is minus 8; the two results differ only in the bit that entered
    Logical and arithmetic right shift on the same byte: only the bit that enters on the left differs

    Bit manipulation for monitoring/control

    Embedded devices often use one bit of a register per signal (e.g. bit $n$ = LED $n$). Using a mask 掩码bit masking — you can:

    • set bit $n$: R = R OR a mask with bit $n$ set.
    • clear bit $n$: R = R AND a mask with bit $n$ clear and the rest set.
    • toggle bit $n$: R = R XOR a mask with bit $n$ set.
    • test bit $n$: R AND the mask, then check if the result is non-zero.
    Bit masking on the byte 01001000: set bit 2 with OR 00000100 to get 01001100; clear bit 6 with AND 10111111 to get 00001000; toggle bit 3 with XOR 00001000 to get 01000000
    Set a bit with OR, clear it with AND, toggle it with XOR — each using a mask

    Bit manipulation is fast, uses little memory, and lets one byte hold up to 8 on/off states.

    In the exam's instruction set these are AND, OR and XOR with a mask written as a denary, binary or hexadecimal operand. With the ACC holding 10101100:

    Instruction Mask Result in ACC Effect
    AND B00001111 00001111 00001100 keeps only the low four bits (clears the others)
    OR #1 00000001 10101101 sets the least significant bit, leaving the rest unchanged
    XOR &FF 11111111 01010011 inverts every bit
    AND B00001000 then CMP #0 00001000 00001000 tests bit 3: the compare is not equal, so bit 3 was set
    LSL #2 10110000 shifts left two places, losing the top two bits
    LSR #3 00010101 shifts right three places, zeros entering on the left

    "Write the instruction that sets the least significant bit to 1 and leaves the others unchanged": OR #1, or OR B00000001. To clear a bit use AND with a mask that has a 0 in that place and 1s elsewhere; to test a bit, AND with a mask that has a 1 only in that place, then compare the result with zero. In a monitoring device, one bit of a register per sensor lets a single AND check whether a particular sensor is on, and one OR switches an actuator's control bit on without disturbing the others.

    Explore

    Shift and mask the bits of a byte

    Pick an operator and watch each result bit. A left shift (<<) moves every bit up one place (×2); a right shift (>>) moves them down (÷2); AND with a mask clears the bits you don't want.

    Vocabulary Train
    English Chinese Pinyin
    bit wèi
    logical shift 逻辑移位 luó jí yí wèi
    cyclic shift 循环移位 xún huán yí wèi
    mask 掩码 yǎn mǎ
    Exercise sheet
    4.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    stored program concept the program instructions and the data are both held in main memory, and instructions are fetched and executed one at a time
    register a small, very fast storage location inside the processor with a specific purpose
    Program Counter the register holding the address of the next instruction to be fetched
    Memory Address Register the register holding the address of the memory location being read from or written to
    Memory Data Register the register holding the data or instruction just read from, or about to be written to, memory
    Current Instruction Register the register holding the instruction currently being decoded and executed
    Accumulator the general-purpose register holding the result of the last arithmetic or logic operation
    cache memory small, fast memory close to the processor holding frequently used instructions and data
    interrupt a signal from a device or program that causes the processor to pause the current task and run an interrupt service routine
    assembly language a low-level language in which each mnemonic instruction corresponds to one machine-code instruction
    immediate addressing the operand is the value written in the instruction
    direct addressing the operand is the contents of the address written in the instruction
    indirect addressing the address in the instruction holds the address of the operand
    indexed addressing the operand's address is the address in the instruction plus the contents of the index register
    relative addressing the operand's address is given as an offset from the address of the current instruction
    logical shift every bit moves the given number of places and zeros fill the vacated places
    4.3

    Exam tips

    • Learn the fetch-execute cycle in register-transfer terms (PC, MAR, MDR, CIR, ACC) and what increments the PC.
    • Name each register's job; the address bus is one-way, the data bus is two-way.
    • Distinguish the addressing modes (immediate, direct, indirect, indexed) — a frequent question.
    • Explain how clock speed, number of cores, cache size and word length affect performance.
    • For a binary shift, state whether it is logical or arithmetic; a left shift multiplies by 2, a right shift divides by 2.

    Common mistakes

    • Saying the PC holds the current instruction, or the MDR holds an address. The PC holds the address of the next instruction; the MDR holds data or an instruction, never an address.
    • Leaving the increment of the PC out of the fetch, or putting it after the execute. It happens as soon as the address has been copied to the MAR.
    • Reading LDD 10 as "load 10". LDD 10 loads the contents of address 10; LDM #10 loads the number 10.
    • Putting a value in the ACC column for CMP or OUT. A compare sets a flag only; an output goes to the output column.
    • Saying an interrupt is handled "immediately". The processor finishes the current instruction and checks for interrupts at the end of the cycle.
    • Using a logical right shift on a negative two's-complement number. Only an arithmetic shift keeps the sign bit.
  • 5

    System Software

    5.1

    Operating systems

    Syllabus
    Candidates should be able to: Notes and guidance
    Explain why a computer system requires an Operating System (OS)
    Explain the key management tasks carried out by the Operating System Including memory management, file management, security management, hardware management (input/output/peripherals), process management
    Show understanding of the need for typical utility software provided with an Operating System Including disk formatter, virus checker, defragmentation software, disk contents analysis / disk repair software, file compression, back-up software
    Show understanding of program libraries Including: • software under development is often constructed using existing code from program libraries • the benefits to the developer of software constructed using library files, including Dynamic Link Library (DLL) files

    Source: Cambridge International syllabus

    Why a computer needs an OS

    Hardware on its own can only fetch and run instructions — it knows nothing about files, programs, networks or users. The operating system 操作系统 (OS) is the software layer that:

    • manages the hardware (processor 处理器, memory, I/O, storage) for the running programs.
    • provides services (file system, network, user accounts) through a clear interface, so programs need not talk to the hardware directly.
    • provides a user interface (command line, GUI, touch).
    • lets several programs share the hardware safely — each gets fair CPU time and is kept out of the others' memory.

    Without an OS, every program would need its own drivers, and only one program could safely run at a time.

    "Describe the purpose of an OS" — the five-mark list. The OS (1) provides an interface between the user and the hardware; (2) hides the complexity of the hardware from the user and from application programs; (3) manages the hardware resources — processor time, memory, storage and input/output devices — and shares them between programs; (4) loads application software into memory and runs it, giving every program the same platform to run on; (5) lets several programs run at once (multitasking 多任务处理) while keeping them, and the users' data, secure. Give five different points; "it runs the computer" or "it manages resources" alone earns nothing.

    A desktop operating system on screen
    A desktop operating system manages the screen, files and programs for the user
    A smartphone held in one hand, showing the Android home screen with its app icons
    A phone needs one just as much: this is a mobile operating system, Android

    Key management tasks

    The syllabus names five. Each point below is one thing the OS actually does, which is what a "describe" question wants.

    • memory management 内存管理 — allocates memory to each program when it is loaded, keeps every program's memory separate (memory protection 内存保护) so one cannot overwrite another, frees the memory when a program ends, and swaps pages between RAM 随机存取存储器 and secondary storage 辅助存储器 (the disk) (virtual memory 虚拟内存 / paging 分页) so more programs can be open than physical memory allows.
    • process management 进程管理 — a running program is a process 进程. The OS creates and ends processes, decides which process gets the CPU next (scheduling 调度) and for how long (a time slice 时间片), switches between them, resolves conflicts when two want the same resource, and can kill one that stops responding.
    • hardware management (input/output and peripherals) — talks to each device through its device driver 设备驱动, queues and buffers data going to slow devices such as a printer, responds to interrupts 中断 from devices, and shares one device between several programs.
    • file management — creates, names, copies, moves and deletes files and folders, keeps the directory 目录 structure and a record of where each file is stored on the disk, allocates disk space to files, and enforces access rights 访问权限 (read / write / execute) for each user.
    • security management — user accounts and passwords (authentication 身份验证), access rights, encryption of stored data, a firewall, automatic security updates, and a log of who did what.
    Hub diagram with the operating system at the centre linked by spokes to memory, process, file, device and security management and the user interface
    The main jobs the operating system manages
    A memory map with the operating system and three applications each in their own block, separated by boundary addresses; an access inside a block is allowed but an access that strays past a boundary is blocked
    Memory protection keeps each application in its own block of memory

    How memory and process management support multitasking (a four-mark favourite). Memory management loads several programs into memory at the same time, each in its own protected area, and keeps track of which addresses belong to which; process management shares the processor between them — each process runs for a time slice, the OS saves its state and switches to the next, and the switching is so fast that all the programs appear to run together. Interrupts let the OS take the processor back from a process whenever a device needs attention.

    Interrupts. A hardware interrupt 硬件中断 comes from a device: a key pressed, a mouse click, a printer out of paper, a disk finishing a transfer, a power failure. A software interrupt 软件中断 comes from a program: division by zero, an invalid instruction, an attempt to use memory it does not own, or a request for an OS service. The OS's interrupt handler 中断处理程序 saves the state of the running process, deals with the interrupt, then restores the process (topic 4 covers the fetch–execute detail).

    Utility software

    Utility programs 实用程序 are system software that maintain, repair or optimise the computer rather than doing a user's task; the examiner accepts "performs a specific maintenance task that improves performance or security". Most OSes bundle these:

    Common utility programs: antivirus, backup, file compression and disk defragmenter
    Utility programs: antivirus, backup, compression and defragmenter
    • disk formatter — prepares a new disk (or wipes an old one) for use: sets up its file system and partitions, deleting any existing data.
    • virus checker (antivirus 杀毒软件) — scans files and memory, compares code against a database of known virus signatures 签名 and watches for suspicious behaviour, then quarantines or deletes what it finds; runs on a schedule and on every download, and needs updating as new viruses appear.
    • defragmentation software (disk defragmenter 碎片整理) — a hard disk stores a file in whatever free blocks it finds, so after many saves and deletes a file is scattered (fragmented 碎片化) across the platter and the read/write head must jump between the pieces. The defragmenter moves the pieces of each file next to each other and gathers the free space into one region, so files load faster and new files are not fragmented. Not needed on an SSD, which has no moving head.
    • disk contents analysis / disk repair software — shows what is using the disk space (large, duplicate or temporary files) so they can be removed; finds and repairs bad sectors, lost clusters and file-system errors.
    • file compression (compression 压缩) — shrinks files so they need less storage and transfer faster; archiving bundles many files into one.
    • back-up software (backup 备份) — copies files to another medium (external disk, network, cloud) on a schedule so data can be restored after loss, corruption or a ransomware attack; a full copy is followed by incremental backups 增量备份 of only what changed.
    • a firewall 防火墙 (filters network traffic by rules) and encryption tools, for security; a system monitor and automatic updates.

    Bundling these with the OS saves the user installing each one.

    Which utility does what. Performance: defragmentation (faster file access), disk repair (a disk with errors is slow or fails), disk contents analysis (free space by deleting junk), compression (more fits on the disk). Security: virus checker, firewall, encryption, and backup (the only recovery from ransomware). A "draw one line" question pairs each utility with exactly one purpose — learn the pairs above and use the syllabus names.

    Worked example. Explain how defragmentation can improve the performance of a computer (3 marks).

    Over time a file is stored in blocks scattered across the hard disk, so reading it needs many movements of the read/write head. The defragmenter rearranges the blocks so each file is stored contiguously and the free space is together. Files are then read with fewer head movements, so they load faster, and new files can be written into one continuous space.

    Explore

    Where the operating system sits

    Tap each layer. The OS is the middle layer — it sits between your applications and the hardware, sharing the machine safely so programs never touch the hardware directly.

    Vocabulary Train
    English Chinese Pinyin
    operating system 操作系统 cāo zuò xì tǒng
    processor 处理器 chǔ lǐ qì
    multitasking 多任务处理 duō rèn wù chǔ lǐ
    memory management 内存管理 nèi cún guǎn lǐ
    memory protection 内存保护 nèi cún bǎo hù
    RAM 随机存取存储器 suí jī cún qǔ cún chǔ qì
    secondary storage 辅助存储器 fǔ zhù cún chǔ qì
    virtual memory 虚拟内存 xū nǐ nèi cún
    paging 分页 fēn yè
    process management 进程管理 jìn chéng guǎn lǐ
    process 进程 jìn chéng
    scheduling 调度 diào dù
    time slice 时间片 shí jiān piàn
    device driver 设备驱动 shè bèi qū dòng
    interrupts 中断 zhōng duàn
    directory 目录 mù lù
    access rights 访问权限 fǎng wèn quán xiàn
    authentication 身份验证 shēn fèn yàn zhèng
    firewall 防火墙 fáng huǒ qiáng
    hardware interrupt 硬件中断 yìng jiàn zhōng duàn
    software interrupt 软件中断 ruǎn jiàn zhōng duàn
    interrupt handler 中断处理程序 zhōng duàn chǔ lǐ chéng xù
    utility program 实用程序 shí yòng chéng xù
    antivirus 杀毒软件 shā dú ruǎn jiàn
    backup 备份 bèi fèn
    compression 压缩 yā suō
    disk defragmenter 碎片整理 suì piàn zhěng lǐ
    signatures 签名 qiān míng
    fragmented 碎片化 suì piàn huà
    incremental backups 增量备份 zēng liàng bèi fèn
    Exercise sheet
    5.1

    Program libraries

    A program library 程序库 is pre-written code (subroutines 子程序, classes, modules) that programs reuse instead of writing it themselves — e.g. a maths library, a network library, a graphics library.

    A new program under development reusing ready-made routines from a maths library, a graphics library and a network library
    A new program reusing ready-made routines from libraries

    Benefits: saves time (off-the-shelf code), reliable (well-tested, widely used), and standardised (consistent behaviour).

    The examiner's benefit list, for the developer. The library routines 库例程 are already written and tested, so development is faster and cheaper; they are reliable and, being used by many programs, largely error-free; the developer needs no expertise in that area (graphics, compression, encryption, path-finding); the program is easier to maintain because common code lives in one place; and a whole team can use the same routines, giving consistent results. Drawbacks: a routine may not do exactly what you need and you cannot change it; your program depends on the library being available, correct and secure — a bug or a security hole in the library is a bug in your program; and you must learn how to call it.

    • a static library 静态库 is copied into the executable at compile time (stands alone, but larger and needs rebuilding to update).
    • a dynamic library 动态库 (DLL, Dynamic Link Library; .so) is loaded at run time (smaller executables, shared by many programs, updated once for all).
    A static library is copied into the executable at compile time, making a bigger standalone program; a dynamic library file (.dll or .so) stays separate, is loaded at run time, and is shared by several programs
    Static: the library is copied into the executable. Dynamic: a shared library file is loaded at run time

    Dynamic Link Library (DLL) files. A DLL is a library that is loaded into memory only when a program calls it, at run time, and stays as a separate file rather than being copied into the executable. Benefits: the executable is smaller; several running programs share one copy of the DLL in memory; a DLL can be updated (bug fix, new device) without recompiling the programs that use it; and memory is used only while the routine is needed. Drawbacks: the program will not run if the DLL is missing, moved or the wrong version; an updated DLL can break a program that relied on the old behaviour; and a fake DLL put in its place runs with the program's rights.

    Worked example. A team writing the software for a restaurant robot uses a program library that includes a routine to find the shortest path between tables. Explain two benefits and one drawback to the team.

    Benefits: the routine is already written and tested, so the team saves time and can trust the result; the team need not understand path-finding algorithms themselves and can spend the time on the robot's own features. Drawback: the routine may not handle the restaurant's exact needs (moving chairs, one-way aisles) and the team cannot alter it, so they may have to work around its limits.

    Explore

    Computing concept lab

    Classify concrete examples by the computing idea they demonstrate.

    Vocabulary Train
    English Chinese Pinyin
    program library 程序库 chéng xù kù
    subroutines 子程序 zi chéng xù
    library routines 库例程 kù lì chéng
    static library 静态库 jìng tài kù
    dynamic library 动态库 dòng tài kù
    5.2

    Language translators

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the need for: • assembler software for the translation of an assembly language program • a compiler for the translation of a high-level language program • an interpreter for translation and execution of a high-level language program
    Explain the benefits and drawbacks of using either a compiler or interpreter and justify the use of each
    Show awareness that high-level language programs may be partially compiled and partially interpreted, such as Java (console mode)
    Describe features found in a typical Integrated Development Environment (IDE) Including: • for coding, including context-sensitive prompts • for initial error detection, including dynamic syntax checks • for presentation, including prettyprint, expand and collapse code blocks • for debugging, including single stepping, breakpoints, i.e. variables, expressions, report window

    Source: Cambridge International syllabus

    You write source code; the computer runs machine code 机器码. A translator 翻译器 converts between them.

    Assembler

    An assembler 汇编器 translates assembly language 汇编语言 into machine code: each mnemonic instruction (LDD, ADD, JMP) becomes exactly one machine-code instruction, and symbolic addresses and labels are replaced by real addresses. It is needed because the processor executes only machine code, and assembly is used where the programmer needs direct control of the hardware (embedded systems, device drivers).

    Compiler

    A compiler 编译器 translates a high-level program into machine code once, before it runs.

    • it reports all errors at compile time; once clean, it produces a stand-alone executable 可执行文件 that runs without the compiler installed and can be run many times.
    • generally faster at run time (no translation while running), but tied to one CPU/OS — recompile for each platform.

    The two-mark description: a compiler translates the whole high-level program into machine code (object code 目标代码) before it is run, produces an executable file, and reports all the syntax errors together as a list at the end of translation. It does not run the program.

    Interpreter

    An interpreter 解释器 translates and runs a high-level program one line at a time, producing no executable.

    • it reports an error when it reaches that line, then stops; you can fix it and continue — good for development.
    • the interpreter must be installed to run the program; generally slower (each run re-translates), but easy to port across platforms.

    The two-mark description: an interpreter translates one statement of the high-level program at a time and executes it immediately before moving to the next; no executable file is produced; it stops at the first error it meets and reports it. Both the source code and the interpreter must be present every time the program runs.

    A compiler translates the source once into an executable that then runs many times with no translator present; an interpreter translates and runs the source one line at a time, on every run
    A compiler translates once into a standalone program; an interpreter translates line by line, every run

    Choosing between them

    Use a compiler when: Use an interpreter when:
    run-time speed matters you want fast edit–run cycles
    distributing to users without dev tools writing cross-platform scripts
    the program runs many times the program is small or run once
    teaching beginners

    Benefits and drawbacks, as the mark scheme lists them.

    compiler interpreter
    execution speed fast — already machine code slower — translated on every run
    what the user needs only the executable; no translator, and the source code stays private the source code and the interpreter
    finding errors all errors listed at once, after the whole program is translated each error reported at the line where it occurs, as you develop
    changing the code recompile the whole program after every change edit and run again immediately
    portability machine code runs on one platform only; recompile for each the same source runs wherever an interpreter exists

    Worked example. A developer uses an interpreter while writing a program and a compiler when it is finished. Explain how each is used (4 marks).

    During development the interpreter runs the partly written program at once, without waiting for a complete translation; when it meets an error it reports the line, so the developer fixes it and runs again immediately — a fast edit–run cycle that is easier for debugging. When the program is finished, the compiler translates the whole program into an executable that runs faster, needs no translator on the user's computer, and does not reveal the source code, so it can be sold to the public.

    Hybrid: Java

    Java is compiled into bytecode 字节码 (a platform-independent intermediate form), which a virtual machine 虚拟机 (the JVM) then interprets — or uses just-in-time compilation 即时编译 to turn hot parts into native code. So errors are caught early, the bytecode runs anywhere with a JVM ("write once, run anywhere"), and long-running programs reach near-native speed. C# and Python use similar designs.

    The syllabus phrase is "partially compiled and partially interpreted": the compiler stage catches syntax errors and produces compact, portable 可移植的 bytecode; the interpreting stage lets that one bytecode file run on any machine that has a virtual machine, at the cost of some speed. Java in console mode (a text program run from the command line) is the syllabus's example.

    Java source is compiled once into platform-independent bytecode (.class), which a JVM on Windows, macOS or Linux then interprets or JIT-compiles into native code
    Java compiles to portable bytecode that any JVM runs — write once, run anywhere

    Worked example. Java source is compiled to bytecode, which a JVM then interprets. Why use both, instead of compiling straight to machine code? A compiler produces machine code for one processor and operating system, so a program compiled on one machine will not run on another. Java's compiler instead targets a virtual machine, so the bytecode it produces is identical everywhere; each platform then supplies its own JVM to interpret that bytecode into its own native instructions. One compiled file therefore runs anywhere a JVM exists - "write once, run anywhere". The price is speed: interpreting bytecode is slower than running native code, which is why a real JVM also uses JIT compilation to turn frequently-run bytecode into native code while the program runs. Name both sides - the marks are for portability bought at the cost of speed.

    Explore

    The compiler route: source to running program

    Step through how a compiler works — translating the whole program once, before it runs. Contrast it with an interpreter, which translates and runs one line at a time.

    Vocabulary Train
    English Chinese Pinyin
    executable 可执行文件 kě zhí xíng wén jiàn
    translator 翻译器 fān yì qì
    machine code 机器码 jī qì mǎ
    assembler 汇编器 huì biān qì
    assembly language 汇编语言 huì biān yǔ yán
    compiler 编译器 biān yì qì
    object code 目标代码 mù biāo dài mǎ
    interpreter 解释器 jiě shì qì
    bytecode 字节码 zì jié mǎ
    virtual machine 虚拟机 xū nǐ jī
    just-in-time compilation 即时编译 jí shí biān yì
    portable 可移植的 kě yí zhí de
    Watch lesson Exercise sheet
    5.2

    Integrated Development Environment (IDE)

    An integrated development environment 集成开发环境 (IDE) brings the tools to write, test and debug code into one application:

    An IDE gathers the code editor, a Run button and a debugger into one program
    An IDE bundles the editor, a Run button and a debugger

    The syllabus groups the features into four kinds. Learn which feature belongs to which, because questions ask you to sort them and to describe one from each group.

    • For coding: context-sensitive prompts 上下文相关提示 — as you type, the IDE pops up the identifiers, keywords or parameters that fit at that point in the code; auto-complete 自动补全 finishes the name for you; automatic indentation and bracket matching keep the layout right as you type.
    • For initial error detection: dynamic syntax checks 动态语法检查 — the editor checks the syntax as you type and underlines or highlights a mistake immediately, before the program is translated; after translation, error messages with line numbers.
    • For presentation: prettyprint 代码美化 — keywords, identifiers, strings and comments shown in different colours or fonts (syntax highlighting 语法高亮) with consistent indentation, so the structure is visible at a glance; expand and collapse code blocks — hide the body of a loop, an IF or a subroutine so you see the outline.
    • For debugging: breakpoints 断点 — the program pauses when it reaches a marked line; single stepping 单步执行 — from the pause, run one line at a time; a window that shows the current values of variables and expressions as they change; and a report window 报告窗口 that lists errors, warnings and output.

    Other features: translator integration (compile or run with one key, errors shown inline), a debugger 调试器 that drives the debugging features above, version control 版本控制 integration (git), project management, a help system, refactoring 重构 tools (safe renaming) and unit test 单元测试 integration.

    An IDE window annotated with numbered tags: coloured keywords (prettyprint), a collapsed code block, a pop-up prompt suggesting a name, a wavy underline from the dynamic syntax check, a breakpoint dot in the margin, an arrow on the current line during single stepping, a variables panel and a report window
    The IDE features the syllabus names, in the places you would see them on screen

    An IDE speeds development by putting writing → running → debugging → fixing behind one interface. Common IDEs: Visual Studio, PyCharm, Eclipse, VS Code.

    A debugger workflow: set a breakpoint, run the program, and when it reaches the breakpoint it pauses so you can inspect the variables, then step a line at a time or continue
    A debugger: set a breakpoint, run, then pause to inspect variables and step through the code

    Worked example. A function Calculate() returns an unexpected value when the program runs. Describe how the debugging features of a typical IDE help find the cause (4 marks).

    Set a breakpoint on the first line of Calculate(), so the program pauses there instead of running through. Then single-step through the function one line at a time. After each step read the values of the variables and of any expression you have asked the IDE to watch, and compare them with the values you expected; the first line after which a value is wrong is where the logic error is. The report window shows any run-time error message and the output produced so far.

    Worked example. Put each feature in its syllabus group: prettyprint, context-sensitive prompt, dynamic syntax check, breakpoint, expand/collapse code blocks, report window.

    Coding: context-sensitive prompt. Initial error detection: dynamic syntax check. Presentation: prettyprint, expand/collapse code blocks. Debugging: breakpoint, report window.

    Vocabulary Train
    English Chinese Pinyin
    integrated development environment 集成开发环境 jí chéng kāi fā huán jìng
    debugger 调试器 tiáo shì qì
    context-sensitive prompts 上下文相关提示 shàng xià wén xiāng guān tí shì
    auto-complete 自动补全 zì dòng bǔ quán
    dynamic syntax checks 动态语法检查 dòng tài yǔ fǎ jiǎn chá
    prettyprint 代码美化 dài mǎ měi huà
    syntax highlighting 语法高亮 yǔ fǎ gāo liàng
    breakpoints 断点 duàn diǎn
    single stepping 单步执行 dān bù zhí xíng
    report window 报告窗口 bào gào chuāng kǒu
    version control 版本控制 bǎn běn kòng zhì
    refactoring 重构 chóng gòu
    unit test 单元测试 dān yuán cè shì
    5.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    operating system software that manages the computer's hardware and resources and provides an interface between the user, the application programs and the hardware
    utility software system software that performs a specific task to maintain, optimise or protect the computer, such as a virus checker or a defragmenter
    program library a collection of pre-written, tested routines (subroutines, classes, modules) that a program can use instead of writing its own
    Dynamic Link Library (DLL) a program library whose routines are loaded into memory only when the program calls them, at run time, and are shared between programs
    assembler a translator that converts an assembly language program into machine code, one instruction for each instruction
    compiler a translator that converts the whole of a high-level language program into machine code before it is run, producing an executable file
    interpreter a translator that translates and executes a high-level language program one statement at a time
    integrated development environment a single application that provides the tools for writing, translating, running and debugging a program
    context-sensitive prompt a pop-up that suggests identifiers, keywords or parameters that fit at the current point in the code
    dynamic syntax check checking the syntax of the code as it is typed and flagging an error before the program is translated
    prettyprint displaying code with keywords, identifiers and comments in different colours or fonts and with consistent indentation
    breakpoint a marked line at which the running program pauses so that variables can be inspected
    single stepping running a paused program one statement at a time under the programmer's control
    5.2

    Exam tips

    • List the OS's jobs by their syllabus names (memory, process, hardware, file and security management) and say what each does — "manages resources" alone is too vague.
    • Compare compiler vs interpreter vs assembler: what each translates, when it translates it, and how errors are reported.
    • Explain what an IDE provides using the syllabus groups: coding, initial error detection, presentation, debugging.
    • A "benefit to the developer" answer names the developer's saving: time, cost, expertise, reliability or maintenance. A "drawback" names a dependence: availability, version, fit, security.
    • For "describe the operation of" a translator, give three things: what is translated (whole program or one statement), when (before running or while running), and how errors are reported (all at once or at the first error).

    Common mistakes

    • Writing "the OS controls the computer" or "manages resources" with no example task. Each mark is one named task with what it does.
    • Saying an interpreter "compiles line by line". An interpreter translates and executes each statement; it never produces an executable.
    • Saying a compiler runs the program. It only translates; the executable runs later, without the compiler.
    • Putting a DLL "inside" the executable. That is a static library; a DLL stays a separate file loaded at run time.
    • Saying defragmentation "deletes" or "compresses" files, or is needed on an SSD. It only moves blocks so each file is stored contiguously.
    • Filing prettyprint or collapsing blocks under "debugging". They are presentation features; debugging is breakpoints, single stepping, watching variables and the report window.
  • 6

    Security, privacy and data integrity

    6.1

    Security, privacy and integrity — three different ideas

    Syllabus
    Candidates should be able to: Notes and guidance
    Explain the difference between the terms security, privacy and integrity of data
    Show appreciation of the need for both the security of data and the security of the computer system
    Describe security measures designed to protect computer systems, ranging from the stand-alone PC to a network of computers Including user accounts, passwords, authentication techniques such as digital signatures and biometrics, firewall, anti-virus software, anti-spyware, encryption
    Show understanding of the threats to computer and data security posed by networks and the internet Including malware (virus, spyware), hackers, phishing, pharming
    Describe methods that can be used to restrict the risks posed by threats
    Describe security methods designed to protect the security of data Including encryption, access rights

    Source: Cambridge International syllabus

    These sound alike but mean different things:

    • security 安全 — protecting data from unauthorised 未授权 access, change or destruction.
    • privacy 隐私 — an individual's right to control who sees their personal data, with consent and a clear purpose.
    • integrity 完整性 — the data being accurate and complete — not corrupted or accidentally changed.

    A file can be secure (only the right people can open it) but lack integrity (a typo corrupted it); or accurate but not private (anyone can read it). All three are needed.

    The differences the scheme wants, one sentence each: security is keeping the data safe from loss and from unauthorised access; privacy is keeping the data confidential, so that only those with the right to see it can; integrity is the data being correct, consistent and complete. So "the difference between security and privacy": security is about protecting the data from being accessed, changed or lost by people who should not; privacy is about the individual's right to decide who may see their personal data. "The difference between security and integrity": security protects the data from unauthorised access; integrity is about the data being accurate and up to date, which validation and verification protect.

    Explore

    Risk and responsibility lab

    Sort examples by the rule, risk or protection involved.

    Vocabulary Train
    English Chinese Pinyin
    security 安全 ān quán
    privacy 隐私 yǐn sī
    integrity 完整性 wán zhěng xìng
    unauthorised 未授权 wèi shòu quán
    Exercise sheet
    6.1

    Why security matters

    Two things to protect: the data itself (keep it confidential, intact and available) and the computer system (a compromised system can attack others, steal credentials, or be held to ransom).

    "Why does the school need to keep both secure?" Data: it is personal and confidential, so it must not be read, changed or deleted by an unauthorised person, and its loss would stop the school working. System: an intruder who reaches the computer system can install malware, use it to attack other systems, damage the hardware or software, or lock it with ransomware; a secure system is the first line of defence for the data on it.

    6.1

    Threats from networks and the internet

    Threats fall into three groups.

    A man-in-the-middle attacker sits between Alice and Bob, reading or altering messages
    A man-in-the-middle attacker sits between the two parties
    1. Malware 恶意软件 (malicious software) — harmful programs:
    • virus 病毒 — self-copying code that attaches to other programs and spreads when they run.
    • worm 蠕虫 — self-copying code that spreads over networks 网络 with no user action.
    • Trojan horse 木马 — looks useful but hides malicious code.
    • spyware 间谍软件 — secretly collects information (keystrokes, passwords).
    • ransomware 勒索软件 — encrypts your files and demands payment.
    • adware 广告软件 — pushes unwanted adverts.

    2. Tricking people (social attacks):

    • phishing 网络钓鱼 — fake emails/sites that trick users into giving credentials.
    • pharming 域名欺骗 — redirects a user to a fake site even when they type the correct address.
    • social engineering 社会工程 — tricking people into giving up information.

    The scheme's descriptions of the four named threats: a virus is malicious software that replicates (copies itself), attaches itself to other files and deletes or corrupts data; spyware is malicious software that records the user's key presses and actions and sends them to a third party, to obtain passwords and personal data; a phishing email pretends to come from a legitimate organisation and contains a link to a fake website where the user is asked for personal or bank details; pharming is malicious code installed on the user's computer or on a web server that redirects the user to a fake website even though they typed the correct address. Similarities of spyware and a virus: both are malware, both are installed without the user's knowledge, both can send data to a third party or damage the system; the difference is that a virus replicates itself while spyware records and transmits information. Phishing and pharming both lead the user to a fake website that collects their data; phishing needs the user to click a link in an email, pharming works through code on the computer or the DNS server and needs no email.

    3. Attacks on the network:

    • hacking 黑客入侵 by hackers 黑客 — unauthorised access, often via weak passwords or software flaws.
    • denial of service 拒绝服务 (DoS/DDoS) — floods a server so real users cannot reach it.
    • eavesdropping 窃听 — capturing data in transit (a risk on open Wi-Fi).
    • man-in-the-middle 中间人攻击 — an attacker secretly relays or alters messages between two parties.

    Worked example. Identify and describe two threats to the data on a school network, and give a different prevention method for each.

    Threat 1, malware: a virus copied onto a computer from an email attachment or a download replicates itself and corrupts or deletes files; prevention: anti-virus software that scans files and is kept up to date. Threat 2, hacking: an unauthorised person gains access to the network, for example by guessing a weak password, and reads or changes the data; prevention: a firewall that blocks unauthorised connections, or strong passwords with two-factor authentication. A third pair, phishing: an email leads a user to a fake site that collects their login; prevention: training users to check the sender and the URL, and filtering email. The measure must match the threat: encryption does not stop a virus, and anti-virus software does not stop phishing.

    Malware grouped by behaviour: self-spreading types are the virus (attaches to programs) and worm (spreads over networks); hidden or disguised types are the Trojan (looks useful), spyware, ransomware and adware
    Malware by behaviour: self-spreading (virus, worm) versus hidden/disguised (Trojan, spyware, ransomware, adware)
    Vocabulary Train
    English Chinese Pinyin
    malware 恶意软件 è yì ruǎn jiàn
    ransomware 勒索软件 lè suǒ ruǎn jiàn
    networks 网络 wǎng luò
    man-in-the-middle 中间人攻击 zhōng jiān rén gōng jī
    virus 病毒 bìng dú
    worm 蠕虫 rú chóng
    Trojan horse 木马 mù mǎ
    spyware 间谍软件 jiàn dié ruǎn jiàn
    adware 广告软件 guǎng gào ruǎn jiàn
    phishing 网络钓鱼 wǎng luò diào yú
    pharming 域名欺骗 yù míng qī piàn
    social engineering 社会工程 shè huì gōng chéng
    hacking 黑客入侵 hēi kè rù qīn
    hackers 黑客 hēi kè
    denial of service 拒绝服务 jù jué fú wù
    eavesdropping 窃听 qiè tīng
    6.1

    Security measures

    Measures protect both the security of data (against loss, theft or corruption) and the security of the computer system (its hardware, software and network).

    A standalone PC

    • a strong password; antivirus kept up to date; prompt software updates; backup 备份 to separate media; full-disk encryption 加密; a locked screen.

    A networked PC

    All the above, plus a firewall 防火墙, per-user permissions (admin rights only for admins), central management of user accounts 用户账户, and audit logs 审计日志 (who logged in, what they touched).

    How the measures work, in the wording the scheme awards:

    • firewall: examines every incoming and outgoing transmission and compares it with set criteria (a whitelist or blacklist of addresses, ports and protocols); blocks any that do not meet the criteria; can prevent access to certain sites and warn of unauthorised access attempts.
    • encryption: the data is scrambled (encoded) with a key into ciphertext, so an intercepted copy cannot be understood without the key; the receiver uses a key to decrypt it. It protects data in transmission and in storage, but it does not stop the data being intercepted or deleted.
    • passwords and user accounts: only a user who knows the password can log in; a strong password (long, mixed characters, changed regularly) cannot be guessed; accounts lock after repeated failures; each account carries its own access rights.
    • anti-virus and anti-spyware software: scans files and programs against a database of known malware signatures, checks behaviour, quarantines or deletes what it finds, and must be updated so that new malware is recognised.
    • access rights: each user (or group) is given permissions for each file or table, such as read-only or read and write, so a user cannot see or change data that is not theirs; a database can also present each user with a view containing only the fields they need.
    • biometrics: the device captures an image of the face, fingerprint or iris, converts it to digital data, compares it with the stored data for that user and allows access only on a match; it cannot be forgotten, lent or guessed like a password.
    • backups: a copy of the data on separate media, kept off-site, so that lost or corrupted data can be restored.

    To restrict the risks of malware, in three marks: install anti-malware software and keep it updated; use a firewall; do not open attachments or download files from unknown sources; keep the operating system and applications patched; and train users.

    A box diagram with the user's computer on the trusted side, then the firewall, then the internet on the untrusted side, connected by double-headed arrows
    A firewall sits between the user's computer and the internet

    Across the internet

    • VPN 虚拟专用网 — encrypts traffic between the user and the corporate gateway.
    • HTTPS / TLS — encrypt web traffic.
    • digital signatures 数字签名 — prove who sent a message and that it was not altered in transit.
    • intrusion detection — watches traffic for known attack patterns.

    How a digital signature authenticates a document (five marks): the sender puts the message through a hash function to produce a digest; the sender encrypts the digest with their private key, and that encrypted digest is the digital signature; the message and the signature are sent together; the receiver decrypts the signature with the sender's public key to recover the digest; the receiver hashes the received message and compares the two digests; if they match, the message came from the sender (only they hold the private key) and was not altered in transmission. A signature proves who sent the message and that it is intact; it does not hide the contents, which is what encryption of the message is for.

    Two lanes: the sender hashes the message into a digest and encrypts the digest with their private key to make the signature, and sends message and signature; the receiver decrypts the signature with the sender's public key to get digest A, hashes the received message to get digest B, and compares them
    A digital signature: a hash of the message, encrypted with the sender's private key, checked by the receiver against a fresh hash
    Vocabulary Train
    English Chinese Pinyin
    firewall 防火墙 fáng huǒ qiáng
    encryption 加密 jiā mì
    backup 备份 bèi fèn
    user accounts 用户账户 yòng hù zhàng hù
    audit logs 审计日志 shěn jì rì zhì
    VPN 虚拟专用网 xū nǐ zhuān yòng wǎng
    digital signatures 数字签名 shù zì qiān míng
    6.1

    Matching measures to threats

    • interception in transitencrypt the data (HTTPS, VPN). Intercepted ciphertext is useless without the key.
    • unauthorised access → strong authentication 身份验证 (long passwords; two-factor authentication 双因素认证 with a phone code or key); user authorisation 授权; lock-out after failed logins.
    • malwareanti-virus software and anti-spyware 反间谍软件 with real-time scanning; patching; avoid untrusted downloads.
    • phishing → user training; email filtering; check the URL before entering credentials.
    • internal threats → the least-privilege 最小权限 principle (give each user only what they need); auditing.
    • DDoS → rate limiting and traffic filtering.

    For confidential data crossing the internet, the scheme's method is encryption: the data is encoded with a key into ciphertext, so that an unauthorised person who intercepts it cannot read it, and only the intended receiver, who has the key, can decode it. For a program file sent by email for testing, the same answer applies (encrypt the file, or send it over an encrypted connection), together with a password on the file itself.

    Vocabulary Train
    English Chinese Pinyin
    two-factor authentication 双因素认证 shuāng yīn sù rèn zhèng
    authentication 身份验证 shēn fèn yàn zhèng
    anti-spyware 反间谍软件 fǎn jiàn dié ruǎn jiàn
    authorisation 授权 shòu quán
    least-privilege 最小权限 zuì xiǎo quán xiàn
    6.1

    Protecting the data itself

    • encryption — turn plaintext 明文 into ciphertext 密文 with a key. Symmetric encryption 对称加密 (AES) uses one shared key; asymmetric encryption 非对称加密 (RSA) uses a public key 公钥 and a private key 私钥. Protects data at rest and in transit.
    • access control 访问控制 — file permissions (read/write/execute) and access rights 访问权限, enforced by the OS.
    • authenticationauthentication techniques verify the user: something you know (password), have (token, phone), or are (biometrics 生物识别 — fingerprint, face, iris); strongest combined.
    • backups — keep copies (some off-site) so loss or corruption is recoverable.
    • physical security — locked server rooms, cable locks.

    Access rights in a database, described for three marks: each user is given an account with a username and password; the database administrator assigns each account permissions for each table, such as read-only, read and write, or no access; users see only the tables and fields they are allowed to, so a customer cannot open the staff table and a clerk can read but not change the prices. The DBMS enforces this with its access rights and with views, and it can encrypt the stored data as well.

    Symmetric encryption uses one shared key to both encrypt and decrypt the message; asymmetric encryption encrypts with the receiver's public key and decrypts with their private key
    Symmetric uses one shared key; asymmetric uses a public key to encrypt and a private key to decrypt
    A grey RSA SecurID key-fob security token with an LCD screen showing a six-digit code
    A security token shows a changing code for two-factor authentication ("something you have")
    A small USB fingerprint reader with an optical sensor pad
    A fingerprint reader checks "something you are" — a feature of the person, not a password
    Explore

    Encrypt with a Caesar cipher

    Change the shift — that is the key. Each letter slides that many places along the alphabet to make the ciphertext, and the same key slides it back. That shared key is symmetric encryption in miniature.

    Vocabulary Train
    English Chinese Pinyin
    ciphertext 密文 mì wén
    access rights 访问权限 fǎng wèn quán xiàn
    biometrics 生物识别 shēng wù shí bié
    private key 私钥 sī yào
    public key 公钥 gōng yào
    plaintext 明文 míng wén
    Symmetric encryption 对称加密 duì chèn jiā mì
    asymmetric encryption 非对称加密 fēi duì chèn jiā mì
    access control 访问控制 fǎng wèn kòng zhì
    6.2

    Data integrity

    Syllabus
    Candidates should be able to: Notes and guidance
    Describe how data validation and data verification help protect the integrity of data
    Describe and use methods of data validation Including range check, format check, length check, presence check, existence check, limit check, check digit
    Describe and use methods of data verification during data entry and data transfer During data entry including visual check, double entry During data transfer including parity check (byte and block), checksum

    Source: Cambridge International syllabus

    Data has integrity when it is accurate and complete. Two techniques: data validation (catch bad data before storing) and data verification (confirm data was entered or transferred correctly).

    Validation — does the data make sense?

    Validation 验证 checks data against sensible rules, automatically:

    • range check — within limits (a month is 1–12).
    • limit check — on the correct side of a single limit (e.g. age ≥ 18).
    • existence check — the referenced item exists (e.g. a product code is in the table).
    • length check — the right number of characters.
    • type / character check — the right kind of data (a phone field allows only digits).
    • format check — matches a pattern (an email must contain @).
    • presence check — required fields are not empty.
    • check digit 校验位 — an extra digit computed from the others (ISBN, card numbers) that spots transcription errors.

    Worked example. In a simple check-digit scheme the check digit is the remainder when the sum of the digits is divided by $10$, appended to the number. The number $4162$ has digit sum $13$, so it is stored as $41623$. A user types $14623$: the first two digits are swapped, but the sum is still $13$, so the check digit still matches and the error is not caught. A user who types $41523$ is caught, because $4 + 1 + 5 + 2 = 12$ gives check digit $2$. A scheme that catches swapped digits weights each position differently, as the ISBN-13 check does (weights $1, 3, 1, 3, \ldots$, then the digit that makes the total a multiple of $10$). A check digit is validation: it tests the number against a rule at the moment it is entered.

    • lookup check and consistency check (e.g. delivery date ≥ order date).

    Validation catches data that is wrongly formatted, but not data that is the right format yet factually wrong ("Bob" for "Bib").

    Worked example. Identify the validation check each piece of pseudocode performs.

    Pseudocode Check
    IF x < 0 OR x > 10 THEN OUTPUT "Invalid" range check: the value must lie between two limits
    IF x = "" THEN OUTPUT "Invalid" presence check: the field must not be empty
    IF NOT(x = "Red" OR x = "Yellow" OR x = "Blue") THEN OUTPUT "Invalid" lookup (existence) check: the value must be one of a list
    IF LENGTH(x) <> 6 THEN OUTPUT "Invalid" length check: the right number of characters
    IF MID(x, 1, 1) < "A" OR MID(x, 1, 1) > "Z" THEN OUTPUT "Invalid" format check: a particular character must be a letter

    To validate a car registration number that must be one letter, three digits and two letters: a format check tests each position against its pattern, and a length check confirms six characters. To validate a date of birth: a format check (DD/MM/YYYY), a range check (the month is $1$ to $12$, the year is not in the future) and a presence check (it is not left blank). A mark between $0$ and the maximum for the test needs a type check (an integer) and a range check, with the upper limit read from the test's own record: that is how validation protects integrity, by refusing data that could not be correct.

    Verification — was the data entered or transferred correctly?

    Verification 核对 checks the data was not changed in moving from one place to another.

    During entry: double entry (type it twice and compare, as for a new password) or visual check.

    In the scheme's words, double entry is entering the data twice, by the same person or by two people, and having the computer compare the two versions and report any difference; a visual check is the person comparing what is on the screen with the original source document and correcting any difference before saving. Both protect integrity by making sure the stored data matches the source. Even after validation and verification the data can still be wrong: it can be sensible and match the source, yet the source itself was wrong, or the user typed a different but valid value from the one intended.

    During transfer (bits can flip):

    • parity check 奇偶校验 — an extra bit makes the number of 1s even (even parity) or odd. The receiver re-counts. Catches single-bit errors.
    • checksum 校验和 — the sender sends a summary value of the data; the receiver recomputes it and compares.
    • cyclic redundancy check 循环冗余校验 (CRC) — a stronger checksum using polynomial division, catching many more error types.

    A parity block check 奇偶块校验 goes further and locates the error. Arrange the bytes in a grid: give each byte a row parity bit, then compute one extra parity byte whose bits are the column parity of the bytes above. A single flipped bit now fails one row and one column – their intersection pinpoints exactly which bit changed, so it can even be corrected.

    Worked example. Four bytes are sent with even parity, followed by a parity byte. Find the bit that was corrupted.

    A grid of four received bytes and a parity byte under even parity, with the parity bit in the first column; the third byte's row has five 1s and the fourth column has three 1s, both odd, and the bit at their crossing is marked as the one that was flipped
    A parity block check: the row that fails and the column that fails cross at the flipped bit

    Count the 1s in each row and each column. Every row and column should have an even number; byte 3 has five and column 4 has three. The bit where that row and that column cross is the one that changed, so it is reset from 1 to 0. A parity check on its own detects an error in a byte but cannot say which bit; two errors in the same byte cancel and pass unnoticed. A checksum, explained for three marks: the sender puts the block of data through an algorithm that produces a checksum value; the data and the checksum are sent together; the receiver runs the same algorithm on the data it received; if the two checksums match, the data is accepted, and if not, it is rejected and sent again.

    The same seven data bits shown twice: a 0 parity bit gives four 1s for even parity, a 1 parity bit gives five 1s for odd parity
    The parity bit is set to make the number of 1s even or odd
    The sender computes a checksum and sends it with the data block; the receiver recomputes the checksum and compares, plus a worked example of the byte-sum-mod-256 calculation
    Working out a checksum for a block of data

    Verification only proves what arrived matches what was sent — not that the data is correct, and not against deliberate tampering. Validation asks "is this sensible?"; verification asks "was this copied correctly?" — use both.

    The table questions sort the methods by when they are used: during data entry, double entry and a visual check; during data transfer, a parity check (byte or block) and a checksum. Transferring video files from a camera to a server uses a checksum: the camera computes it, the server recomputes it, a mismatch means retransmit.

    Side by side: validation asks "is this data sensible?" and checks rules like range, type and format before storing (catching nonsense data); verification asks "was it copied correctly?" and uses double entry, parity and checksums (catching copying errors)
    Validation checks the data makes sense; verification checks it was copied without change

    Worked example. A user types their date of birth as 31/02/2009, and types their email address twice. Which check catches which error, and what is the difference? Validation asks "is this data sensible?" - the computer tests it against a rule, and a format or range check rejects 31/02/2009 because February never has 31 days. Verification asks "was this data entered correctly?" - typing the email twice is double entry, and comparing the two copies catches a typing slip. The limit is what makes this a favourite question: validation can never tell you the data is right, only that it is possible - 01/02/2009 passes every validation rule even if the user was actually born on a different day. Say what each check can and cannot catch.

    Explore

    Computing concept lab

    Classify concrete examples by the computing idea they demonstrate.

    Vocabulary Train
    English Chinese Pinyin
    validation 验证 yàn zhèng
    verification 核对 hé duì
    check digit 校验位 jiào yàn wèi
    parity check 奇偶校验 jī ǒu jiào yàn
    checksum 校验和 jiào yàn hé
    cyclic redundancy check 循环冗余校验 xún huán rǒng yú jiào yàn
    parity block check 奇偶块校验 jī ǒu kuài jiào yàn
    Watch lesson Exercise sheet
    6.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly.

    Term Definition
    data security keeping data safe from loss and from unauthorised access, change or deletion
    data privacy keeping data confidential, so that it is seen only by those who have the right to see it
    data integrity the data being accurate, consistent and complete
    malware malicious software that is installed without the user's knowledge to damage a system or steal data
    virus malware that replicates itself, attaches to other files and corrupts or deletes data
    spyware malware that records the user's key presses or actions and sends them to a third party
    phishing an email pretending to be from a legitimate organisation that leads the user to a fake website to collect personal data
    pharming malicious code that redirects the user to a fake website even when the correct address is entered
    firewall hardware or software that examines all traffic entering or leaving a system against set criteria and blocks what does not meet them
    encryption scrambling data with a key into ciphertext, so that it cannot be understood without the key to decrypt it
    digital signature a hash of a message encrypted with the sender's private key, used to prove who sent it and that it was not altered
    data validation an automatic check that entered data is reasonable and follows set rules
    data verification a check that data has been entered or transferred correctly, by comparing it with the source or with a recomputed value
    check digit an extra digit calculated from the other digits of a number and appended to it, so that an error in the number can be detected
    parity check an extra bit added to a byte so that the number of 1s is even (or odd), which the receiver recounts
    checksum a value calculated from a block of data by an algorithm and sent with it, recalculated by the receiver and compared
    6.2

    Exam tips

    • Keep the three ideas separate: security (keeping data safe), privacy (who may see it), integrity (keeping it correct).
    • Match each threat (malware, hacking, phishing, interception) to a measure (firewall, encryption, authentication, access rights).
    • Encryption protects confidentiality, not integrity — use a checksum, parity or check digit for integrity.
    • Distinguish a virus, worm and Trojan and how each spreads.

    Common mistakes

    • Giving the same measure for two threats, or a measure that does not fit the threat. Each threat in the table needs a different prevention that actually stops it.
    • Naming a measure without saying how it works. "Firewall" scores when it is followed by "compares traffic with set criteria and blocks what fails".
    • Calling validation a check that the data is correct. Validation checks that data is reasonable; verification checks that it matches the source. Neither proves it is true.
    • Saying a digital signature encrypts the message. It encrypts a hash of the message with the private key; the receiver decrypts it with the public key and compares hashes.
    • Describing a check digit as verification, or a parity check as validation. The check digit is a validation rule on entry; parity and checksums verify a transfer.
    • Writing that a virus "sends data to a third party" and spyware "replicates". The replicating one is the virus; the recording one is spyware.
  • 7

    Ethics and Ownership

    7.1

    Ethics for computing professionals

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the need for and purpose of ethics as a computing professional Understand the importance of joining a professional ethical body including BCS (British Computer Society), IEEE (Institute of Electrical and Electronic Engineers)
    Show understanding of the need to act ethically and the impact of acting ethically or unethically for a given situation
    Show understanding of the need for copyright legislation
    Show understanding of the different types of software licencing and justify the use of a licence for a given situation Licences to include free Software Foundation, the Open Source Initiative, shareware and commercial software
    Show understanding of Artificial Intelligence (AI) Understand the impact of AI including social, economic and environmental issues
    Understand the applications of AI

    Source: Cambridge International syllabus

    A computing professional is someone whose work — software, systems, networks, data — affects other people. Because the work is technical, others often cannot judge whether it was done well or honestly. So the profession follows shared ethics 伦理 (principles for good behaviour).

    Why ethics matters

    • trust — users and employers trust professionals to act in their interest. Without that trust, software loses credibility.
    • impact — software runs medical devices, banking, vehicles. Careless or dishonest work can hurt people.

    Professional bodies (BCS, ACM, IEEE) publish codes of ethics for members.

    A wall of CCTV monitors in a control room
    CCTV raises privacy concerns — one of the ethical issues a computing professional must weigh
    A pile of discarded electronic equipment
    Discarded electronics (e-waste) are a growing environmental cost of computing
    A hub diagram with public wellbeing at the centre, linked to health and safety concerns, the public interest, benefits to the public and concerns of the public
    Software development affects the public's wellbeing in several ways

    Typical principles

    • public interest first — protect the safety and welfare of those affected.
    • honesty and competence — be honest about your skills; don't claim expertise you lack.
    • confidentiality 保密性 — protect clients' and employers' private information.
    • avoid conflicts of interest 利益冲突 — don't take work where your interest clashes with the client's.
    • keep your skills current; respect intellectual property 知识产权 and privacy 隐私; treat colleagues fairly.

    Joining a professional body

    The syllabus names two: the BCS (British Computer Society) and the IEEE (Institute of Electrical and Electronics Engineers). Both publish a code of conduct 行为准则 that members agree to follow. The benefits of joining, in the scheme's words: a set of ethical guidelines to follow, so decisions are not left to personal judgement; training, conferences and publications that keep the member up to date; advice and support, including legal help, when a problem arises; and recognised professional status, so employers and clients trust the member's work. The consequences of not joining: no guidance on ethical decisions, so the programmer may act unethically without realising; less credibility with employers and customers, so it is harder to win work; no support in a dispute; and being out of date with developments and law. The purpose of a code of conduct (two marks): to create a safe, respectful and professional working environment, and to make sure every employee understands what is expected and the consequences of their actions.

    Worked example. Explain why a programmer needs to act ethically towards colleagues and towards the public.

    Colleagues: treat them fairly and without discrimination; respect their work, their ideas and their confidential information; be honest about mistakes and give credit where it is due; support their development rather than undermine it. The public: protect their personal data and privacy; produce software that is safe, reliable and properly tested, because faults can cause harm; be honest about what the software can do; take on only work within your competence; obey the law and consider the wider effects on society and the environment. Each side earns marks for a reason and its consequence, not for the word "fair" alone.

    Acting ethically vs unethically

    Acting ethically protects users, strengthens reputation, reduces legal risk, and builds trust. Acting unethically (skipping testing, hiding bugs, misusing data) can harm real users, lead to dismissal or legal action, damage reputation, and erode trust in technology generally.

    When you face a borderline decision: identify whose interests are affected, check the code of ethics and the law, weigh the consequences, ask a trusted senior, and choose the option that protects users above short-term convenience.

    Worked example. Your team's new AI hiring tool sorts CVs ten times faster, but you notice it rejects more older applicants. Shipping it pleases your manager, but it treats one group unfairly. The ethical choice is to hold it back until the bias is fixed — public interest and fairness come before short-term convenience.

    Ethics also applies to users. A student who connects a personal computer to the school network should respect other people's privacy and data, not use social media inappropriately or bully others, not download or share copyrighted material, not introduce malware or try to access systems they are not allowed to, and use the network for the purpose it was provided. A "give three ethical considerations" answer lists three of these.

    Explore

    Risk and responsibility lab

    Sort examples by the rule, risk or protection involved.

    Vocabulary Train
    English Chinese Pinyin
    ethics 伦理 lún lǐ
    privacy 隐私 yǐn sī
    confidentiality 保密性 bǎo mì xìng
    conflicts of interest 利益冲突 lì yì chōng tū
    intellectual property 知识产权 zhī shí chǎn quán
    code of conduct 行为准则 xíng wéi zhǔn zé
    Exercise sheet
    7.1

    Copyright

    Copyright 版权 is the legal right of the creator of an original work to control how it is copied, distributed, modified and performed. It applies automatically (no registration) to source code, software, documents, images, audio and video.

    Without copyright, anyone could copy software freely, the developer would not be paid, and plagiarism would be legal. With copyright, developers can earn from their work (encouraging more software), users know who made it, and re-use happens on the developer's terms through licensing. Copyright lasts a long time (often 70 years after the creator's death). General ideas and algorithms are not covered by copyright but may be covered by a patent 专利.

    Why a programmer should copyright a program, in the scheme's words: to be identified as the owner and author (formal recognition of ownership); so that there are legal consequences if anyone copies or steals it; to restrict competitors from selling the same work; and to be able to earn money by licensing it. Copyright applies to the program as written; a different program that does the same job does not infringe it.

    Copyright is automatic with no registration and lasts about 70 years after the creator's death, covering code, images and documents; a patent must be filed and lasts about 20 years, covering inventions and algorithms
    Copyright is automatic and long-lasting; a patent must be filed and lasts about 20 years
    Explore

    Risk and responsibility lab

    Sort examples by the rule, risk or protection involved.

    Vocabulary Train
    English Chinese Pinyin
    copyright 版权 bǎn quán
    patent 专利 zhuān lì
    7.1

    Software licences

    A software licence 软件许可证 is a contract granting permission to use software on the owner's terms; choosing and applying one is called software licencing.

    Commercial (proprietary)

    • commercial software is sold: you buy a licence; the software is used only within its terms.
    • the source code is not given (a proprietary 专有 product); you cannot modify or redistribute it.
    • examples: Microsoft Office, Adobe Photoshop, most games.

    Used when the developer wants revenue per user and to keep control of the code.

    Open-source

    • the source code is public; users can read, modify and redistribute it (open-source 开源).
    • permissive licences (MIT, BSD) allow almost any use; copyleft 著佐权 licences (GPL) require that modified versions are released under the same licence ("share-alike").
    • the Free Software Foundation (FSF) and the Open Source Initiative (OSI) promote and approve open-source licences.

    The syllabus names both, and they are marked as distinct answers. Free Software (the FSF's term) means free as in freedom, not price: the user may run the program for any purpose, study and change it (so the source code must be available), redistribute copies, and distribute modified versions; a fee may still be charged for a copy. Open Source (the OSI's definition) requires that the source code is available, that the program may be modified and redistributed, and that the licence does not discriminate against any person or field of use. "Identify two licence types that let other people edit and redistribute the program" is answered with these two.

    • examples: Linux, Python, Apache.

    Used when the developer wants the software widely used and improved by the community.

    Freeware and shareware

    • freeware 免费软件 — free of charge, no source code, may be redistributed but not modified (Acrobat Reader, WhatsApp).
    • shareware 共享软件 — free for a trial period, then you pay to keep using it; no source code.

    The scheme's descriptions: shareware is distributed free for a trial (a limited time or limited features) and the user pays to continue using the full version; commercial software is sold for a fee, the source code is not supplied, the licence protects the developer's intellectual property, and the fee usually buys support and updates. Benefits of shareware to the programmer: users can try the program before buying, so they are more likely to purchase; it spreads widely at almost no advertising cost; and those who keep it pay. Benefits of a commercial licence: the developer earns a fee for every copy; the code and its rights stay protected; and the income funds support, updates and further development.

    Type Cost Source Redistribute Modify
    Commercial Paid No No No
    Open-source Free Yes Yes Often, with conditions
    Freeware Free No Yes No
    Shareware Free trial, then paid No Sometimes No
    A decision tree for choosing a licence: if you want to sell it or keep control, choose commercial; otherwise if you share the source code, choose open-source; otherwise if it is free forever, choose freeware, else shareware (a free trial then pay)
    Choosing a licence from the developer's goal

    To justify a licence choice, link it to the developer's goal (revenue, reach, community), the user's needs (cost, customising), and the use case.

    Worked example. A programmer has written a game to sell to the public. Identify the most appropriate licence and justify it.

    A commercial licence: the game is sold for a fee, so the programmer earns money from every copy; the source code is not released, so nobody can copy the game or change it and sell it as their own; the licence protects the intellectual property; and buyers receive updates and support. Open source would not fit, because the source code would be available, so the game could be copied, changed and redistributed without payment.

    Worked example. A program helps shoppers by reading product labels aloud. Explain why an open source licence might not be appropriate.

    The source code would be accessible, so it could be changed; a changed version might output the wrong product information, so shoppers could buy the wrong item; and the programmer would lose control over the quality and safety of what is distributed under the program's name. Going the other way, programs are released as open source so that other developers can improve and extend them, so that they are adopted widely at no cost, and so that users can adapt them to their own needs.

    Vocabulary Train
    English Chinese Pinyin
    software licence 软件许可证 ruǎn jiàn xǔ kě zhèng
    proprietary 专有 zhuān yǒu
    open-source 开源 kāi yuán
    copyleft 著佐权 zhù zuǒ quán
    freeware 免费软件 miǎn fèi ruǎn jiàn
    shareware 共享软件 gòng xiǎng ruǎn jiàn
    7.1

    Artificial Intelligence (AI)

    Artificial intelligence 人工智能 builds systems that do tasks once thought to need human intelligence — recognising speech and images, translating, playing games, driving.

    Most modern AI uses machine learning 机器学习 — algorithms that improve at a task by learning patterns from large amounts of data, instead of being programmed step by step. Deep learning 深度学习, using neural networks 神经网络 with many layers, is the leading approach today.

    Everyday examples

    AI tasks split into two kinds — understanding input, and producing output or decisions.

    Understanding input:

    • speech recognition 语音识别 — spoken words to text (voice assistants).
    • image recognition 图像识别 — finding objects, faces or text in images.

    Producing output or decisions:

    • machine translation 机器翻译 — automatic translation between languages.
    • recommendation systems 推荐系统 — suggesting products, videos or music.
    • autonomous vehicles 自动驾驶汽车 and robots.

    A common exam scenario: a program reads a label with a camera, translates it, and reads it aloud — using optical character recognition 光学字符识别 to find the words, machine translation to convert them, and text-to-speech 文本转语音 for the audio.

    Reading a foreign label aloud: the camera image goes to OCR to find the words, then to machine translation, then to text-to-speech for the audio
    A common scenario: OCR → machine translation → text-to-speech reads a foreign label aloud

    A four-mark "explain how AI is used" answer follows the pipeline step by step: image recognition (OCR) analyses the pixels of the photograph to locate the characters; the patterns of pixels are converted into individual characters and words; machine translation converts the words into the user's language; and text-to-speech produces the spoken output. Each step is a mark.

    Benefits

    • accessibility — speech/image AI helps users with impairments; translation helps non-native speakers.
    • productivity — automating repetitive tasks frees people for creative work.
    • decision support — AI spots patterns in huge datasets (medical diagnosis, fraud detection).
    • always available, and personalised to each user.

    Impacts: social, economic, environmental

    The syllabus asks for the impact of AI under three headings, and a question names one of them. Give the impact and its consequence.

    • Social: benefits — a label-reading program helps people with a visual impairment, people who cannot read the language, and people with reading difficulties; facial recognition at an airport speeds up identity checks and can stop wanted people entering. Harms — facial recognition can misidentify people and tracks everyone without consent, so privacy is lost; students who use AI to do their homework may not develop reasoning and problem-solving skills, may rely on it instead of learning, and may lose the collaboration and face-to-face communication that working together brings.
    • Economic: an AI fault-diagnosis module in a repair garage diagnoses faults faster and more accurately, so more vehicles are repaired per day and costs fall; but fewer skilled mechanics may be needed, so jobs are lost, and the module must be bought and maintained. More generally, AI raises productivity and creates new jobs in some fields while removing routine jobs in others.
    • Environmental: training and running large models uses a great deal of electricity and water for cooling in data centres, and the hardware becomes e-waste; on the other side, AI is used to cut energy use in buildings, optimise transport and monitor the environment.
    • Ethical (the classroom question): an AI that marks work or watches students must be fair to every student, must not leak their data, must be explainable when it makes a decision about them, and must not replace the judgement of a teacher where that matters.

    Concerns

    • bias 偏见 — unfair patterns in the training data become unfair AI decisions (hiring, lending).
    • job displacement — AI may replace some roles.
    • privacy — training often uses large amounts of personal data.
    • transparency — large models are "black boxes", hard to explain.
    • accountability — when AI is wrong, who is responsible: developer, user, or operator?
    • misuse — deepfakes, misinformation, surveillance.
    Biased training data leads the model to learn the bias, which then produces unfair decisions such as in hiring or lending
    How bias gets into AI: biased data → a biased model → unfair decisions

    Professionals must understand the limits of the AI they build, inform users, and reduce harm.

    Explore

    Computing concept lab

    Classify concrete examples by the computing idea they demonstrate.

    Vocabulary Train
    English Chinese Pinyin
    bias 偏见 piān jiàn
    artificial intelligence 人工智能 rén gōng zhì néng
    machine learning 机器学习 jī qì xué xí
    Deep learning 深度学习 shēn dù xué xí
    neural networks 神经网络 shén jīng wǎng luò
    speech recognition 语音识别 yǔ yīn shí bié
    image recognition 图像识别 tú xiàng shí bié
    machine translation 机器翻译 jī qì fān yì
    recommendation systems 推荐系统 tuī jiàn xì tǒng
    autonomous vehicles 自动驾驶汽车 zì dòng jià shǐ qì chē
    optical character recognition 光学字符识别 guāng xué zì fú shí bié
    text-to-speech 文本转语音 wén běn zhuǎn yǔ yīn
    7.1

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly.

    Term Definition
    ethics the moral principles that govern how a person behaves, in a profession the standards set out in its code of conduct
    code of conduct the rules an organisation or professional body sets for how its members must behave
    copyright the legal right of the creator of an original work to control how it is copied, distributed and modified
    software licence the legal agreement that states how a piece of software may be used, copied and distributed
    commercial software software sold for a fee, without source code, under a licence that protects the developer's intellectual property
    free software (FSF) software whose users are free to run, study, change and redistribute it, so its source code is available
    open source (OSI) software whose source code is available and which may be modified and redistributed under its licence
    shareware software distributed free for a trial period or with limited features, after which the user pays to continue
    freeware software that is free of charge to use and copy, but whose source code is not released and may not be modified
    artificial intelligence computer systems that perform tasks which normally need human intelligence, such as recognising images and speech
    machine learning a form of AI in which a system improves at a task by learning patterns from data rather than by explicit programming
    7.1

    Exam tips

    • Answer ethics questions against a professional code of conduct (public interest, competence, honesty), not personal opinion.
    • Distinguish copyright (protects the expression) from a patent (protects an invention).
    • Compare software licences: proprietary, open-source, freeware, shareware and FOSS.

    Common mistakes

    • Giving a personal opinion ("it is wrong") instead of a reason with a consequence ("faulty software could harm users, so it must be tested").
    • Treating free software and freeware as the same thing. Free software is about the freedom to study and change the code; freeware is merely free of charge.
    • Saying open source means free of charge. It means the source code is available and may be modified and redistributed; a fee may still be charged.
    • Writing that copyright must be registered. It applies automatically to the work as written.
    • Naming an impact without its consequence. "Job losses" scores when it is tied to why: the AI does the diagnosis, so fewer mechanics are needed.
    • Describing what AI is instead of how it is used. The marks are for the steps: recognise, convert, translate, speak.
  • 8

    Databases

    8.1

    File-based storage and its limits

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the limitations of using a file-based approach for the storage and retrieval of data
    Describe the features of a relational database that address the limitations of a file-based approach
    Show understanding of and use the terminology associated with a relational database model Including entity, table, record, field, tuple, attribute, primary key, candidate key, secondary key, foreign key, relationship (one-to-many, one-to-one, many-to-many), referential integrity, indexing
    Use an entity-relationship (E-R) diagram to document a database design
    Show understanding of the normalisation process First Normal Form (1NF), Second Normal Form (2NF) and Third Normal Form (3NF)
    Explain why a given set of database tables are, or are not, in 3NF
    Produce a normalised database design for a description of a database, a given set of data, or a given set of tables

    Source: Cambridge International syllabus

    Before databases, programs stored data in flat files 平面文件 — usually one file per program. This is fine for small data but breaks down at scale.

    A hand searching a card-index filing cabinet
    File-based storage keeps data in separate files, like papers in a filing cabinet — hard to search and easy to duplicate

    Limitations

    • data redundancy 数据冗余 — the same data (a customer's address) is held in several files, one per program, so storage is wasted and every copy must be updated.
    • data inconsistency 数据不一致 — when one copy is updated and another is not, the files disagree and nobody knows which is right.
    • data dependence — each program is written for the exact layout of its files; change a field's length or add a field and every program that reads the file must be rewritten.
    • no shared access — a file is locked while one program uses it, so users cannot work on the data at the same time.
    • weak integrity 完整性 — no central rules stop an invalid value or a link to a customer who does not exist; weak security — access is per file, not per field; and queries across files need a new program each time.
    The Payroll and Sales programs each link to their own separate data file, so the Staff Number field is stored twice
    The file-based approach: each program keeps its own files

    A relational database 关系数据库 fixes these by storing data in tables managed by one piece of software (the DBMS) that all programs use.

    One DBMS holding tables design, validation rules, access rights and the data, with a single shared database, used by both the payroll and sales applications
    The database approach: one DBMS serves all the programs

    Why a relational database is better — the three-mark answer. Each item of data is stored once, in one table, and tables are linked by keys, so there is no redundancy and no inconsistency; the data is independent of the programs, which ask the DBMS for what they need and are unaffected when the structure changes; and the DBMS enforces integrity rules, controls access per user and per field, allows many users at once, and answers any query without a new program being written.

    Worked example. A repair shop stores its customers, devices and repair jobs using a file-based approach, one file per program. Give three problems this causes, and describe how a relational database would remove them.

    The customer's name and phone number are stored in the repairs file and the invoices file (redundancy); when a customer changes number, one file is updated and the other is not (inconsistency); and when the shop wants a new report — repairs per technician — a new program has to be written to read the files (no ad-hoc queries). In a relational database the customer is stored once in a CUSTOMER table and referred to by CustomerID from the REPAIR table, so a change is made once and is seen everywhere; the report is a single SQL query.

    Vocabulary Train
    English Chinese Pinyin
    flat files 平面文件 píng miàn wén jiàn
    data redundancy 数据冗余 shù jù rǒng yú
    data inconsistency 数据不一致 shù jù bù yī zhì
    integrity 完整性 wán zhěng xìng
    relational database 关系数据库 guān xì shù jù kù
    Exercise sheet
    8.1

    Relational model — terms

    • table (relation) — a grid of rows and columns; one table per type of entity 实体 (e.g. CUSTOMER).
    • record 记录 (row, also called a tuple 元组) — one row; one instance of the entity.
    • field 字段 (column, also called an attribute 属性) — one column; one piece of information about each record.
    • primary key 主键 — a field (or fields) that uniquely identifies each record; never null or duplicated.
    • foreign key 外键 — a field whose value matches the primary key of another table, linking the two.
    • composite key 复合键 — a primary key made of two or more fields together.
    • candidate key 候选键 — any field(s) that could be the primary key.
    • secondary key 次键 — a non-primary field that is indexed for fast searching.
    • indexing 索引 — building an index on a field so look-ups and joins run faster.
    • referential integrity 参照完整性 — every foreign-key value must match an existing primary key (no orphan records).

    A table is written in shorthand with the primary key underlined and foreign keys noted:

    CUSTOMER(CustomerID, Name, Phone)
    ORDER(OrderID, CustomerID, OrderDate)   -- CustomerID is FK → CUSTOMER
    
    Two tables linked by a foreign key: the CUSTOMER table has primary key CustomerID; the ORDER table has its own primary key OrderID plus a CustomerID foreign key whose value matches a CustomerID in CUSTOMER
    A foreign key links two tables: ORDER.CustomerID matches the primary key CUSTOMER.CustomerID

    Worked example. State what is meant by entity, primary key and referential integrity in a relational database, and complete the term ↔ description table for tuple and attribute.

    An entity is something about which data is stored — a person, object or event — which becomes one table. A primary key is the attribute (or combination of attributes) that uniquely identifies each record in a table. Referential integrity means that every foreign-key value must match the value of a primary key in the table it refers to, so a record cannot refer to one that does not exist. A tuple is one row of a table (one record); an attribute is one column (one field). Learn the pairs: table/relation, record/tuple, field/attribute.

    Explore

    Read a relational table with SELECT

    A relational table is just rows (records) and columns (fields). WHERE keeps the rows that match a condition; SELECT then keeps only the columns you asked for.

    Vocabulary Train
    English Chinese Pinyin
    field 字段 zì duàn
    table biǎo
    entity 实体 shí tǐ
    record 记录 jì lù
    tuple 元组 yuán zǔ
    attribute 属性 shǔ xìng
    primary key 主键 zhǔ jiàn
    foreign key 外键 wài jiàn
    composite key 复合键 fù hé jiàn
    candidate key 候选键 hòu xuǎn jiàn
    secondary key 次键 cì jiàn
    indexing 索引 suǒ yǐn
    referential integrity 参照完整性 cān zhào wán zhěng xìng
    8.1

    Entity-relationship (E-R) diagrams

    An entity-relationship diagram 实体关系图 shows the structure: each entity is a rectangle, each relationship a line, with the cardinality 基数 marked at each end:

    • one-to-one (1:1).
    • one-to-many 一对多 (1:M) — each Customer has many Orders; each Order has one Customer.
    • many-to-many (M:N) — Students take many Courses, and Courses have many Students.
    An E-R diagram with a STUDENT entity and a CLASS entity joined by a relationship line, crow's-foot many at the student end and one bar at the class end
    An E-R diagram: one class has many students
    Crow's-foot line-end symbols for one, many, one and only one, zero or one, one or many, and zero or many
    Crow's-foot symbols for the cardinality of a relationship

    A many-to-many relationship cannot be stored directly. Break it into two one-to-many relationships through a link table 连接表 holding the two foreign keys:

    ENROLMENT(StudentID, CourseID, EnrolmentDate)
    
    A many-to-many relationship between STUDENT and COURSE stored as two one-to-many relationships through an ENROLMENT link table holding StudentID and CourseID
    A link table resolves a many-to-many relationship into two one-to-many relationships

    Drawing the E-R diagram for a given set of tables. Each table becomes an entity. A relationship exists wherever one table holds a foreign key to another; it runs from the table holding the foreign key (the many end) to the table whose primary key it is (the one end). A table with two foreign keys and no other identity is usually a link table resolving a many-to-many relationship. Label each line with the relationship type.

    An E-R diagram for a repair-shop database with four entities: CUSTOMER one-to-many DEVICE, DEVICE one-to-many REPAIR and TECHNICIAN one-to-many REPAIR, with crow's-foot notation and the primary and foreign keys shown
    Drawing the diagram from the tables: every foreign key is a one-to-many relationship, with the "many" at the table that holds it

    Worked example. A repair shop has the tables CUSTOMER(CustomerID, Name, Phone), DEVICE(DeviceID, CustomerID, Type, Model), TECHNICIAN(TechnicianID, Name) and REPAIR(RepairID, DeviceID, TechnicianID, RepairDate, Cost). Identify the relationships and their types.

    DEVICE holds CustomerID, so CUSTOMER–DEVICE is one-to-many (one customer, many devices). REPAIR holds DeviceID, so DEVICE–REPAIR is one-to-many; it also holds TechnicianID, so TECHNICIAN–REPAIR is one-to-many. There is no direct CUSTOMER–REPAIR line: the link runs through DEVICE. Three lines, three crow's feet, all at the REPAIR or DEVICE ends.

    Vocabulary Train
    English Chinese Pinyin
    entity-relationship diagram 实体关系图 shí tǐ guān xì tú
    cardinality 基数 jī shù
    one-to-many 一对多 yī duì duō
    link table 连接表 lián jiē biǎo
    8.1

    Normalisation

    Normalisation 规范化 organises tables to cut redundancy and inconsistency, going through normal forms 范式 in order.

    • First normal form (1NF) — every field holds a single (atomic 原子) value, with no repeating groups, and a primary key.
    • Second normal form (2NF) — in 1NF, and every non-key field depends on the whole primary key (only matters for a composite key).
    • Third normal form (3NF) — in 2NF, and every non-key field depends only on the primary key, not on another non-key field (no transitive dependency 传递依赖).

    A 3NF design stores each fact once, so insert/update/delete anomalies disappear. The trade-off is more tables and more joins. Aim for 3NF.

    To produce a 3NF design: find the entities and their attributes; choose a primary key for each; split repeating/non-atomic fields (1NF); split fields depending on part of a composite key (2NF); split fields depending transitively on the key (3NF); add foreign keys for the relationships.

    Normalisation: one table where the customer name and phone repeat on every order is split into a separate ORDER table and CUSTOMER table, so each fact is stored once
    Normalisation removes redundancy by splitting repeated data into its own table

    Worked example. The table ORDER(OrderID, CustomerID, CustomerName, ProductID, Quantity) has the composite primary key (OrderID, ProductID). Normalise it to 3NF. Test each non-key field against the key. Quantity depends on both OrderID and ProductID, which is fine. But CustomerID depends on OrderID alone - only part of the composite key. That is a partial dependency, so the table is not in 2NF. Split it into ORDER_LINE(OrderID, ProductID, Quantity) and ORDER(OrderID, CustomerID, CustomerName). Now test 3NF: in that new ORDER table, CustomerName depends on CustomerID, which is not the key - a transitive dependency. Split again: ORDER(OrderID, CustomerID) and CUSTOMER(CustomerID, CustomerName). Name the dependency that breaks each form (partial breaks 2NF, transitive breaks 3NF); "it has repeated data" describes the symptom and earns nothing.

    The three questions to ask of any table. Is every cell a single value, with no repeating group? If not, it is not in 1NF. If the key is composite, does every non-key field depend on the whole key? If some field depends on part of it, there is a partial dependency 部分依赖 and the table is not in 2NF. Does every non-key field depend on the key alone? If a field depends on another non-key field, there is a transitive dependency and the table is not in 3NF. An "explain why the table is not in 3NF" answer names the dependency and the fields involved.

    Normalising a car-rental table in three steps: the repeating group of cars is removed for 1NF, the car details that depend on CarReg alone are moved to a CAR table for 2NF, and the customer details that depend on CustomerID are moved to a CUSTOMER table for 3NF
    1NF removes the repeating group, 2NF the partial dependency, 3NF the transitive dependency

    Worked example. A car-rental shop records each rental as RENTAL(RentalID, RentalDate, CustomerID, CustomerName, CustomerPhone, CarReg, CarModel, DailyRate, Days), where one rental can include several cars. Explain why the table is not normalised and produce a 3NF design.

    Not in 1NF: the car fields CarReg, CarModel, DailyRate, Days form a repeating group — one rental has several cars. Move them to RENTAL_CAR(RentalID, CarReg, CarModel, DailyRate, Days) with the composite key (RentalID, CarReg). Not in 2NF: in RENTAL_CAR, CarModel and DailyRate depend on CarReg alone — a partial dependency. Move them to CAR(CarReg, CarModel, DailyRate), leaving RENTAL_CAR(RentalID, CarReg, Days). Not in 3NF: in RENTAL, CustomerName and CustomerPhone depend on CustomerID, a non-key field — a transitive dependency. Move them to CUSTOMER(CustomerID, CustomerName, CustomerPhone), leaving RENTAL(RentalID, RentalDate, CustomerID). The 3NF design is four tables — CUSTOMER, RENTAL, RENTAL_CAR, CAR — with CustomerID, RentalID and CarReg as foreign keys; underline every primary key.

    Vocabulary Train
    English Chinese Pinyin
    normalisation 规范化 guī fàn huà
    normal forms 范式 fàn shì
    atomic 原子 yuán zi
    transitive dependency 传递依赖 chuán dì yī lài
    partial dependency 部分依赖 bù fèn yī lài
    8.2

    Database Management System (DBMS)

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the features provided by a Database Management System (DBMS) that address the issues of a file based approach Including: • data management, including maintaining a data dictionarydata modellinglogical schemadata integritydata security, including backup procedures and the use of access rights to individuals / groups of users
    Show understanding of how software tools found within a DBMS are used in practice Including the use and purpose of: • developer interfacequery processor

    Source: Cambridge International syllabus

    A DBMS 数据库管理系统 manages the database centrally. Features that fix the file-based limits:

    • data dictionary 数据字典 — a description of every table, field, type and key; programs query it instead of hard-coding the structure.
    • redundancy/consistency control — each fact stored once.
    • concurrent access 并发访问 control — locks and transactions let many users work at once.
    • backup 备份 and recovery; security and per-user permissions.
    • integrity rules — keys, unique and range constraints, enforced centrally.
    • transactions 事务 — a group of operations that all succeed or all fail.
    • views 视图 — virtual tables that show each user "their" slice of the data.
    • data management 数据管理 and data modelling 数据建模 — control how data is stored and define its structure as a logical schema 逻辑模式 (the logical design, independent of physical storage).
    • data integrity 数据完整性 and data security 数据安全 — enforce correctness and control access centrally.
    • a query processor 查询处理器 runs queries; a developer interface 开发者接口 gives tools and APIs for building applications.

    Its tools include a data-dictionary editor, a query builder, a forms builder, a report generator, user management, and an SQL editor.

    What the data dictionary holds (a "give three items" question): the names of the tables; the names of the fields in each table; each field's data type and length; the primary and foreign keys and the relationships between tables; validation rules; indexes; and who may access each table. It is metadata — data about the data — and the DBMS uses it to check every query and every change.

    How the DBMS keeps the data secure (a "describe two methods" question): authentication 身份验证 — a username and password, or a biometric, before any access; access rights — each user or group is allowed to read, write or delete only certain tables or fields, often through a view; encryption of the stored data and of data sent to it, so a copied file is unreadable; backups taken regularly, so the data can be restored after loss; and a transaction log that records who changed what.

    The two software tools. The developer interface is what a programmer uses to build the database and the applications on it: create tables and set keys and validation, write queries and SQL, and design forms and reports, without knowing how the data is physically stored. The query processor takes a query (SQL from a program, or a query built in the interface), checks it against the data dictionary, works out the most efficient way to run it, retrieves the data and returns the results.

    Logical schema. The DBMS keeps the logical design (which tables and fields exist and how they relate) separate from the physical storage (files, indexes, disk blocks). Programs work with the logical schema, so the physical storage can be reorganised without changing a single program — this is the data independence the file-based approach lacked.

    A hard disk drive with its cover removed, showing the stacked mirror-like platters and the read/write head arm resting over them
    The physical storage the logical schema hides: a hard disk's spinning platters and read/write head
    Explore

    Database service lab

    Watch how a DBMS turns a query into safe shared data access.

    Explore

    Database service lab

    Watch how a DBMS turns a query into safe shared data access.

    Vocabulary Train
    English Chinese Pinyin
    DBMS 数据库管理系统 shù jù kù guǎn lǐ xì tǒng
    data dictionary 数据字典 shù jù zì diǎn
    concurrent access 并发访问 bìng fā fǎng wèn
    transactions 事务 shì wù
    backup 备份 bèi fèn
    views 视图 shì tú
    data management 数据管理 shù jù guǎn lǐ
    data modelling 数据建模 shù jù jiàn mó
    logical schema 逻辑模式 luó jí mó shì
    data integrity 数据完整性 shù jù wán zhěng xìng
    data security 数据安全 shù jù ān quán
    query processor 查询处理器 chá xún chǔ lǐ qì
    developer interface 开发者接口 kāi fā zhě jiē kǒu
    authentication 身份验证 shēn fèn yàn zhèng
    Watch lesson Exercise sheet
    8.3

    DDL and DML

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding that the DBMS carries out all creation/modification of the database structure using its Data Definition Language (DDL)
    Show understanding that the DBMS carries out all queries and maintenance of data using its DML
    Show understanding that the industry standard for both DDL and DML is Structured Query Language (SQL) Understand a given SQL statement
    Understand given SQL (DDL) statements and be able to write simple SQL (DDL) statements using a sub-set of statements Create a database (CREATE DATABASE) Create a table definition (CREATE TABLE), including the creation of attributes with appropriate data types: • CHARACTER • VARCHAR(n) • BOOLEAN • INTEGER • REAL • DATE • TIME change a table definition (ALTER TABLE) add a primary key to a table (PRIMARY KEY (field)) add a foreign key to a table (FOREIGN KEY (field) REFERENCES Table (Field))
    Write an SQL script to query or modify data (DML) which are stored in (at most two) database tables Queries including SELECT... FROM, WHERE, ORDER BY, GROUP BY, INNER JOIN, SUM, COUNT, AVG
    Data maintenance including INSERT INTO, DELETE FROM, UPDATE

    Source: Cambridge International syllabus

    SQL 结构化查询语言 (Structured Query Language) has two halves:

    SQL splits into DDL (builds the structure) and DML (works with the data)
    DDL builds the database structure; DML works with the data
    • Data Definition Language 数据定义语言 (DDL) — creates or changes the structure (tables, keys, constraints).
    • Data Manipulation Language 数据操纵语言 (DML) — works with the data (insert, update, delete, query 查询).

    DDL basics

    CREATE TABLE CUSTOMER (
      CustomerID INTEGER PRIMARY KEY,
      Name VARCHAR(50) NOT NULL,
      Phone VARCHAR(20)
    );
    

    Add a foreign key:

    CREATE TABLE ORDER (
      OrderID INTEGER PRIMARY KEY,
      CustomerID INTEGER,
      OrderDate DATE,
      FOREIGN KEY (CustomerID) REFERENCES CUSTOMER(CustomerID)
    );
    

    Modify and drop:

    ALTER TABLE CUSTOMER ADD Email VARCHAR(100);
    DROP TABLE CUSTOMER;
    

    Common types: INTEGER, REAL, VARCHAR(n), CHAR(n) (also CHARACTER(n)), DATE, TIME, BOOLEAN, DECIMAL(p, s).

    DML basics

    Query with SELECT:

    A SELECT query returns just the rows that match its condition
    A SELECT query returns only the rows that match its condition
    SELECT Name, Phone
    FROM CUSTOMER
    WHERE City = 'London'
    ORDER BY Name ASC;
    

    SELECT lists fields, FROM names the table, WHERE filters rows, ORDER BY sorts.

    A join 连接 combines two tables using a foreign-key relationship:

    SELECT C.Name, O.OrderDate
    FROM CUSTOMER C INNER JOIN ORDER O
      ON C.CustomerID = O.CustomerID
    WHERE O.OrderDate >= '2024-01-01';
    
    An SQL query annotated line by line: SELECT names the fields and a COUNT column, FROM names the first table with an alias, INNER JOIN ON links the second table through the foreign key, WHERE keeps matching rows, GROUP BY makes one row per customer, ORDER BY sorts the result
    The parts of a query, in the order they must be written

    Aggregate functions 聚合函数 (COUNT, SUM, AVG, MIN, MAX) are often used with GROUP BY:

    SELECT CustomerID, COUNT(*) AS NumOrders
    FROM ORDER
    GROUP BY CustomerID;
    

    Insert, update, delete:

    INSERT INTO CUSTOMER (CustomerID, Name, Phone)
    VALUES (101, 'Ada Lovelace', '020-1234-5678');
    
    UPDATE CUSTOMER SET Phone = '020-9999-0000' WHERE CustomerID = 101;
    
    DELETE FROM CUSTOMER WHERE CustomerID = 101;
    

    Always put a WHERE clause on UPDATE and DELETE, or the change hits every row.

    Tips for exam SQL

    • use the exact table and field names from the question.
    • quote strings with single quotes ('Smith'); don't quote numbers.
    • comparisons: =, <, >, <=, >=, <>.
    • LIKE 'A%' matches anything starting with A (% = any string, _ = one character); IN (1,2,3); BETWEEN 10 AND 20.
    • combine conditions with AND / OR / NOT, and end each statement with a semicolon.

    The DDL pattern the exam wants. Every CREATE TABLE names each field with its type, marks the primary key, and declares each foreign key with the table it references; a composite key is declared on its own line:

    CREATE TABLE RENTAL_CAR (
      RentalID INTEGER,
      CarReg VARCHAR(8),
      Days INTEGER,
      PRIMARY KEY (RentalID, CarReg),
      FOREIGN KEY (RentalID) REFERENCES RENTAL(RentalID),
      FOREIGN KEY (CarReg) REFERENCES CAR(CarReg)
    );
    

    Worked example. Using CUSTOMER(CustomerID, Name, Phone) and DEVICE(DeviceID, CustomerID, Type, Model), write SQL scripts to: (a) list the name and phone number of every customer who owns a device of type 'tablet', in alphabetical order of name; (b) count the devices of each type; (c) record that customer 17 now has the phone number '0771 234 5678'; (d) add a new device, ID 305, a 'laptop' of model 'X1' belonging to customer 17.

    (a)

    SELECT CUSTOMER.Name, CUSTOMER.Phone
    FROM CUSTOMER INNER JOIN DEVICE
      ON CUSTOMER.CustomerID = DEVICE.CustomerID
    WHERE DEVICE.Type = 'tablet'
    ORDER BY CUSTOMER.Name ASC;
    

    (b)

    SELECT Type, COUNT(DeviceID) AS NumberOfDevices
    FROM DEVICE
    GROUP BY Type;
    

    (c) UPDATE CUSTOMER SET Phone = '0771 234 5678' WHERE CustomerID = 17; (d) INSERT INTO DEVICE (DeviceID, CustomerID, Type, Model) VALUES (305, 17, 'laptop', 'X1');

    Marks are given per clause — the fields, the tables, the join condition, the WHERE, the ORDER BY — so a script with one wrong clause still scores the rest. Write Table.Field whenever two tables are involved.

    Worked example. Explain what this script does: SELECT T.Name, SUM(R.Cost) AS Total FROM TECHNICIAN T INNER JOIN REPAIR R ON T.TechnicianID = R.TechnicianID GROUP BY T.Name;

    It outputs each technician's name with the total cost of the repairs that technician has carried out, one row per technician: the two tables are joined on TechnicianID, the rows are grouped by name, and the costs in each group are added. When asked what a script does, describe the result, not the syntax.

    Explore

    Stitch two tables with INNER JOIN

    A join matches rows where the foreign key equals the primary key — here Orders.CustomerID = Customer.CustomerID — and combines each matching pair into one wider row.

    Explore

    SELECT … WHERE

    Step through a query: WHERE keeps the rows that match, then SELECT picks the columns you asked for.

    Vocabulary Train
    English Chinese Pinyin
    query 查询 chá xún
    SQL 结构化查询语言 jié gòu huà chá xún yǔ yán
    join 连接 lián jiē
    Data Definition Language 数据定义语言 shù jù dìng yì yǔ yán
    Data Manipulation Language 数据操纵语言 shù jù cāo zòng yǔ yán
    aggregate functions 聚合函数 jù hé hán shù
    Watch lesson Exercise sheet
    8.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    entity something about which data is stored — a person, object or event — which becomes a table in a relational database
    attribute one item of data about an entity (a column of the table)
    tuple one row of a table: one instance of the entity
    primary key an attribute, or combination of attributes, that uniquely identifies each record in a table
    foreign key an attribute in one table whose value matches a primary key in another table, used to link the two
    candidate key any attribute (or combination) that could be chosen as the primary key
    secondary key a non-primary attribute that is indexed so the table can be searched or sorted on it quickly
    composite key a primary key made of two or more attributes together
    referential integrity every foreign-key value must match an existing primary-key value in the table it refers to
    first normal form a table in which every attribute is atomic, there are no repeating groups, and there is a primary key
    second normal form in 1NF, and every non-key attribute depends on the whole of the primary key (no partial dependency)
    third normal form in 2NF, and no non-key attribute depends on another non-key attribute (no transitive dependency)
    data dictionary the metadata a DBMS keeps about the structure of the database: tables, fields, types, keys, relationships, validation
    DDL / DML the language used to define or change the structure of a database / the language used to query and maintain the data in it
    8.3

    Exam tips

    • Define the terms exactly: entity, attribute, primary key, foreign key, and the relationship types (1:1, 1:many, many:many).
    • Give a reason at each normal form: 1NF (no repeating groups), 2NF (no partial dependency), 3NF (no non-key dependency) — and name the fields involved.
    • Explain what a DBMS provides (data independence, security, integrity, concurrent access, a data dictionary, a developer interface, a query processor).
    • Distinguish DDL (define the structure) from DML (query and change the data), and write SQL clause by clause: SELECT, FROM, INNER JOIN … ON, WHERE, GROUP BY, ORDER BY.
    • To draw an E-R diagram from tables, find each foreign key first: every foreign key is one one-to-many relationship, with the "many" at the table that holds it.

    Common mistakes

    • Drawing a many-to-many relationship directly. It must be split into two one-to-many relationships through a link table holding both foreign keys.
    • Explaining "not in 3NF" by "the data is repeated". Name the dependency (partial or transitive) and the fields involved.
    • Double quotes round strings in SQL, or quotes round numbers. Strings take 'single quotes'; numbers take none.
    • Leaving out the ON condition after INNER JOIN. Without it the two tables are not linked.
    • Putting an ordinary field next to COUNT or SUM in a SELECT without a GROUP BY.
    • UPDATE or DELETE without a WHERE. It changes or removes every row in the table.
  • 9

    Algorithm Design and Problem-solving

    9.1

    Computational thinking

    Syllabus
    Candidates should be able to: Notes and guidance
    Show an understanding of abstraction Need for and benefits of using abstraction Describe the purpose of abstraction Produce an abstract model of a system by only including essential details
    Describe and use decomposition Break down problems into sub-problems leading to the concept of a program module (procedure / function)

    Source: Cambridge International syllabus

    Computational thinking 计算思维 is the set of mental tools for analysing a problem and designing a solution a computer can run. Two key ones are abstraction and decomposition.

    A part-finished jigsaw puzzle
    Computational thinking breaks a big problem into smaller, easier parts — like solving a jigsaw

    Abstraction

    Abstraction 抽象 means keeping the essential features of a problem and ignoring the irrelevant detail, giving a simpler model.

    Examples:

    • a train-network map keeps the stations and lines but drops the geography.
    • a class in object-oriented programming keeps only the attributes and methods the system needs.
    • a function hides a piece of work behind a name.

    A full model of any real problem would be too big to reason about, so abstraction is essential.

    The examiner asks for the purpose of abstraction and for its benefits. Purpose: to produce a simpler model of a problem that contains only the details needed to solve it. Benefits: the problem is easier to understand and to program; the program is smaller and faster to write and test; the same model can be reused for similar problems. When you are asked to produce an abstract model of a system, list only the data and actions the task needs. For a school timetable that means the classes, rooms, teachers and periods; it does not mean the colour of the rooms or the age of the teachers.

    Abstraction turns a cluttered real geography (a wiggly route with scattered buildings) into a clean metro map — evenly spaced station circles on a straight line, keeping the stations and lines and dropping the geography
    Abstraction keeps the essentials (stations and lines) and drops irrelevant detail (the geography)

    Decomposition

    Decomposition 分解 means breaking a large problem into smaller sub-problems, each easier to solve and tackled one at a time.

    1. find the main parts of the task.
    2. break each into smaller sub-tasks.
    3. continue until each is small enough to design directly.
    4. solve the small tasks and combine them.

    For stock control: "manage stock" → "record sales", "record deliveries", "produce reports" → ("record sales") "look up product", "decrease stock count", "save the transaction". Decomposition makes big problems manageable, lets a team divide the work, and gives modular code — each module becomes a procedure 过程 or function.

    "Explain why decomposition is used" is a three-mark question with a fixed shape. Give three separate benefits: each sub-problem 子问题 is small enough to design, code and test on its own; different programmers can work on different modules 模块 at the same time; a module that already exists (or a library routine) can be reused, and a fault is easier to find because it lies inside one module. A structure chart (topic 12) is the diagram of a decomposition: the program at the top, its modules beneath, and the data passed between them.

    A tree with "Manage stock" at the top branching into the modules "Record sales", "Record deliveries" and "Produce reports", and "Record sales" splitting into the sub-tasks "Look up product", "Decrease stock count" and "Save the transaction"
    Decomposing a program into modules and sub-modules
    Explore

    Solving a problem the computational way

    Step through the four cornerstones in the order you'd use them — break the problem down, spot what repeats, strip it to essentials, then write the steps.

    Vocabulary Train
    English Chinese Pinyin
    computational thinking 计算思维 jì suàn sī wéi
    abstraction 抽象 chōu xiàng
    decomposition 分解 fēn jiě
    sub-problem 子问题 zi wèn tí
    procedure 过程 guò chéng
    modules 模块 mó kuài
    Exercise sheet
    9.2

    Algorithms

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding that an algorithm is a solution to a problem expressed as a sequence of defined steps
    Use suitable identifier names for the representation of data used by a problem and represent these using an identifier table
    Write pseudocode that contains input, process and output
    Write pseudocode using the three basic constructs of sequence, selection and iteration (repetition)
    Document a simple algorithm using a structured English description, a flowchart or pseudocode
    Write pseudocode from: • a structured English description • a flowchart
    Draw a flowchart from: • a structured English description • pseudocode
    Describe and use the process of stepwise refinement to express an algorithm to a level of detail from which the task may be programmed
    Use logic statements to define parts of an algorithm solution

    Source: Cambridge International syllabus

    Bubble sort, pass by pass

    An algorithm 算法 is a solution expressed as a sequence of defined steps. Each step is unambiguous 无歧义 (one meaning), deterministic 确定性 (same input → same output), finite (the steps end), and effective (each can be done). An algorithm says what to do, independent of the programming language used to implement it.

    Explore

    Selection: follow the IF / ELSE branches

    Drag the score and watch which branch runs. Selection tests each condition in turn and takes the FIRST one that is true — that is how IF … ELSE IF … ELSE works.

    Vocabulary Train
    English Chinese Pinyin
    algorithm 算法 suàn fǎ
    unambiguous 无歧义 wú qí yì
    deterministic 确定性 què dìng xìng
    Watch lesson Exercise sheet
    9.2

    Identifier table

    When you start an algorithm, list every piece of data in an identifier table 标识符表 — its identifier 标识符 (the variable 变量 name), data type 数据类型, and description. The exam's table has exactly these three columns:

    Identifier Data type Description
    Category STRING the product category
    SaleDate DATE when the item was sold
    ItemCost REAL cost of the item
    InStock BOOLEAN TRUE if in stock
    Sales ARRAY[1:30] OF REAL the last 30 daily sales totals

    Use descriptive names (ItemCost, not x): an identifier starts with a letter, contains no spaces, and is written the same way every time it appears. Common types are INTEGER, REAL, STRING, CHAR, BOOLEAN, DATE, plus arrays. The table forces you to name every piece of data before writing code, and a "complete the identifier table" question gives one mark for each correct data type or description, so write the type exactly as the pseudocode guide does.

    An identifier table listing each variable with its name, data type and description, for example ItemCost as a REAL for the cost of the item
    An identifier table names every piece of data before you write code
    Vocabulary Train
    English Chinese Pinyin
    identifier table 标识符表 biāo shí fú biǎo
    identifier 标识符 biāo shí fú
    variable 变量 biàn liàng
    data type 数据类型 shù jù lèi xíng
    9.2

    Pseudocode — the three basic constructs

    Pseudocode 伪代码 is a structured, language-neutral way to describe algorithms.

    The three basic constructs as mini-flowcharts: sequence runs step A then B then C; selection tests a condition and does X or Y; iteration repeats a body while a condition holds, looping back
    The three building blocks of any algorithm: sequence, selection and iteration

    1. Sequence

    Steps run one after another (sequence 顺序):

    INPUT Name
    INPUT Age
    OUTPUT "Hello", Name
    

    2. Selection

    A choice of which steps run, based on a condition (selection 选择):

    IF Age >= 18 THEN
        OUTPUT "Adult"
    ELSE
        OUTPUT "Minor"
    ENDIF
    

    For more options, use CASE OF ... ENDCASE.

    3. Iteration

    Repeating a block (iteration 迭代, a loop 循环):

    FOR i ← 1 TO 10
        OUTPUT i
    NEXT i
    

    A WHILE loop tests the condition before each pass (may run zero times); a REPEAT...UNTIL loop tests after each pass (always runs at least once).

    WHILE Total < 100 DO
        INPUT Value
        Total ← Total + Value
    ENDWHILE
    
    REPEAT
        INPUT Mark
    UNTIL Mark >= 0 AND Mark <= 100
    
    Two flowcharts side by side. WHILE tests the condition first, so the body may never run: the diamond sits above the body and the No branch leaves the loop. REPEAT UNTIL runs the body first and tests after it, so the body always runs at least once: the body sits above the diamond and the No branch returns to it
    A WHILE loop tests before the body runs; a REPEAT ... UNTIL loop tests after it, so its body always runs at least once

    Choosing the loop is itself a mark: FOR when you know how many times (a count-controlled loop 计数循环); WHILE when the loop might not run at all (a pre-condition loop 前测循环); REPEAT ... UNTIL when it must run at least once, as in validating an input (a post-condition loop 后测循环). A "describe the iteration construct" answer names the construct, says where the condition is tested, and gives the consequence (zero times or at least once).

    Common operations

    • assignment 赋值: x ← 5 (an arrow; = is for comparison).
    • input/output: INPUT variable, OUTPUT expression.
    • comparisons =, <>, <, >, <=, >=; logic AND, OR, NOT.
    • arithmetic + - * /, plus DIV (integer division) and MOD (remainder).
    • strings: LENGTH, LEFT, RIGHT, MID, and & for concatenation 拼接 (joining).

    The pseudocode the exam expects

    Every pseudocode answer is marked against Cambridge's published pseudocode guide. Write these forms exactly:

    Construct Pseudocode
    declare a variable DECLARE Total : INTEGER
    declare an array DECLARE Marks : ARRAY[1:30] OF REAL
    a constant CONSTANT MaxTries = 3
    assignment Total ← Total + Value
    input and output INPUT Name and OUTPUT "Hello ", Name
    several options CASE OF Choice ... 1 : OUTPUT "Add" ... OTHERWISE OUTPUT "Error" ... ENDCASE
    count-controlled loop FOR i ← 1 TO 10 STEP 2 ... NEXT i
    pre-condition loop WHILE Total < 100 DO ... ENDWHILE
    post-condition loop REPEAT ... UNTIL Mark >= 0
    integer division and remainder DIV and MOD: 17 DIV 5 = 3, 17 MOD 5 = 2
    string functions LENGTH(S), LEFT(S, 3), RIGHT(S, 2), MID(S, 2, 4), UCASE(S), LCASE(S)
    conversions INT(3.7) = 3, NUM_TO_STR(12), STR_TO_NUM("4.5"), ASC('A') = 65, CHR(66) = 'B'
    a random number RAND(100) gives a real number from 0 up to (but not including) 100; INT(RAND(100)) + 1 gives an integer from 1 to 100

    Two habits earn marks on every question: declare every variable you use, with the type from your identifier table, and initialise 初始化 every counter 计数器 and total (Count ← 0, Total ← 0) before the loop that changes it.

    Input → Process → Output

    Every program follows this shape:

    INPUT Length
    INPUT Width
    Area ← Length * Width
    OUTPUT "Area = ", Area
    

    Listing the inputs and outputs first makes the algorithm cleaner.

    Worked example. Write pseudocode that inputs 100 integers and outputs how many of them, and the total of those, that lie between 10 and 20 inclusive.

    Identifier table: Count : INTEGER (loop counter), Value : INTEGER (the integer just input), InRange : INTEGER (how many were in range), Total : INTEGER (their sum).

    DECLARE Count, Value, InRange, Total : INTEGER
    InRange ← 0
    Total ← 0
    FOR Count ← 1 TO 100
        INPUT Value
        IF Value >= 10 AND Value <= 20 THEN
            InRange ← InRange + 1
            Total ← Total + Value
        ENDIF
    NEXT Count
    OUTPUT InRange, Total
    

    If the question then asks you to "identify two constructs and state how each is used", answer in the same shape: iteration, the FOR loop, repeats the input 100 times; selection, the IF statement, adds a value only when it is in range.

    Worked example. A program picks a secret integer from 1 to 100. The user guesses until they are right; after each wrong guess the program says "Too low" or "Too high", and at the end it outputs how many guesses were made.

    Identifier table: Secret : INTEGER (the number to guess), Guess : INTEGER (the user's input), Tries : INTEGER (how many guesses so far).

    DECLARE Secret, Guess, Tries : INTEGER
    Secret ← INT(RAND(100)) + 1
    Tries ← 0
    REPEAT
        INPUT Guess
        Tries ← Tries + 1
        IF Guess < Secret THEN
            OUTPUT "Too low"
        ELSE
            IF Guess > Secret THEN
                OUTPUT "Too high"
            ENDIF
        ENDIF
    UNTIL Guess = Secret
    OUTPUT "You took ", Tries, " guesses"
    

    A REPEAT ... UNTIL loop is the right choice because the user must guess at least once. The marks are for: the random number in the right range, a loop that ends on a correct guess, the counter that starts at zero and increases inside the loop, the two messages under the right conditions, and the final output.

    Flowchart of the guessing game: Start, then set Secret to a random integer from 1 to 100 and Tries to 0, then input a guess, add one to Tries, test whether the guess equals the secret (Yes leads to output Tries and Stop), otherwise test whether the guess is smaller (Yes outputs Too low, No outputs Too high), and both outputs loop back to the input
    The same guessing game as a flowchart: the two decision diamonds are the two IF statements, and the return arrow is the REPEAT ... UNTIL loop

    Worked example. Output two different random integers, each between $-10$ and $10$ inclusive.

    There are 21 possible values, so INT(RAND(21)) gives 0 to 20 and subtracting 10 shifts it to the range $-10$ to $10$. The second number must be generated again until it differs from the first:

    DECLARE First, Second : INTEGER
    First ← INT(RAND(21)) - 10
    REPEAT
        Second ← INT(RAND(21)) - 10
    UNTIL Second <> First
    OUTPUT First, Second
    
    Every program follows the shape input, then process, then output, shown with the area example: input the length and width, process by multiplying, output the area
    Every program follows the Input, Process, Output shape
    Explore

    IF … ELSE selection

    Change the value and watch which branch runs — how a program makes a decision.

    Vocabulary Train
    English Chinese Pinyin
    sequence 顺序 shùn xù
    pseudocode 伪代码 wěi dài mǎ
    selection 选择 xuǎn zé
    iteration 迭代 dié dài
    loop 循环 xún huán
    count-controlled loop 计数循环 jì shù xún huán
    pre-condition loop 前测循环 qián cè xún huán
    post-condition loop 后测循环 hòu cè xún huán
    assignment 赋值 fù zhí
    concatenation 拼接 pīn jiē
    initialise 初始化 chū shǐ huà
    counter 计数器 jì shù qì
    9.2

    Three notations

    The same algorithm can be written three ways.

    • structured English 结构化英语 — natural language with indentation and fixed keywords; good for a high-level description.
    • flowchart 流程图 — a diagram with standard shapes:
    Shape Meaning
    Rounded rectangle Start / Stop
    Parallelogram Input / Output
    Rectangle Process
    Diamond Decision
    Arrow Flow of control
    • pseudocode — the keyword notation above; closest to code.

    You should be able to convert between any pair: each IF is a decision diamond, each loop is a back-arrow, and a sequence is stacked rectangles.

    Converting a flowchart into pseudocode: start at the terminator and follow the arrows in order; a parallelogram becomes INPUT or OUTPUT; a rectangle becomes an assignment; a diamond with two exits that rejoin further down becomes IF ... THEN ... ELSE ... ENDIF; a diamond whose one exit arrows back upwards is a loop, and it is a WHILE loop if the diamond comes before the repeated boxes and a REPEAT ... UNTIL loop if it comes after them. Converting the other way, draw exactly one box per statement and one diamond per condition, and label every exit of a diamond Yes or No.

    A flowchart for averaging numbers: rounded Start and Stop terminators, input/output parallelograms, process rectangles, and a "count < n?" decision diamond whose Yes branch loops back to read the next value
    A flowchart for averaging a list of numbers, using the standard shapes
    Vocabulary Train
    English Chinese Pinyin
    flowchart 流程图 liú chéng tú
    structured English 结构化英语 jié gòu huà yīng yǔ
    9.2

    Stepwise refinement

    Stepwise refinement 逐步求精 starts with a high-level outline and expands each step until it is small enough to code. For an average of $n$ numbers:

    Level 1:

    Read in the numbers
    Compute the average
    Output the average
    

    Level 2:

    INPUT n
    total ← 0
    FOR i ← 1 TO n
        INPUT value
        total ← total + value
    NEXT i
    average ← total / n
    OUTPUT average
    

    Each refinement keeps the previous structure and adds detail.

    A six-mark "apply stepwise refinement" question gives you a high-level outline and wants each step expanded into the concrete statements a programmer could code. Keep the steps in the same order, name the data each step reads or produces, and stop when every line is a single input, assignment, output, loop or condition. For example, "validate the password" becomes: input the password; check its length is at least 8; check it contains at least one digit; output "accepted" if both checks pass, otherwise output "rejected".

    Stepwise refinement: a Level 1 outline (read in the numbers, compute the average, output the average) is expanded into Level 2 detailed pseudocode with the input loop and the division
    Stepwise refinement: expand each high-level step into detailed pseudocode
    Explore

    Stepwise refinement: outline to code

    Step down the levels. You start with the whole task in one line and keep expanding each step into smaller ones — until every step is simple enough to code directly.

    Vocabulary Train
    English Chinese Pinyin
    stepwise refinement 逐步求精 zhú bù qiú jīng
    9.2

    Logic statements

    A logic statement 逻辑语句 is a Boolean 布尔 condition that controls branching, built from comparisons (x > 10), connectives (AND, OR, NOT) and brackets. Use it as the condition of IF, WHILE or REPEAT...UNTIL:

    WHILE attempts < 3 AND NOT loggedIn DO
        INPUT password
        IF password = correctPassword THEN
            loggedIn ← TRUE
        ELSE
            attempts ← attempts + 1
        ENDIF
    ENDWHILE
    

    Precedence 优先级 (highest to lowest): NOT, then AND, then OR. Use brackets when unsure. Common mistakes:

    • a = 1 OR 2 is wrong — write a = 1 OR a = 2.
    • NOT a > 5 means NOT (a > 5), i.e. a <= 5.
    • NOT (A AND B) is the same as (NOT A) OR (NOT B) (De Morgan's law 德摩根定律) — handy for simplifying conditions.

    Turning a sentence into a logic statement is a skill the papers test directly. "A ticket is free for anyone under 5 or over 65" becomes Age < 5 OR Age > 65. "A mark is valid if it is a whole number from 0 to 100" becomes Mark >= 0 AND Mark <= 100. "The loop stops when the file is finished or ten records have been read" becomes UNTIL EOF(File) OR Count = 10. Write each comparison in full: Age > 65 and Age < 5, never Age > 65 OR < 5.

    A parse tree for "attempts < 3 AND NOT loggedIn": NOT applies to loggedIn first, then AND joins that with attempts < 3
    Precedence: NOT binds to loggedIn first, then AND combines the two sides

    Worked example. Write an identifier table and pseudocode to read 10 numbers and output the largest. The identifier table names each variable with its data type and purpose: Count : INTEGER (loop counter), Num : REAL (the number just read), Max : REAL (largest so far).

    Max ← -999999
    FOR Count ← 1 TO 10
        INPUT Num
        IF Num > Max THEN
            Max ← Num
        ENDIF
    NEXT Count
    OUTPUT Max
    

    The design decision carrying the marks is initialising Max: it must start lower than any possible input - or, safer still, be set to the first number read. Initialise it to 0 and the algorithm wrongly returns 0 for a list of negative numbers, a bug your trace only exposes if the test data include a negative.

    Vocabulary Train
    English Chinese Pinyin
    Boolean 布尔 bù ěr
    logic statement 逻辑语句 luó jí yǔ jù
    precedence 优先级 yōu xiān jí
    De Morgan's law 德摩根定律 dé mó gēn dìng lǜ
    9.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    abstraction keeping the essential details of a problem and leaving out the details that are not needed
    decomposition breaking a problem down into smaller sub-problems, each of which can be solved separately
    algorithm a solution to a problem expressed as a sequence of defined steps
    identifier table a table listing each identifier used in an algorithm with its data type and a description of its purpose
    pseudocode a structured, language-independent way of writing the steps of an algorithm
    flowchart a diagram that shows the steps and decisions of an algorithm using standard symbols joined by arrows
    sequence statements executed one after another in the order written
    selection choosing which statements to execute according to a condition
    iteration repeating a group of statements while, or until, a condition holds
    stepwise refinement breaking each step of an outline into smaller steps, repeatedly, until each step can be coded directly
    logic statement a condition built from comparisons and the operators AND, OR and NOT that evaluates to TRUE or FALSE
    9.2

    Exam tips

    • Define an algorithm as an unambiguous, finite, deterministic sequence of steps, independent of language.
    • Use the three constructs correctly — sequence, selection, iteration — and keep an identifier table with data types.
    • Break a problem down by decomposition and abstraction, then stepwise refinement.
    • Write pseudocode that would actually run: declare variables and follow the exam's pseudocode style.

    Common mistakes

    • Using = to assign a value. Assignment is ; = is a comparison.
    • Forgetting ENDIF, ENDWHILE, ENDCASE or NEXT. Every construct closes, and the closing word is where the mark for the construct is checked.
    • Not initialising a total or counter before the loop, so the algorithm adds to a value that never existed.
    • Using a FOR loop when the number of repetitions is unknown. Reading until a sentinel value or a correct guess needs WHILE or REPEAT ... UNTIL.
    • Writing Age > 65 OR < 5. Each side of OR and AND must be a complete comparison.
    • Answering "explain why decomposition is used" with one benefit written three ways. Three marks need three different benefits.
  • 10

    Data Types and Structures

    10.1

    Choosing data types

    Syllabus
    Candidates should be able to: Notes and guidance
    Select and use appropriate data types for a problem solution including integer, real, char, string, Boolean, date (pseudocode will use the following data types: INTEGER, REAL, CHAR, STRING, BOOLEAN, DATE, ARRAY, FILE)
    Show understanding of the purpose of a record structure to hold a set of data of different data types under one identifier Write pseudocode to define a record structure
    Write pseudocode to read data from a record structure and save data to a record structure

    Source: Cambridge International syllabus

    Every variable needs a data type 数据类型 — the kind of value it holds and the operations allowed:

    • INTEGER — a whole number (42, -7). For counts, indexes, IDs.
    • REAL — a number with a fractional part (3.14). For money, measurements.
    • STRING — characters in quotes ("Hello"). For text.
    • CHAR — a single character ('A').
    • BOOLEANTRUE or FALSE. For flags.
    • DATE — a calendar date.

    Pick the smallest precise type that fits: INTEGER for whole counts, BOOLEAN for flags (not the strings "yes"/"no").

    The "give the appropriate data type" tables are decided by how the value is used: the average mark of a class is REAL (it has a fractional part); an email address is STRING; the number of students is INTEGER; whether a student has paid is BOOLEAN; a date of birth is DATE; an array index is always INTEGER; a single grade letter is CHAR; a phone number is a STRING, because it starts with 0 and is never used in arithmetic. A BOOLEAN is used for a flag with only two states: whether a search has found its target, whether a member has paid, whether a seat is booked. For the identifier table, the variable name must be meaningful too: NumberOfPeople, not n.

    Vocabulary Train
    English Chinese Pinyin
    data type 数据类型 shù jù lèi xíng
    Exercise sheet
    10.1

    Records

    A record 记录 (a record structure 记录结构) holds several fields of different types under one name — useful when several values describe one thing.

    TYPE TStockItem
        DECLARE ItemID : INTEGER
        DECLARE Category : STRING
        DECLARE ItemCost : REAL
        DECLARE InStock : BOOLEAN
    ENDTYPE
    

    This defines the type TStockItem; declare variables of it:

    DECLARE Item1 : TStockItem
    DECLARE Items : ARRAY[1:100] OF TStockItem
    

    Use dot notation to reach each field 字段:

    Item1.Category ← "Fruit"
    OUTPUT Item1.Category, " costs ", Item1.ItemCost
    

    Use a record when values always belong together (a customer, a stock item); use separate variables for unrelated values.

    Worked example. A club stores, for each student, a student ID (a string), a name, a date of birth and up to three club numbers (integers). Write pseudocode to declare the record type, an array to hold $3000$ students, and a statement that stores a name in the first element.

    TYPE Student
        DECLARE StudentID : STRING
        DECLARE Name : STRING
        DECLARE DateOfBirth : DATE
        DECLARE Club : ARRAY[1:3] OF INTEGER
    ENDTYPE
    
    DECLARE Membership : ARRAY[1:3000] OF Student
    Membership[1].Name ← "Li Wei"
    

    The marks: TYPE with the identifier and ENDTYPE; each field declared with a suitable type; the array declared with its bounds and OF Student; the field reached with the index and a dot. A "state the error in the record declaration" question usually points at a missing ENDTYPE, a field with no type, or a field declared as a STRING that must hold arithmetic. Two conventions score marks on their own: an unused element is marked with a value that cannot be real data (an empty string, -1, an ID of 0), and it is good practice to use the same marker everywhere so that every module can recognise an unused slot; an unused club field is 0. The benefits of an array of records, for a "state three benefits": all the data for one entity is held under one identifier; the fields can have different data types; one array replaces several parallel arrays that would have to be kept in step; the whole set can be processed by one loop or passed as one parameter; and adding a field changes the type definition only. For one customer the suitable structure is a record (fields of different types under one name); for all customers it is an array of records.

    A TStockItem record drawn as a stack of four fields under one name — ItemID (INTEGER), Category (STRING), ItemCost (REAL), InStock (BOOLEAN) — reached with dot notation like Item1.Category
    A record holds several fields of different types under one name
    Explore

    A record groups fields under one name

    A record bundles related fields together. Each field is a named label you reach with dot notation — Item1.Category — not by a numeric index.

    Vocabulary Train
    English Chinese Pinyin
    record 记录 jì lù
    record structure 记录结构 jì lù jié gòu
    field 字段 zì duàn
    10.2

    Arrays

    Syllabus
    Candidates should be able to: Notes and guidance
    Use the technical terms associated with arrays Including index, upper bound and lower bound
    Select a suitable data structure (1D or 2D array) to use for a given task
    Write pseudocode for 1D and 2D arrays
    Write pseudocode to process array data Sort using a bubble sort Search using a linear search

    Source: Cambridge International syllabus

    An array 数组 is an ordered collection of items of the same type, under one name, reached by an index 索引.

    • element 元素 — one item in the array.
    • bounds 边界 — the lowest and highest valid indices.
    • dimension 维度 — 1-D (a list), 2-D (a table), etc.
    • lower bound 下界 and upper bound 上界 — the first and last valid index; the number of elements is upper bound minus lower bound plus one, and for a 2-D array the product of the two counts.

    So in ThisArray[n] ← 42 the array has one dimension, the index is the variable n (an INTEGER), and the element at that index receives 42. Before an array can be declared you need its data type as well as its bounds. To declare $120$ values that may include a decimal place: DECLARE Data : ARRAY[1:120] OF REAL; a $150$-row, two-column table of strings: DECLARE Data : ARRAY[1:150, 1:2] OF STRING, which has $300$ elements. The benefits of an array over separate variables, for a two-mark explain: one identifier instead of thirty; the elements can be processed by a loop with the index as the counter; the size is easy to change; and the whole set can be passed to a module as one parameter. An array can also replace a chain of selection statements: DaysInMonth[Month] looks up the answer directly instead of twelve IF clauses, which is shorter, faster to write and easier to maintain.

    1-D arrays

    DECLARE Names : ARRAY[1:5] OF STRING
    Names[3] ← "Cara"
    OUTPUT Names[3]
    

    Process every element with a FOR loop:

    FOR i ← 1 TO 5
        OUTPUT Names[i]
    NEXT i
    
    A row of indexed cells named myList, with indices 0 to 8 and the lower bound (first index) and upper bound (last index) marked
    A 1-D array (a list) with indices and bounds

    2-D arrays (2D array)

    DECLARE Grid : ARRAY[1:3, 1:4] OF INTEGER
    Grid[2, 3] ← 99
    

    The first index is the row, the second the column. Use nested loops to visit every cell. Use 1-D for a single sequence, 2-D for two natural dimensions (a grid, rows × columns).

    A 3 by 4 grid with row indices and column indices; the cell at row 2, column 3 is highlighted
    A 2-D array (a table) with row and column indices

    Common operations

    A linear search 线性查找 checks each element until found:

    FOR i ← 1 TO n
        IF A[i] = Target THEN
            OUTPUT "Found at ", i
        ENDIF
    NEXT i
    

    To find a sum, count, maximum or minimum, set a running variable then sweep through:

    Max ← A[1]
    FOR i ← 2 TO n
        IF A[i] > Max THEN Max ← A[i]
    NEXT i
    

    A bubble sort 冒泡排序 puts an array in order: pass through it comparing each adjacent pair and swapping any that are out of order; repeat the passes until one pass makes no swaps.

    Paper 2 asks for these algorithms both as pseudocode and as steps in words, and sometimes in their "efficient" form:

    • Largest value: set Largest to the first element; for each remaining element, if it is bigger than Largest, store it in Largest; after the loop output Largest. For the position of the largest, keep a second variable that stores the index each time Largest changes.
    • Linear search returning a position: set FoundAt ← -1 before the loop (a value that can never be a valid index, so it means "not found"); loop through the array; when the element matches, store the index and leave the loop; after the loop test FoundAt.
    • Count or output the non-blank elements: compare each element with the marker for an unused element ("" or -1) and count or output only those that differ.
    • Remove an item: find its index by a linear search; move every later element one place towards the start, so the gap closes; mark the last element as unused (or decrease the count).
    • Insert into a sorted array: find the first index whose element is larger; move that element and every later one one place towards the end; store the new value in the gap.
    • Efficient bubble sort: a Swapped flag so that the passes stop as soon as a pass makes no swap, and an upper limit that falls by one each pass because the largest value has already reached the end.
    REPEAT
        Swapped ← FALSE
        FOR Index ← 1 TO Limit - 1
            IF Data[Index] > Data[Index + 1] THEN
                Temp ← Data[Index]
                Data[Index] ← Data[Index + 1]
                Data[Index + 1] ← Temp
                Swapped ← TRUE
            ENDIF
        NEXT Index
        Limit ← Limit - 1
    UNTIL Swapped = FALSE
    

    The marks are for the outer loop that repeats until no swaps, the flag set inside the IF, the three-line swap with a temporary variable, and the shrinking limit. A sort in "steps" (stepwise refinement) is: repeat until sorted; on each pass compare adjacent pairs; swap a pair that is out of order; after each pass the largest unsorted value is at the end. Two 1-D arrays of records or of parallel data are processed with one loop and one index; a 2-D array needs a nested loop, the outer over rows and the inner over columns, and a search in one row fixes the row index and loops over the column.

    One pass of a bubble sort over 5, 2, 8, 1: compare 5 and 2 and swap to give 2, 5, 8, 1; compare 5 and 8 (already in order); compare 8 and 1 and swap to give 2, 5, 1, 8, so the largest value 8 reaches the end
    One pass of a bubble sort: adjacent pairs are compared and swapped, bubbling the largest value to the end
    Explore

    A 2-D array

    Pick a row and column to read one element — how a grid of data is stored and indexed.

    Vocabulary Train
    English Chinese Pinyin
    index 索引 suǒ yǐn
    array 数组 shù zǔ
    element 元素 yuán sù
    bounds 边界 biān jiè
    dimension 维度 wéi dù
    lower bound 下界 xià jiè
    upper bound 上界 shàng jiè
    linear search 线性查找 xiàn xìng chá zhǎo
    bubble sort 冒泡排序 mào pào pái xù
    Watch lesson Exercise sheet
    10.3

    Files

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of why files are needed
    Write pseudocode to handle text files that consist of one or more lines

    Source: Cambridge International syllabus

    A file 文件 is data stored on secondary storage 辅助存储器, kept between program runs. Variables in RAM disappear when the program ends, so to save data permanently (high scores, records, settings) the program writes to a file. Files also let programs share data and restart from a saved state.

    Variables in RAM are lost when the program ends, but a file on disk is kept between runs, so the program saves to and loads from it
    Variables in RAM vanish when the program ends; a file on disk persists between runs

    A text file 文本文件 holds one or more lines of readable characters; programs read and write text files line by line. Open a file before use and close it after:

    OPENFILE "data.txt" FOR READ      // or FOR WRITE, FOR APPEND
    WHILE NOT EOF("data.txt") DO
        READFILE "data.txt", LineString
        OUTPUT LineString
    ENDWHILE
    CLOSEFILE "data.txt"
    

    EOF tests the end of file 文件结束 before reading. To write:

    OPENFILE "log.txt" FOR WRITE
    FOR i ← 1 TO 100
        WRITEFILE "log.txt", "Event " & i
    NEXT i
    CLOSEFILE "log.txt"
    

    Always close every file — otherwise buffered writes may be lost and other programs may be locked out.

    Why files (two marks): the data is kept after the program ends, so it is available the next time the program runs; it can be shared with other programs; and it can hold more than fits in memory. The characteristic of a text file that lets a program work through it is that it is a sequence of lines, read one after another from the start. The three modes: READ to read from the start; WRITE to create a new file, which deletes any existing contents, so it cannot be used to add to a file; APPEND to add lines at the end of an existing file. Test EOF before every read, and open the file only once, even when several modules use it.

    Worked example. Write pseudocode for a procedure LastLines(FileName : STRING) that outputs the last three lines of a text file, in order.

    PROCEDURE LastLines(BYVAL FileName : STRING)
        DECLARE LineX, LineY, LineZ : STRING
        LineX ← ""
        LineY ← ""
        LineZ ← ""
        OPENFILE FileName FOR READ
        WHILE NOT EOF(FileName) DO
            LineX ← LineY
            LineY ← LineZ
            READFILE FileName, LineZ
        ENDWHILE
        CLOSEFILE FileName
        OUTPUT LineX
        OUTPUT LineY
        OUTPUT LineZ
    ENDPROCEDURE
    

    Each new line pushes the previous three along, so when the file ends the three variables hold its last three lines; a file with fewer lines outputs empty strings. To output the first five lines, count the lines read and stop the loop at five or at EOF, whichever comes first; a file that is empty is detected by EOF being TRUE immediately after opening.

    Fields in a line. A text file holds strings, so a record is written as one line with its fields joined by a separator 分隔符 character, and each number or Boolean converted with NUM_TO_STR (and read back with STR_TO_NUM, or by comparing with "TRUE"). Choose a separator that can never appear in the data: a comma or | for names and numbers, never a space when a name may contain one. If a field may contain any character, the separator can be confused with data; the fix is to put each field on its own line, or to write the field's length before it. One item per line is simple to read back but uses more lines and makes a record harder to see as a unit. Reading a file whose lines are in a known order (ascending by an ID) allows the search to stop as soon as a larger ID is read, instead of reading to the end. A save file that is created each time the game is saved needs a meaningful filename, for instance the player's name and the date and time, so that any earlier save can be restored.

    One line of a text file, 1023,Ali,12.50,TRUE, split at the comma separator into the four fields of a stock-item record, with the conversion each field needs: STR_TO_NUM for the number fields, the string as it is, and a comparison with TRUE for the Boolean
    One line of a text file is one record: fields joined by a separator, converted to their types when read back
    Explore

    Handling a file: open → use → close

    Step through the lifecycle every file follows. The two easy-to-forget parts are testing EOF while reading in a loop, and always closing at the end.

    Vocabulary Train
    English Chinese Pinyin
    file 文件 wén jiàn
    secondary storage 辅助存储器 fǔ zhù cún chǔ qì
    text file 文本文件 wén běn wén jiàn
    end of file 文件结束 wén jiàn jié shù
    separator 分隔符 fēn gé fú
    Watch lesson Exercise sheet
    10.4

    Abstract Data Types (ADTs)

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding that an ADT is a collection of data and a set of operations on those data
    Show understanding that a stack, queue and linked list are examples of ADTs Describe the key features of a stack, queue and linked list and justify their use for a given situation
    Use a stack, queue and linked list to store data Candidates will not be required to write pseudocode for these structures, but they should be able to add, edit and delete data from these structures
    Describe how a queue, stack and linked list can be implemented using arrays

    Source: Cambridge International syllabus

    Linked list: insert by rewiring pointers
    Stack vs queue: LIFO and FIFO

    An Abstract Data Type 抽象数据类型 (ADT) is a collection of data plus operations on it, defined by what it does, not how it is stored. The user works only through the operations; the implementation is hidden, so it can change without affecting code that uses the ADT. Know three: stack, queue, linked list.

    The one-mark definition: an ADT is a collection of data together with a set of operations on that data. A stack, a queue, a linked list, a binary tree and an array are all ADTs. To justify a choice: a queue when items must be handled in the order they arrived (print jobs, key presses, customers in a shop), because it is first in, first out; a stack when the most recent item must be handled first (undo, going back through web pages, reversing an order, the return addresses of nested calls), because it is last in, first out; a linked list when items are inserted and deleted in the middle of an ordered sequence often, because only pointers change and nothing has to be shifted. To compare a stack and a queue: both are linear structures of items with an order, both are implemented with an array and pointers, and both need a check for full before adding and for empty before removing; a stack has one pointer and adds and removes at the same end, a queue has two pointers and adds at one end and removes at the other.

    Stack

    A stack works in LIFO 后进先出 order (Last In, First Out). Operations: push 入栈 (add to the top), pop 出栈 (remove from the top), peek (look at the top), and tests for empty/full. Uses: undo history, function-call return addresses, expression parsing, backtracking.

    A stack stored in an array shown in three states; the Top pointer moves up after a push and down after a pop, while the base of the stack stays fixed
    Push and pop change the top pointer; the base pointer stays put

    Worked example. A stack of characters holds, from the bottom, 'P', 'N', 'Z', 'X', 'Y', 'W', with the top-of-stack pointer at 'W' (memory location 202 of 200–207). The operations POP, POP, PUSH 'A', PUSH 'B', POP are performed. What is on the stack, and where does the pointer point?

    The two pops remove 'W' then 'Y'; the pushes add 'A' then 'B' in their places; the last pop removes 'B'. The stack now holds 'P', 'N', 'Z', 'X', 'A' and the pointer is at 'A', location 203. The value that has been on the stack longest is the bottom item, 'P'; at most five further pops are possible before the stack is empty, and a pop on an empty stack is an error, which is why Pop() tests for empty first. A Push() function that returns TRUE on success first tests whether the pointer is at the top of the array (full) and returns FALSE if so. The array elements need no initialising before use, because the pointer alone says which elements are in use.

    A tall pile of books stacked flat on top of one another
    A pile of books is a stack you can see. You can only add or take a book from the top, so the last one you put on is the first one you take off — that is exactly LIFO

    Queue

    A queue 队列 works in FIFO 先进先出 order (First In, First Out). Operations: enqueue 入队 (add to the rear), dequeue 出队 (remove from the front), and tests for empty/full. Uses: print spooling, scheduling, breadth-first search, buffering.

    A linear queue stored in an array shown in three states; enqueue advances the Rear pointer and dequeue advances the Front pointer, leaving the start cell empty and wasted
    Enqueue adds at the rear; dequeue removes from the front

    To describe adding an item: check that the queue is not full; store the item at the position given by the end-of-queue pointer; increment the end pointer (and the count). To describe removing: check that the queue is not empty; read the item at the front pointer; increment the front pointer (and decrement the count). State the convention you use: if the end pointer marks the next free space, front and end pointers being equal means the queue is empty; if it marks the last item, equal pointers mean one item. In a linear queue the front pointer only ever moves forward, so cells behind it are wasted; that is what the circular queue below fixes. The two features of a queue to state: items are added at the rear and removed from the front, so the first item added is the first removed.

    A very long line of people waiting one behind another, stretching along a wall into the distance
    A line of people is a queue you can see. You join at the back and are served from the front, so whoever waited longest is served first — that is exactly FIFO

    Linked list

    A linked list 链表 stores data as a sequence of nodes 节点. Each node holds a value and a pointer 指针 to the next node; a head pointer marks the start, and the last node's pointer is a sentinel (e.g. NULL). Operations: insert, delete, search, and traverse 遍历 (visit each node in order). Its advantage over an array is cheap insertion/deletion (just adjust pointers); its disadvantage is slow random access (you must follow pointers from the head).

    Four nodes in a row, each holding a value and a next-pointer field; a head pointer points to the first node and the last node's pointer is NULL
    A linked list: each node points to the next

    Adding a node in order (four marks): traverse the list from the head, following the pointers, until the node before the position is found (the last node whose value is smaller); take a free node and store the new value in it; set the new node's pointer to the address the previous node pointed to; set the previous node's pointer to the new node. If the new value belongs at the front, the head pointer is changed instead. Deleting a node: find the node before it, and set that node's pointer to the address the deleted node pointed to, so the list bypasses it; the freed node returns to the free list. Compared with a 1-D array, inserting or deleting in a linked list needs no shifting of the other items, and the list can grow until memory runs out; the cost is the extra pointer stored with every item, and that reaching the $n$th item means following $n$ pointers, since there is no direct index.

    Explore

    A linked list: nodes joined by pointers

    Each node stores a value and a pointer to the next node. Inserting or deleting just re-links pointers — no items shift along, unlike an array.

    Explore

    Stacks and queues

    Push and pop. A stack is last-in-first-out; a queue is first-in-first-out — two key ADTs.

    Vocabulary Train
    English Chinese Pinyin
    stack zhàn
    push 入栈 rù zhàn
    Abstract Data Type 抽象数据类型 chōu xiàng shù jù lèi xíng
    linked list 链表 liàn biǎo
    pointer 指针 zhǐ zhēn
    queue 队列 duì liè
    LIFO 后进先出 hòu jìn xiān chū
    FIFO 先进先出 xiān jìn xiān chū
    pop 出栈 chū zhàn
    enqueue 入队 rù duì
    dequeue 出队 chū duì
    nodes 节点 jié diǎn
    node 节点 jié diǎn
    traverse 遍历 biàn lì
    Watch lesson Exercise sheet
    10.4

    Implementing ADTs using arrays

    Stack using an array

    Hold items in Stack[1:MaxSize] with an integer Top (0 when empty).

    • Push(x): if Top = MaxSize the stack is full (overflow 溢出); else Top ← Top + 1; Stack[Top] ← x.
    • Pop(): if Top = 0 the stack is empty (underflow 下溢); else return Stack[Top] and Top ← Top - 1.

    Queue using a circular array

    A simple queue lets Front and Rear march off the end, wasting the start. The fix is a circular array 循环数组 — when a pointer reaches MaxSize it wraps back to 1:

    • Enqueue(x): check full; else Rear ← (Rear MOD MaxSize) + 1; Queue[Rear] ← x.
    • Dequeue(): check empty; else return Queue[Front] and Front ← (Front MOD MaxSize) + 1.

    Track a separate count to tell empty from full.

    The algorithm for the end pointer, in words: if the count equals the size, report that the queue is full and stop; otherwise add one to the end pointer; if it is now past the last index, set it to the first index; store the item there and add one to the count. The declarations that a five-mark "describe the declaration and initialisation" answer lists: the array with its size and element type; a front pointer and an end pointer, both initialised to the first index (or the front to the first index and the end to the next free space); and a count of items, initialised to $0$.

    For example, with MaxSize = 6: if Rear = 5, then (5 MOD 6) + 1 = 6, so the next item goes in cell 6; if Rear = 6, then (6 MOD 6) + 1 = 1, so the pointer wraps back to cell 1.

    A circular queue stored in an array; the filled cells wrap past the last cell back to the start, with a curved arrow showing the pointer wrapping from the last index to cell 1
    A circular queue wraps the pointers back to the start of the array

    Linked list using an array

    Use an array of records, each with a Next index:

    TYPE TNode
        DECLARE Value : INTEGER
        DECLARE Next : INTEGER     // index of the next node, or -1 for end
    ENDTYPE
    
    DECLARE Nodes : ARRAY[1:MaxSize] OF TNode
    DECLARE Head : INTEGER         // index of first node, -1 if empty
    DECLARE FreeListHead : INTEGER // first available free node
    

    A free list 空闲列表 chains the unused slots, just as the data list chains its used ones. To insert: take a slot from FreeListHead, set the new node's value and Next, and update the previous node's Next (or Head). To delete: unlink the node and return its slot to the free list. This gives the flexibility of a linked structure with the static allocation of an array.

    A Value array and a parallel Next array implementing a linked list; a Head pointer chains the used nodes and a FreeListHead pointer chains the free slots, each ending in Next = -1
    A linked list stored in an array: a data array and a pointer array

    Worked example. A linked list is held in a Data array and a Pointer array, with Start pointing to index 1. The list is 1 → 3 → 4 (index 1 holds D40, index 3 holds D32, index 4 holds D11, whose pointer is $\emptyset$); the free list starts at index 2 and continues 2 → 5. Insert D6 between D32 and D11.

    Take the first free node, index 2, and set FreeStart to its pointer, 5; store D6 in Data[2]; set Pointer[2] to the value Pointer[3] held, which is 4; set Pointer[3] to 2. The list reads 1 → 3 → 2 → 4 and the free list is 5 → $\emptyset$. The answer to "how can the linked list be implemented" is exactly these parts: an array (or array of records) for the data, a parallel array for the pointers holding indices, a start pointer, a free-list pointer and a null value such as $-1$ for the end.

    Worked example. A circular queue is held in an array of size 5 (indices 0 to 4) with Front = 3, Rear = 3 and one item stored. Two items are added, then two are removed. Where are the pointers, and why use a circular queue at all? Every move uses (pointer + 1) MOD size, so the pointers wrap. Adding twice moves Rear: $3 \rightarrow 4$, then $4 \rightarrow 0$ (because $(4+1) \bmod 5 = 0$), so Rear = 0 and three items are stored. Removing twice moves Front the same way: $3 \rightarrow 4$, then $4 \rightarrow 0$, leaving Front = 0 and one item. The wrap is the whole point: in a linear array queue the pointers march to the end and the freed space at the front is wasted even when the queue is empty. Remember a queue removes at the Front and adds at the Rear - a stack uses one pointer for both.

    Explore

    Implementing ADTs with arrays

    FIFO

    A queue is first-in-first-out — enqueue at the back, dequeue from the front.

    Vocabulary Train
    English Chinese Pinyin
    free list 空闲列表 kòng xián liè biǎo
    overflow 溢出 yì chū
    underflow 下溢 xià yì
    circular array 循环数组 xún huán shù zǔ
    10.4

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly.

    Term Definition
    record a data structure that holds a set of data items (fields) of different data types under one identifier
    array a data structure that holds a fixed number of elements of the same data type under one identifier, each accessed by an index
    index the number that identifies one element of an array
    upper bound, lower bound the largest and smallest valid index of an array
    text file a file that stores data as lines of characters, which a program reads and writes one line at a time
    abstract data type a collection of data together with a set of operations on that data
    stack a list in which items are added to and removed from the same end, the top, so the last item added is the first removed (LIFO)
    queue a list in which items are added at the rear and removed from the front, so the first item added is the first removed (FIFO)
    linked list a list in which each node holds a data item and a pointer to the next node, with a start pointer to the first node
    pointer a variable that holds the address (or index) of a node or of a position in a structure
    linear search checking each element in turn from the first until the target is found or the end is reached
    bubble sort repeated passes through the array comparing adjacent pairs and swapping those out of order, until a pass makes no swaps
    10.4

    Exam tips

    • Choose the right data structure and justify it (a record for mixed fields, a 2-D array for a grid).
    • Know how to implement a stack, queue and linked list with an array and pointers (top; front/rear; next).
    • Distinguish an ADT (its behaviour) from its implementation (array plus pointers).

    Common mistakes

    • A record declaration without ENDTYPE, or fields without types. Every field is a DECLARE line with a type.
    • Reading past the end of a file, or writing with WRITE when the file must keep its contents. Test EOF before each read; use APPEND to add.
    • Writing a number to a text file without converting it. A file holds strings: NUM_TO_STR out, STR_TO_NUM back.
    • Forgetting the checks. Push and enqueue test for full first; Pop and dequeue test for empty first, and the answer says so.
    • Losing the rest of the list when inserting a node. Set the new node's pointer to the old next node before changing the previous node's pointer.
    • A linear search that never says "not found". Initialise the position to $-1$ and test it after the loop.
  • 11

    Programming

    11.1

    Programming basics

    Syllabus
    Candidates should be able to: Notes and guidance
    Implement and write pseudocode from a given design presented as either a program flowchart or structured English
    Write pseudocode statements for: • the declaration and initialisation of constants • the declaration of variables • the assignment of values to variables • expressions involving any of the arithmetic or logical operators input from the keyboard and output to the console
    Use built-in functions and library routines Any functions not given in the pseudocode guide will be provided String manipulation functions will always be given

    Source: Cambridge International syllabus

    Lines of source code on a dark screen
    Programming turns a design into instructions written as code
    A programmer working at a computer
    A programmer writes the code and tests it as they go

    From design to code

    You should be able to turn a design — a flowchart 流程图 (program flowchart) or structured English 结构化英语 — into pseudocode 伪代码, and then into a real language:

    1. find the variables 变量 and their data types 数据类型.
    2. turn input/output boxes into INPUT / OUTPUT.
    3. turn decision diamonds into IF...ELSE...ENDIF (or CASE).
    4. turn loop arrows into WHILE, REPEAT...UNTIL, or FOR.
    5. turn process boxes into assignments or calculations.
    6. check by tracing a small input.
    A mapping from flowchart symbols to pseudocode: an input/output parallelogram becomes INPUT or OUTPUT, a decision diamond becomes IF...THEN or CASE, a process box becomes an assignment x = expression, and a loop arrow becomes WHILE, FOR or REPEAT
    Each flowchart symbol becomes a pseudocode keyword

    Constants and variables

    A constant 常量 holds a value that never changes; a variable holds one that may change. Declare them with a type:

    A variable's value can change; a constant stays fixed
    A variable's value can change; a constant stays fixed
    CONSTANT Pi ← 3.14159
    DECLARE Radius : REAL
    DECLARE Area : REAL
    
    Radius ← 5
    Area ← Pi * Radius * Radius
    

    Use constants for fixed values that recur (Pi, MaxScore); they make code clearer and easy to change in one place.

    In the exam, a constant is the answer to "identify a more appropriate way of representing" a fixed value, such as a tax rate or a maximum score, that appears at several places in the pseudocode. The benefits the scheme lists: the value is set once and cannot be changed accidentally by the program; a change is made in one place and reaches every statement that uses it; the identifier gives the value a meaning (MaxScore rather than 100), so the code is easier to read and to check; and there is less risk of a typing error in a long value such as 3.14159. A "state a value that could be replaced by a constant" question wants the literal from the pseudocode (0.2, 40), not a new name.

    Every variable is declared once, with an identifier 标识符 (its name) and a data type, before it is used. The six types in the 9618 pseudocode guide:

    Type Holds Written in the code as Typical use
    INTEGER whole numbers 42, -3 a count, an array index, a loop counter
    REAL numbers with a fractional part 3.75 a price, an average
    CHAR one character 'A' (single quotes) a grade letter, a menu key
    STRING a sequence of characters "Hello" (double quotes) a name, a postcode
    BOOLEAN TRUE or FALSE TRUE a flag such as Found
    DATE a calendar date 12/05/2026 a date of birth

    A "give the appropriate data type" question is answered from how the variable is used in the pseudocode: a value with a decimal point is REAL; something set to TRUE or FALSE is BOOLEAN; a value in single quotes is CHAR; a value used as an array index, or with DIV and MOD, is INTEGER. Write the type in capitals, spelled as the guide spells it.

    Worked example. State the appropriate data type for each variable.

    Found ← FALSE
    Initial ← 'K'
    Price ← 12.99
    Count ← Count + 1
    Name ← "Li Wei"
    

    Found is BOOLEAN (it holds FALSE); Initial is CHAR (one character in single quotes); Price is REAL (a decimal value); Count is INTEGER (a counter that goes up by one); Name is STRING (text in double quotes).

    Assignment and expressions

    Use for assignment 赋值:

    Total ← Total + 1
    Average ← Sum / Count
    

    Expressions use operators 运算符:

    • arithmetic + - * /, plus DIV (integer division) and MOD (remainder): 7 DIV 2 = 3; 7 MOD 2 = 1.
    • comparisons =, <>, <, >, <=, >=.
    • logic AND, OR, NOT.

    Precedence 优先级 (highest to lowest): NOT* / DIV MOD+ - → comparisons → ANDOR. Use brackets when unsure.

    Input and output

    OUTPUT "Enter your name:"
    INPUT Name
    OUTPUT "Hello, ", Name
    

    Built-in functions and library routines

    Many tasks have ready-made library routines 库例程, so you need not write them. The Paper 2 insert 附页 lists the ones you may use, with their exact names, parameters and return types; any other function a question needs is given in the question. The names below are the 9618 names — the IGCSE names (UCASE, VAL, STR) are not accepted.

    A program library 程序库 holds routines that have already been written, compiled and tested; a program calls them instead of writing its own. The benefits the scheme accepts, for a "state three benefits" question: the routines are already tested, so they are less likely to contain errors; they save development time; they may do things the programmer could not write (complex statistics, graphics); they are written by experts and reused across many programs; and a routine with a fixed interface can be called from anywhere in the program.

    Routine Returns Example
    LENGTH(s) the number of characters in s LENGTH("Hello") = 5
    LEFT(s, n) / RIGHT(s, n) the first / last n characters RIGHT("Hello", 2) = "lo"
    MID(s, start, n) n characters from position start (positions count from 1) MID("Hello", 2, 3) = "ell"
    TO_UPPER(s) / TO_LOWER(s) s in capitals / in small letters TO_UPPER("ab1") = "AB1"
    NUM_TO_STR(x) / STR_TO_NUM(s) a number as a string / a string as a number STR_TO_NUM("3.5") = 3.5
    IS_NUM(s) TRUE if s is a valid number IS_NUM("12a") = FALSE
    ASC(c) / CHR(n) the character code of c / the character with code n ASC('A') = 65, CHR(66) = 'B'
    INT(x) the whole-number part of x INT(7.9) = 7
    RAND(n) a random real number from 0 up to, but not including, n INT(RAND(6)) + 1 is a dice roll
    DAY(d), MONTH(d), YEAR(d) the parts of a DATE YEAR(TODAY())
    DAYINDEX(d), SETDATE(d, m, y), TODAY() the day of the week (1 = Sunday); a date built from three integers; today's date
    EOF(f) TRUE when the file f has no more lines to read WHILE NOT EOF("data.txt")

    Strings are joined with & (concatenation 连接): "A" & "BC" is "ABC". Use the exact names from the insert, with the parameters in its order.

    Dates and random numbers come up as one-line statements. SETDATE(17, 11, 2007) builds 17 November 2007; 12 - MONTH(MyDOB) is the number of months from the month of birth to the end of the year; IF DAYINDEX(MyDOB) = 5 THEN tests for a Thursday, because Sunday is day 1. RAND(n) returns a real number from 0 up to, but not including, n, so a random integer from Low to High inclusive is INT(RAND(High - Low + 1)) + Low: INT(RAND(21)) - 10 gives a value from -10 to 10.

    The string COMPUTER shown as eight numbered character boxes (positions 1 to 8), with worked results: LENGTH(s) = 8, LEFT(s, 3) = COM, MID(s, 4, 3) = PUT, RIGHT(s, 2) = ER, and UCASE/LCASE changing the letter case
    The common string routines acting on s = "COMPUTER" (positions 1–8)

    Worked example. Evaluate each expression, given Word ← "Program", Code ← 'Q' and N ← 7.

    Expression Value Why
    LENGTH(Word) 7 seven characters
    MID(Word, 4, 2) "gr" two characters, starting at position 4
    LEFT(Word, 3) & "!" "Pro!" joined with &
    TO_UPPER(RIGHT(Word, 2)) "AM" the inner function runs first
    ASC(Code) - ASC('A') 16 'Q' is 81 and 'A' is 65
    N DIV 2 + N MOD 2 4 3 + 1
    NUM_TO_STR(N) & "th" "7th" the number becomes a string first
    INT(N / 2) 3 3.5 cut to its whole part

    Work from the inside out, and keep the quotes: "7" is a string and 7 is a number.

    Worked example. Each statement may contain an error in its use of a function or operator. Describe the error, or write NO ERROR. (Assume every variable has the correct type.)

    Statement Error
    Result ← 2 & 4 & joins strings; 2 and 4 are integers, so + is needed
    SubString ← MID("pseudocode", 4, 1) NO ERROR: one character from position 4, "u"
    IF x = 3 OR 4 THEN OR needs a Boolean on each side: IF x = 3 OR x = 4 THEN
    Result ← Status AND INT(x / 2) AND needs two Booleans; INT(x / 2) is an integer
    Message ← "Done" + LENGTH(MyString) + cannot add a string to an integer: "Done" & NUM_TO_STR(LENGTH(MyString))

    Every operator works on particular types: & on strings, + - * / DIV MOD on numbers, AND OR NOT on Booleans, and = <> on two values of the same type. An "evaluate each expression, or write ERROR" table is marked the same way: LENGTH(42) and "A" + 1 are ERROR, because the type does not match the function or the operator.

    Worked example. With Points ← 100, Active ← TRUE and Exempt ← FALSE, evaluate each expression.

    Expression Value Why
    (Points > 99) OR Active TRUE both sides are true; one would do
    (Points MOD 2 = 0) OR Exempt TRUE 100 MOD 2 is 0
    (Points <= 75) AND (Active OR Exempt) FALSE the first side is false, and AND needs both
    (Active OR NOT Active) AND NOT Exempt TRUE Active OR NOT Active is always true

    The last expression simplifies: X OR NOT X is TRUE whatever X is, so the whole expression is just NOT Exempt. Evaluate the brackets first, then NOT, then AND, then OR.

    Explore

    A variable is a labelled box

    Each assignment stores one value in a named box; reassigning the same name overwrites it. Step through the program and watch each box take its current value.

    Vocabulary Train
    English Chinese Pinyin
    flowchart 流程图 liú chéng tú
    structured English 结构化英语 jié gòu huà yīng yǔ
    pseudocode 伪代码 wěi dài mǎ
    variables 变量 biàn liàng
    data types 数据类型 shù jù lèi xíng
    assignment 赋值 fù zhí
    constant 常量 cháng liàng
    identifier 标识符 biāo shí fú
    operators 运算符 yùn suàn fú
    precedence 优先级 yōu xiān jí
    library routines 库例程 kù lì chéng
    insert 附页 fù yè
    program library 程序库 chéng xù kù
    concatenation 连接 lián jiē
    Exercise sheet
    11.2

    Selection

    Syllabus
    Candidates should be able to: Notes and guidance
    Use pseudocode to write: • an ‘IF’ statement including the ‘ELSE’ clause and nested IF statements • a ‘CASE’ structure • a ‘count-controlled’ loop: • a ‘post-condition’ loop • a ‘pre-condition’ loop
    Justify why one loop structure may be better suited to solve a problem than the others

    Source: Cambridge International syllabus

    Selection 选择 chooses which steps run.

    IF age >= 18 THEN
        OUTPUT "Adult"
    ELSE
        OUTPUT "Minor"
    ENDIF
    
    A flowchart: from start, a decision diamond tests age >= 18; the TRUE branch outputs Adult and the FALSE branch outputs Minor, and both rejoin at end
    An IF...ELSE tests the condition once, then runs exactly one branch

    For more than two cases you can use a nested 嵌套 IF, but deep nesting is hard to read — a CASE is cleaner when testing one value against several options:

    CASE OF Grade
        "A": OUTPUT "Excellent"
        "B": OUTPUT "Good"
        OTHERWISE: OUTPUT "Try again"
    ENDCASE
    

    Cambridge CASE allows single values, value lists (1, 2, 3:), and ranges (1 TO 5:).

    A nested IF is an IF inside a branch of another IF. Each IF needs its own ENDIF, and the examiner checks that every construct is closed:

    IF Mark >= 50 THEN
        IF Mark >= 80 THEN
            OUTPUT "Distinction"
        ELSE
            OUTPUT "Pass"
        ENDIF
    ELSE
        OUTPUT "Fail"
    ENDIF
    

    Boundaries are where marks are lost. "A mark of 50 or more passes" is Mark >= 50, not Mark > 50; the last CASE branch, for "anything else", is written OTHERWISE, not a condition such as > 200. A wrong comparison here is a logic error 逻辑错误: the program runs, but gives the wrong output for some inputs — and a trace table with a boundary value such as 50 is how you find it.

    A flowchart of a CASE OF Grade statement: the value is tested against each guard in turn (a single value, a value list, then a range); the first matching branch runs its statement, otherwise the OTHERWISE branch runs, and all branches rejoin at ENDCASE
    A CASE statement runs the branch that matches the value

    Worked example. Rewrite this with the same functionality, without using a CASE structure.

    CASE OF MySwitch
        1: ThisChar ← 'a'
        2: ThisChar ← 'y'
        3: ThisChar ← '7'
        OTHERWISE: ThisChar ← '*'
    ENDCASE
    

    Each value becomes a branch of a chain of IFs, and OTHERWISE becomes the last ELSE:

    IF MySwitch = 1 THEN
        ThisChar ← 'a'
    ELSE
        IF MySwitch = 2 THEN
            ThisChar ← 'y'
        ELSE
            IF MySwitch = 3 THEN
                ThisChar ← '7'
            ELSE
                ThisChar ← '*'
            ENDIF
        ENDIF
    ENDIF
    

    Two clauses that assign the same value are merged into one clause with a value list: 1, 2: ThisChar ← 'a'. The guards are tested in order: with ranges such as 1 TO 50: followed by 40 TO 60:, a value of 45 takes the first branch that matches, so an assignment in a later branch may never be performed — and when the earlier branches already cover every possible value, the OTHERWISE branch is never reached either.

    Going the other way, nested IFs that test several Booleans are clearer as one condition per outcome: IF A AND B AND C THEN CALL Sub1(), then IF A AND B AND NOT C THEN CALL Sub2(), and so on. Joining tests with AND and OR removes the nesting, and IF A THEN is accepted in place of IF A = TRUE THEN.

    Explore

    Selection (IF / ELSE)

    Change the input and see which branch runs — the essence of selection.

    Vocabulary Train
    English Chinese Pinyin
    selection 选择 xuǎn zé
    nested 嵌套 qiàn tào
    logic error 逻辑错误 luó jí cuò wù
    Watch lesson Exercise sheet
    11.2

    Iteration

    Iteration 迭代 repeats a block. Three loops differ in how many times the body runs.

    Count-controlled (FOR) loop

    A count-controlled loop 计数循环 — use it when you know how many times to repeat:

    FOR i ← 1 TO 10
        OUTPUT i
    NEXT i
    

    A STEP can change the count (e.g. FOR i ← 10 TO 1 STEP -1). Best for a fixed number of repeats or processing each element of an array 数组.

    Pre-condition (WHILE) loop

    A pre-condition loop 前测循环 tests the condition before each pass, so it may run zero times:

    WHILE total < 100 DO
        INPUT n
        total ← total + n
    ENDWHILE
    

    Post-condition (REPEAT...UNTIL) loop

    A post-condition loop 后测循环 tests the condition after each pass, so it always runs at least once:

    REPEAT
        INPUT password
    UNTIL password = correctPassword
    

    Choosing the right loop

    Three flowchart columns. FOR: a count box (i = 1 to N) then a body box, looping back, for a set number of passes. WHILE: a test diamond above a body box, so the condition is checked before the body and the loop may run zero times. REPEAT: a body box above a test diamond, so the condition is checked after the body and the loop runs at least once
    The three loops differ in where the condition is tested — before the body (WHILE), after it (REPEAT), or a set number of times (FOR)
    • count known up front → FOR.
    • may need zero passes → WHILE.
    • always at least one pass → REPEAT...UNTIL.

    Justify your choice by whether the count is known and whether the body must run at least once. A typical question gives a scenario ("ask for a password until correct, but always ask at least once") and asks which loop fits.

    The two marks are for the name of the loop and the reason, in the scheme's words: count-controlled, because the number of iterations is known before the loop starts; post-condition, because the loop body must be executed at least once; pre-condition, because the loop may not need to execute at all. A loop over the four elements of an array that has been written as a WHILE with a counter is "not the most appropriate": the count, four, is known, so a FOR loop fits.

    Worked example. Which loop suits each task? (a) print the 12 times table; (b) keep reading numbers until the user enters 0; (c) ask for a password until it is correct. Choose by asking how many times the body runs and when the test happens. (a) The count is known in advance (12), so use a FOR loop. (b) The count is unknown, and the very first input might already be 0 - so the test must come before the body: a WHILE loop, which runs zero or more times. (c) The count is unknown, but you must always ask at least once before there is anything to test - so the test comes after the body: a REPEAT...UNTIL, which runs one or more times. The deciding question is whether the body must run at least once: WHILE may run zero times, REPEAT always runs once.

    Dry running with a trace table

    A trace table 跟踪表 records the value of each variable as you dry run 手工跟踪 (work through by hand) an algorithm. It is how you test a loop on paper, and a six-mark question on most Paper 2s.

    DECLARE Count, Total : INTEGER
    Count ← 1
    Total ← 0
    WHILE Total < 10
        Total ← Total + Count * 2
        Count ← Count + 1
    ENDWHILE
    OUTPUT Count, Total
    
    Count Total Total < 10 OUTPUT
    1 0 TRUE
    2 2 TRUE
    3 6 TRUE
    4 12 FALSE 4, 12

    Rules that earn the marks: one column per variable, in the order the question gives; write a value only when it changes; start a new row each time the loop repeats; evaluate the condition with the current values, and stop the moment it is FALSE; put the output in its own column, exactly as it would appear. Trace the algorithm as written, not the one you think was intended — if it never stops, say so.

    Worked example. Which constructs does each line use — selection, iteration or a subroutine call?

    Pseudocode Selection Iteration Subroutine
    IF Ready = TRUE THEN CALL Start() ENDIF yes yes
    FOR I ← 1 TO 20 ... NEXT I yes
    WHILE NOT IsFull() ... ENDWHILE yes yes
    CASE OF Key ... OTHERWISE ... ENDCASE yes

    IF and CASE are selection; FOR, WHILE and REPEAT are iteration; a name followed by brackets — Start(), IsFull() — is a call to a procedure or a function, wherever it appears, including inside a condition.

    Explore

    Trace a loop, pass by pass

    A trace table records each variable after every pass of the loop. Watch the counter i climb while the running total builds up — exactly what an exam trace question asks you to fill in.

    Explore

    Tracing a loop

    Step through the loop and watch the variables change each pass — exactly what a trace table records.

    Vocabulary Train
    English Chinese Pinyin
    array 数组 shù zǔ
    trace table 跟踪表 gēn zōng biǎo
    iteration 迭代 dié dài
    count-controlled loop 计数循环 jì shù xún huán
    pre-condition loop 前测循环 qián cè xún huán
    post-condition loop 后测循环 hòu cè xún huán
    dry run 手工跟踪 shǒu gōng gēn zōng
    11.3

    Procedures and functions

    Syllabus
    Candidates should be able to: Notes and guidance
    Define and use a procedure
    Explain where in the construction of an algorithm it would be appropriate to use a procedure
    Use parameters A procedure may have none, one or more parameters A parameter can be passed by reference or by value
    Define and use a function
    Explain where in the construction of an algorithm it is appropriate to use a function A function is used in an expression, e.g. the return value replaces the call
    Use the terminology associated with procedures and functions including procedure/function header, procedure/function interface, parameter, argument, return value
    Write efficient pseudocode

    Source: Cambridge International syllabus

    Structured programming 结构化编程 builds a program from small named subroutines 子程序, each with one job.

    Procedure

    A procedure 过程 is a named block that does an action; it may take parameters 参数 but does not return a value.

    PROCEDURE Greet(name : STRING)
        OUTPUT "Hello, ", name
    ENDPROCEDURE
    
    CALL Greet("Ada")
    

    Function

    A function 函数 is like a procedure but it returns a value that becomes part of an expression.

    FUNCTION Square(x : INTEGER) RETURNS INTEGER
        RETURN x * x
    ENDFUNCTION
    
    result ← Square(5) + 1     // result = 26
    

    Use a procedure when the subroutine performs an action; use a function when it computes a value for the caller.

    The syllabus asks where in the construction of an algorithm each is appropriate. A procedure is appropriate where the same group of steps is needed at several points (validate an input, print a menu, swap two values): the steps are written once and CALLed by name. A function is appropriate where a single value must be calculated and then used in an expression — a total, a TRUE/FALSE result, the larger of two numbers — because the return value 返回值 replaces the call: IF IsValid(Code) THEN.

    Two panels. Procedure: call Greet(Ada) does an action and prints Hello, Ada, returning no value. Function: set y = Square(5) computes 5 times 5 = 25, returns 25, so y then holds 25
    A procedure does an action and returns nothing; a function returns a value you use in an expression

    Parameters

    A parameter is a variable a subroutine declares to receive input; the values the caller supplies are arguments 实参. Two ways to pass them:

    • pass by value 传值 — the routine gets a copy; changes inside it do not affect the caller. Use for inputs it only reads.
    • pass by reference 传引用 — the routine gets a reference to the caller's variable; changes do affect the caller. Use when it must update a parameter.
    Two memory-box diagrams. Pass by value: the caller's variable x = 5 is copied into a separate parameter box a = 5, so changing a leaves x as 5. Pass by reference: the parameter a is an arrow pointing to the caller's own x box, so changing a changes x too
    Pass by value copies the value into a new box; pass by reference lets the routine change the caller's own variable
    PROCEDURE Swap(BYREF a : INTEGER, BYREF b : INTEGER)
        DECLARE temp : INTEGER
        temp ← a
        a ← b
        b ← temp
    ENDPROCEDURE
    

    Cambridge pseudocode writes the mode in the header, BYVAL or BYREF, before each parameter. If neither is written, BYVAL is assumed, so a routine that must change the caller's variable — Swap, or a procedure that updates a running total — needs BYREF in its header.

    Worked example. What is output?

    PROCEDURE Adjust(BYREF X : INTEGER, BYVAL Y : INTEGER)
        X ← X + Y
        Y ← Y * 2
    ENDPROCEDURE
    
    A ← 5
    B ← 3
    CALL Adjust(A, B)
    OUTPUT A, B
    

    X is a reference to A, so A becomes 8. Y is a copy of B, so doubling Y leaves B at 3. The output is 8, 3. Had the header said BYVAL X, A would still be 5.

    Local vs global variables

    A local variable 局部变量 is declared inside a subroutine and exists only while it runs. A global variable 全局变量 is declared outside and is visible everywhere. Prefer locals and parameters — heavy use of globals makes code hard to follow and test. (The region where a name is visible is its scope 作用域.)

    The one-line difference: a global variable can be accessed from anywhere in the program, a local variable only inside the subroutine that declares it. Benefits of local variables the scheme accepts: the same identifier can be used in another subroutine without a clash; the value cannot be changed accidentally by other parts of the program; the memory is released when the subroutine ends; and the subroutine is self-contained, so it can be tested on its own and reused in another program.

    A local variable is created each time the subroutine is called and destroyed when it returns, so it cannot carry a value from one call to the next. A procedure that builds up a string over repeated calls therefore needs that string to be global (or passed BYREF). If MyString is changed from a global to a local declared inside MyOutput(), every call starts with a new, empty MyString, the text added by earlier calls is lost, and the procedure "does not work as expected".

    Three calls of the same procedure on a timeline; each call creates its own local MyString box, new and empty, which is gone when the call returns, while one global MyString box above them keeps its value between the calls
    A local variable is a new, empty box on every call; only a global variable (or a BYREF parameter) keeps a value between calls
    A large outer box labelled global scope holds the global variable Total, visible everywhere, and a smaller inner box labelled PROCEDURE Calc, local scope, holds the local variable temp, which exists only while Calc runs
    A global variable is visible everywhere; a local variable exists only inside its own procedure

    When to use a subroutine

    Use a subroutine when:

    • the same logic appears in more than one place — write it once, call it many times.
    • a block has a clear named purpose — the name documents what it does.
    • the program is complex — break it into parts (decomposition 分解).
    • you want to test a piece in isolation.

    Don't make them so tiny that the call costs more than the work inside.

    Terminology

    • definition — the PROCEDURE ... ENDPROCEDURE (or function) block.
    • call — where it is invoked. argument — a value passed in. parameter — the variable that receives it.
    • return value — what a function passes back.
    • procedure/function header — the first line giving the name and parameters (PROCEDURE Name(params) or FUNCTION Name(params) RETURNS type).
    • procedure/function interface / signature 签名 — name + parameters + return type: what a caller must know to use it.

    Worked example. Describe each term used in the header FUNCTION Pass2(Count : INTEGER) RETURNS BOOLEAN.

    Term Meaning
    FUNCTION a subroutine that returns a value
    Pass2 the identifier used to call it
    Count the parameter: the identifier that receives the argument passed in
    INTEGER the data type of the parameter
    RETURNS BOOLEAN the data type of the value the function returns

    The two identifiers in PROCEDURE MyProc(Count : INTEGER, Message : STRING) are parameters: they receive the values passed in when the procedure is called, and are used inside it like local variables.

    To convert a procedure into a function: change PROCEDURE to FUNCTION and add RETURNS <type>; replace the OUTPUT (or the BYREF parameter that carried the result out) with a RETURN statement; and change every call so that the returned value is used, Result ← Unpack(Text) instead of CALL Unpack(Text, Result). For a "write the header" question, write the whole line: FUNCTION Calculate(Expression : STRING) RETURNS INTEGER. An array parameter is passed by reference, so a procedure that writes into an array changes the caller's array.

    When a program gains a new module, the interface is what is agreed first: the name, the parameters (how many, in what order, of what type) and the return type, plus any global data the module reads or writes. A module that sends a reminder before a due date needs the record (or its index) as a parameter and returns nothing, so it is a procedure; the main program calls it once per record.

    Writing a module for Paper 2

    Half of Paper 2 is "write pseudocode for module X". The scheme awards a mark per feature, so a module that is not finished still scores for every correct part. The parts the examiner looks for:

    An annotated pseudocode function, CountAbove, with a callout on each part that earns a mark: the header with its parameter and return type, the local declarations, the total initialised before the loop, the FOR loop over every element, the IF condition with the right boundary, the update inside the IF, the closed constructs, and the RETURN after the loop
    Each part of a module answer carries its own mark, so write all of them even when one is uncertain
    1. The header, as the question describes it: PROCEDURE Name(Param : TYPE) or FUNCTION Name(Param : TYPE) RETURNS TYPE, with BYREF where the routine must change the argument.
    2. Local declarations: DECLARE every local variable with its type, and initialise counters and totals (Count ← 0).
    3. The loop that visits every element: FOR Index ← 1 TO 50 for an array whose size is given; WHILE NOT EOF(...) for a file.
    4. The condition, with the right comparison and boundary, on the right item: IF Score[Index] > Limit THEN.
    5. The update inside the branch: the count increased, the value stored, or the message output.
    6. The end: RETURN once, after the loop, in a function; ENDFUNCTION or ENDPROCEDURE; and every IF, FOR and WHILE closed.

    Worked example. A global array Score : ARRAY[1:50] OF INTEGER holds test scores. Write a function CountAbove(Limit : INTEGER) that returns how many scores are greater than Limit.

    FUNCTION CountAbove(BYVAL Limit : INTEGER) RETURNS INTEGER
        DECLARE Index, Count : INTEGER
        Count ← 0
        FOR Index ← 1 TO 50
            IF Score[Index] > Limit THEN
                Count ← Count + 1
            ENDIF
        NEXT Index
        RETURN Count
    ENDFUNCTION
    

    Marks: the header with its parameter and RETURNS INTEGER; Count declared and set to 0; a loop over all 50 elements; the comparison > Limit (not >=); the count updated inside the IF; RETURN Count after the loop. The main program uses the return value in an expression or an output: OUTPUT "Above 70: ", CountAbove(70).

    Worked example. Write a function IsValid(Code : STRING) that returns TRUE when Code is two capital letters followed by four digits — the format 格式 AB1234 — and FALSE otherwise.

    FUNCTION IsValid(BYVAL Code : STRING) RETURNS BOOLEAN
        DECLARE Index : INTEGER
        DECLARE Ch : STRING
        IF LENGTH(Code) <> 6 THEN
            RETURN FALSE
        ENDIF
        FOR Index ← 1 TO 6
            Ch ← MID(Code, Index, 1)
            IF Index <= 2 THEN
                IF Ch < "A" OR Ch > "Z" THEN
                    RETURN FALSE
                ENDIF
            ELSE
                IF Ch < "0" OR Ch > "9" THEN
                    RETURN FALSE
                ENDIF
            ENDIF
        NEXT Index
        RETURN TRUE
    ENDFUNCTION
    

    The length check comes first, so MID is never asked for a position that does not exist. Validation 验证 like this returns a BOOLEAN so the caller can write IF IsValid(Entry) THEN ... ELSE OUTPUT "Invalid code" ENDIF: a message to the user is output by the caller, not by the function — a function calculates, a procedure acts.

    Worked example. Write a function IsPalindrome(Word : STRING) that returns TRUE when Word reads the same backwards, such as "RACECAR".

    Compare the characters from the two ends, moving inwards: position Index is paired with position Len - Index + 1, and only the first half needs testing.

    The word RACECAR in seven numbered boxes; arcs pair position 1 with 7, 2 with 6 and 3 with 5, labelled position i and position Len minus i plus 1; the middle character has no pair
    A palindrome check pairs position i with position Len - i + 1 and stops at the middle
    FUNCTION IsPalindrome(BYVAL Word : STRING) RETURNS BOOLEAN
        DECLARE Len, Index : INTEGER
        Len ← LENGTH(Word)
        FOR Index ← 1 TO Len DIV 2
            IF MID(Word, Index, 1) <> MID(Word, Len - Index + 1, 1) THEN
                RETURN FALSE
            ENDIF
        NEXT Index
        RETURN TRUE
    ENDFUNCTION
    

    The same three tools — a FOR over the positions, MID(s, i, 1) to read one character, and & to build a new string — answer most string modules on Paper 2: counting how often a character occurs (IF MID(s, i, 1) = Ch THEN Count ← Count + 1), replacing every instance of a character (add either NewChar or the original character to NewString at each position), hiding all but the last four digits of a card number (add '*' for every position up to Len - 4), or writing your own MID() by joining the characters from Start to Start + Length - 1. Asking MID for a position past the end of the string is a run-time error, so check LENGTH first.

    Files. Values in variables disappear when the program ends, so a module that must keep data for the next run writes it to a file: OPENFILE "scores.txt" FOR WRITE, one WRITEFILE "scores.txt", NUM_TO_STR(Score[Index]) per line inside the loop, and CLOSEFILE "scores.txt" once, after the loop; reading back uses FOR READ, READFILE and WHILE NOT EOF("scores.txt"). Topic 10 has the full file section; here the marks are for opening in the right mode, the read or write inside the loop, and closing once after it.

    Explore

    The call stack: push on call, pop on return

    Calling a subroutine pushes a new frame on top; returning pops it and hands a value back to the caller. The call that is running is always the frame on top.

    Vocabulary Train
    English Chinese Pinyin
    function 函数 hán shù
    parameters 参数 cān shù
    procedure 过程 guò chéng
    structured programming 结构化编程 jié gòu huà biān chéng
    subroutines 子程序 zi chéng xù
    return value 返回值 fǎn huí zhí
    arguments 实参 shí cān
    pass by value 传值 chuán zhí
    pass by reference 传引用 chuán yǐn yòng
    global variable 全局变量 quán jú biàn liàng
    local variable 局部变量 jú bù biàn liàng
    scope 作用域 zuò yòng yù
    decomposition 分解 fēn jiě
    signature 签名 qiān míng
    format 格式 gé shì
    Validation 验证 yàn zhèng
    Watch lesson Exercise sheet
    11.3

    Writing efficient pseudocode

    Three features that make pseudocode easier to understand — the answer to a "state three features" question — are meaningful identifiers (Total, not t), indentation of the statements inside each construct, and comments (// ...) that explain the purpose; keywords in capitals, one statement per line and blank lines between sections are also accepted. Efficient pseudocode goes further:

    • move invariants out of loops — if a value (an invariant 不变量) does not change with the loop counter, compute it once before the loop.
    • exit a loop early when the answer is found (stop a linear search 线性查找 as soon as the target appears).
    • avoid redundant work — store a result and reuse it instead of recomputing.
    • choose the right data structure — an array beats many separate variables when the items belong together.
    • replace deep nested IFs with CASE when testing one value against many.
    • comment the intent, not the mechanics (// validate the postcode, not // loop 6 times).
    • use meaningful names (numberOfPupils, not n) and initialise variables before use.
    Move work that never changes out of the loop, so it runs once instead of every pass
    Move unchanging work out of the loop so it runs once
    Vocabulary Train
    English Chinese Pinyin
    invariant 不变量 bù biàn liàng
    linear search 线性查找 xiàn xìng chá zhǎo
    11.3

    Testing and errors

    Three kinds of error, each found in a different way:

    Error What it is Example Found by
    syntax error 语法错误 a statement that breaks the rules of the language a missing ENDIF; OUTPT "Hi" the translator, before the program runs
    run-time error 运行时错误 the program runs, but a statement cannot be carried out division by zero; an array index of 0 or 51; a function called with an invalid parameter; a loop that never ends, so the program "freezes" while running: the program stops or hangs
    logic error the program runs to the end, but the output is wrong > where >= was needed; a total never set to 0 testing with a trace table and chosen test data

    An IDE 集成开发环境 helps find the last two: a breakpoint 断点 stops the program at a chosen line; single stepping 单步执行 then runs one statement at a time; and the report (or watch) window shows the value of each variable at that moment, so the line where a value goes wrong is seen directly. Test methods and test data are in topic 12.

    Vocabulary Train
    English Chinese Pinyin
    run-time error 运行时错误 yùn xíng shí cuò wù
    syntax error 语法错误 yǔ fǎ cuò wù
    IDE 集成开发环境 jí chéng kāi fā huán jìng
    breakpoint 断点 duàn diǎn
    single stepping 单步执行 dān bù zhí xíng
    11.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly.

    Term Definition
    procedure a subroutine that carries out a task (a sequence of steps) and does not return a value; it is called with CALL
    function a subroutine that returns a single value to the point where it was called, so it can be used in an expression
    parameter the identifier in a subroutine header that receives a value or a reference when the subroutine is called
    argument the value (or variable) supplied in the call, matched to a parameter
    passing by value a copy of the argument's value is given to the subroutine, so changes inside it do not affect the original variable
    passing by reference the address of the variable is given to the subroutine, so changes inside it change the original variable
    header the first line of a subroutine definition: its name, its parameters and, for a function, its return type
    interface what a calling program must know to use a subroutine: its name, its parameters (number, order, type) and its return type
    return value the value a function passes back to the expression that called it
    local variable declared inside a subroutine; it exists only while the subroutine runs and can be used only inside it
    global variable declared outside every subroutine; it can be used anywhere in the program
    count-controlled loop repeats a fixed number of times, controlled by a counter (FOR ... NEXT)
    pre-condition loop tests its condition before each iteration, so the body may never run (WHILE ... ENDWHILE)
    post-condition loop tests its condition after each iteration, so the body runs at least once (REPEAT ... UNTIL)
    constant a named value that cannot change while the program runs
    subroutine a self-contained block of code that performs a task and is called by name: a procedure or a function
    library routine a subroutine that has already been written and tested, and is available to be called from a program
    11.3

    Exam tips

    • Distinguish a procedure (no return value) from a function (returns a value); know pass by value vs by reference.
    • Choose the right loop: count-controlled (FOR) when the number of repeats is known, condition-controlled (WHILE/REPEAT) otherwise.
    • Distinguish local vs global variables and scope; prefer local variables in reusable modules.
    • Use the insert's exact routine names and parameter order; UCASE and VAL are IGCSE names and score nothing here.
    • In a "write pseudocode" answer the header, the declarations, the loop, the condition, the update and the RETURN each carry a mark: write all six parts, even if one is uncertain.

    Common mistakes

    • Calling a function and not using what it returns. Assign the result, or use it in the expression or output: Sorted ← BubbleSort(MyArray, 7).
    • Passing a length one out: 6 for a seven-element array, or the last index where the length was wanted. Decide whether the parameter is a length or an index, and check that the last element is visited.
    • Closing a file inside the loop that reads it. Open once, close once, after the loop.
    • Using the input as a filename directly. Add the extension the question gave: FileName ← Choice & ".txt".
    • Leaving constructs open. Every IF needs its ENDIF, every FOR its NEXT, every WHILE its ENDWHILE, and every function its RETURN; the scheme has a mark for it.
    • Wrong boundaries: > for "at least" (which is >=), or a FOR that starts at 0 for an array declared [1:50].
    • A counter or total that is never set to 0 before the loop.
    • In a trace table, rewriting every variable on every row, or changing a value before the statement that changes it has run.
    • Half a condition: IF x = 3 OR 4 — each side of OR and AND must be a complete comparison. And + does not join strings; & does.
    • Declaring as local a value that must survive between calls. A running total or a string built up over several calls is global or BYREF.
  • 12

    Software Development

    12.1

    Program development life cycle

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the purpose of a development life cycle
    Show understanding of the need for different development life cycles depending on the program being developed Including: waterfall, iterative, rapid application development (RAD)
    Describe the principles, benefits and drawbacks of each type of life cycle
    Show understanding of the analysis, design, coding, testing and maintenance stages in the program development life cycle

    Source: Cambridge International syllabus

    A development life cycle 开发生命周期 is the set of stages from idea to finished, maintained software. It exists to plan, manage and control a project — to build the right product, on time, with good quality.

    A software team collaborating around a table
    Software is built by teams who follow a development life cycle to stay coordinated
    A flowchart with terminators, process boxes and decision diamonds
    A flowchart plans a program's logic during the design stage of the cycle

    Why a life cycle is needed

    The examiner's list for "the purpose of a development life cycle": it breaks a large project into stages that can be planned and managed; it makes sure the requirements are found and agreed before design and coding begin; it builds in testing and documentation rather than leaving them to the end; it lets the team track progress against milestones and manage risk; and it gives the customer defined points at which to review the work. Without one, a team codes first and discovers late that it built the wrong thing.

    Why there are different ones

    No single life cycle fits every project, so several development life cycles exist. The choice depends on the size and complexity, how clear the requirements 需求 are at the start, how much change is expected, the risk level, the team, and the deadline.

    Common models

    • Waterfall 瀑布模型 — a linear sequence (Analysis → Design → Coding → Testing → Maintenance), each stage finished before the next. Clear and well-documented; good for stable requirements, but poor at coping with mid-project change, and the customer sees nothing working until the end.
    • Iterative model 迭代模型 — repeated passes, each producing a partial version that is reviewed and refined. Catches problems earlier; good when requirements are discovered over time, but harder to estimate.
    • Rapid Application Development 快速应用开发 (RAD) — heavy use of a prototype 原型 and user feedback. Very fast first delivery; good for changing requirements, but depends on user availability and suits smaller systems.
    • Agile 敏捷 — short iterations ("sprints"), constant collaboration and testing. Flexible and adaptive, but needs a committed customer and a skilled team.
    Five boxes (Analysis, Design, Coding, Testing, Maintenance) cascading down, each leading to the next
    The waterfall model: each stage is finished before the next begins
    A Design-Build-Test-Review cycle with a repeat loop back to Design, and version bars growing taller each pass until complete
    The iterative model: repeated passes refine the program
    Three parts built in parallel as prototypes that refine with user feedback, then combine into the final system
    Rapid application development: teams work on parts in parallel

    Principles, benefits and drawbacks — as the mark scheme lists them.

    Model Principle Benefits Drawbacks
    waterfall the stages run in a fixed order, each completed and signed off before the next starts; going back means restarting the sequence simple to manage; every stage is fully documented; requirements are fixed early, so costs and dates can be estimated inflexible once a stage is finished; no working software until late; a mistake in analysis is expensive to fix later; the customer cannot see progress
    iterative a small working version is built first, then repeatedly improved through further versions until complete working software early and often; problems found in early versions; the customer's feedback shapes each version; requirements can change hard to estimate the total time and cost; repeated testing costs effort; needs the customer to be available; can drift if versions are not planned
    RAD prototypes of parts of the system are built quickly and refined with the user until accepted, often in parallel by several teams very fast delivery of a first version; the user is involved throughout, so the product fits their needs; changes are easy to absorb needs skilled developers and committed users; documentation is weak; less suited to large or safety-critical systems

    Worked example. A company must be the first to launch a website for a new games console, and the design will change as the console's features are announced. Name the most suitable life cycle and justify it.

    RAD. A prototype of the site can be built and shown to the users within days, and refined as the requirements change; the site is small enough for a prototype-driven approach, and speed of delivery is the main requirement. Waterfall would fix the requirements before any page was built and deliver nothing until the end.

    The standard stages

    Each stage has a purpose, an output and typical activities — a "describe the … stage" question wants two or three of these.

    • analysis — find out what the program must do. Activities: interviews, questionnaires and observation of the current system; a feasibility study; agreeing the requirements specification, which every later stage is checked against.
    • design — decide how it will do it. Outputs: the structure chart (modules and parameters), flowcharts or pseudocode for each module, identifier tables and data structures, screen and file layouts, and the test plan written now, from the specification, before any code exists.
    • coding (implementation 实现) — write the program in a high-level language, module by module, following the design; each module is tested as it is written.
    • testing — run the program against the test plan (normal, abnormal, extreme and boundary data) and correct the errors found; integration, alpha, beta and acceptance testing follow.
    • maintenance 维护 — after release, correct faults, adapt the program to new hardware, software or law, and improve it (see below).

    Worked example. Complete the waterfall diagram Analysis → ? → ? → ? → Maintenance and describe what happens at the design stage.

    The missing stages are Design, Coding, Testing. At the design stage the requirements are turned into a plan for the program: the problem is decomposed into modules (a structure chart), the algorithm for each module is written as pseudocode or a flowchart, the data structures and identifiers are chosen, the screens and files are laid out, and the test plan is written from the specification.

    Explore

    The program development life cycle

    Step through the stages every project passes through. Getting the requirements right in analysis matters most — a mistake caught in testing is far costlier to fix than one caught early.

    Explore

    Software process lab

    Classify development examples by the stage or tool they belong to.

    Vocabulary Train
    English Chinese Pinyin
    development life cycle 开发生命周期 kāi fā shēng mìng zhōu qī
    requirements 需求 xū qiú
    waterfall 瀑布模型 pù bù mó xíng
    maintenance 维护 wéi hù
    iterative model 迭代模型 dié dài mó xíng
    Rapid Application Development 快速应用开发 kuài sù yìng yòng kāi fā
    prototype 原型 yuán xíng
    Agile 敏捷 mǐn jié
    implementation 实现 shí xiàn
    Exercise sheet
    12.2

    Program design tools

    Syllabus
    Candidates should be able to: Notes and guidance
    Use a structure chart to decompose a problem into sub-tasks and express the parameters passed between the various modules/procedures/functions which are part of the algorithm design Describe the purpose of a structure chart Construct a structure chart for a given problem Derive equivalent pseudocode from a structure chart
    Show understanding of the purpose of state-transition diagrams to document an algorithm

    Source: Cambridge International syllabus

    Structure chart

    A structure chart 结构图 shows the hierarchical decomposition 分解 of a program into modules (subroutines 子程序) and the parameters 参数 passed between them. Each module is a rectangle; lines link caller (above) to callee (below); small arrows show data going down and results coming back up. The design can then be turned into equivalent pseudocode 伪代码.

                    CalculatePay
                /        |         \
           GetEmployee  CalculateBonus  CalculateTax
           Returns:     Takes: sales    Takes: gross
           employeeID   Returns: bonus  Returns: tax
    

    It is a design-stage tool, and you can read the procedure signatures off it.

    A structure chart with Convert temperature at the top and INPUT, Convert to Celsius and OUTPUT modules below, with temperature parameters on the links
    A structure chart: modules with the parameters passed between them

    The symbols the examiner asks about. A box is a module; a line links a caller (above) to the modules it calls (below), read left to right in the order they are called. A small arrow with an open circle at its tail is a data couple — a parameter passed down into a module or a value returned up; an arrow with a filled circle is a control couple, a flag (usually BOOLEAN) that tells the caller what happened. A diamond at a branch means selection: only one of the modules below it is called, depending on a condition. A curved arrow sweeping across the links means iteration: the modules under it are called repeatedly in a loop.

    A structure chart showing every symbol: module boxes, calling lines, an open-circle data couple carrying item ID down, a filled-circle control couple returning an in-stock flag up, a diamond selecting between Print invoice and Reject order, and a curved arrow marking the modules repeated for each order
    The structure-chart symbols: data and control couples, a selection diamond and an iteration arrow

    Worked example. Four modules are defined as PROCEDURE Main(), PROCEDURE ReadData(BYREF Count : INTEGER), FUNCTION IsValid(Value : INTEGER) RETURNS BOOLEAN and PROCEDURE Report(Total : INTEGER, Count : INTEGER). Main calls ReadData, then calls IsValid once for each value read, then calls Report. Describe the structure chart.

    Main at the top; ReadData, IsValid and Report in a row beneath it, left to right in calling order. On the ReadData link an upward data couple Count (a BYREF parameter comes back). On the IsValid link a downward data couple Value and an upward control couple (the BOOLEAN result), with a curved iteration arrow across that link because it is called for each value. On the Report link two downward data couples, Total and Count. Reading the other way, a function is any module that returns a value — its header needs RETURNS and the returned type.

    State-transition diagram

    A state-transition diagram 状态转换图 shows the states 状态 a system can be in and the events that move it between them — good for vending machines, traffic lights, user interfaces. State-transition diagrams are used to document the behaviour of an algorithm or system. Each state is a circle; each transition is an arrow labelled with the event.

       coin inserted               item selected
    [Idle] --------------→ [Awaiting selection] ----------→ [Dispensing]
    

    It makes missing transitions easy to spot ("what if a second coin is inserted while awaiting selection?").

    A state diagram: Locked to Waiting for second digit to Waiting for third digit to Unlocked, with correct-digit and wrong-digit transitions
    A state-transition diagram for a door lock with code 259

    Reading and drawing one. Each transition is labelled input | output (or condition | action): what happened, then what the system does as it changes state. A question gives a table of current state, input, output, next state and asks for the diagram, or the reverse — every row of the table is exactly one arrow. Check that every state has an arrow leaving it for every input that can occur, including the ones that leave the state unchanged (an arrow that loops back to the same state).

    Worked example. A pump controller has states pump off and pump on. In pump off, the input low level detected produces the output activate pump and moves to pump on; in pump on, normal level detected produces deactivate pump and moves to pump off. Any other input leaves the state unchanged. Draw the table.

    Current state Input Output Next state
    pump off low level detected activate pump pump on
    pump off normal level detected pump off
    pump on normal level detected deactivate pump pump off
    pump on low level detected pump on

    The two "no change" rows become loop arrows on the diagram; leaving them out loses the mark for completeness.

    Explore

    Software process lab

    Classify development examples by the stage or tool they belong to.

    Vocabulary Train
    English Chinese Pinyin
    structure chart 结构图 jié gòu tú
    parameters 参数 cān shù
    pseudocode 伪代码 wěi dài mǎ
    hierarchical decomposition 分解 fēn jiě
    decomposition 分解 fēn jiě
    subroutines 子程序 zi chéng xù
    state-transition diagram 状态转换图 zhuàng tài zhuǎn huàn tú
    states 状态 zhuàng tài
    Watch lesson Exercise sheet
    12.3

    Errors

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of ways of exposing and avoiding faults in programs
    Locate and identify the different types of errors syntax errorslogic errorsrun-time errors
    Correct identified errors
    Show understanding of the methods of testing available and select appropriate data for a given method Including dry run, walkthrough, white-box, black-box, integration, alpha, beta, acceptance, stub
    Show understanding of the need for a test strategy and test plan and their likely contents
    Choose appropriate test data for a test plan Including normal, abnormal and extreme/boundary
    Show understanding of the need for continuing maintenance of a system and the differences between each type of maintenance Including perfective, adaptive, corrective
    Analyse an existing program and make amendments to enhance functionality

    Source: Cambridge International syllabus

    • syntax error 语法错误 — breaks the language's grammar (missing bracket, misspelled keyword). Caught at translation time; the program won't run until fixed.
    • run-time error 运行时错误 — happens while running (divide by zero, file not found, array index out of range). The program crashes or raises an exception; fix by adding checks.
    • logic error 逻辑错误 — the program runs but gives wrong results (using + for -, an off-by-one loop, conditions in the wrong order). The hardest to find; the only sign is wrong output, so use careful testing and tracing.
    A pipeline from write code to translate to run to output: a syntax error stops it at translation, a run-time error crashes during the run, and a logic error runs fine but gives the wrong output
    When each error shows up: syntax at translation, run-time during the run, logic in the output

    Exposing and avoiding faults. Faults are exposed by testing against a test plan, by a dry run or trace table, by a walkthrough with colleagues, and by the IDE's debugger (breakpoints, single stepping, watching variables). They are avoided by designing before coding (structure chart, pseudocode), by modular code with meaningful identifiers and comments, by validation of every input, by handling exceptions rather than letting a run-time error crash the program, and by the IDE's dynamic syntax checks as you type.

    Worked example. State the type of error in each case and how it shows itself. (a) Result <- STR_TO_NUM(x) / STR_TO_NUM(y) is run with y = "0". (b) The same line is run with x = "12a". (c) A loop written as FOR i <- 1 TO 9 processes a ten-element array. (d) OUTPUT "Total: " Total is missing a comma.

    (a) Run-time error — division by zero; the program crashes when this line is executed with that data. (b) Run-time error — the string cannot be converted to a number. (c) Logic error — the program runs but the tenth element is never processed, so the output is wrong. (d) Syntax error — the statement breaks the language's rules and is reported by the translator before the program runs.

    Worked example. Correct the errors in this pseudocode, which should output the average of ten marks.

    Total <- 0
    FOR i <- 1 TO 10
        INPUT Mark
        Total <- Total + Mark
    NEXT i
    Average <- Total / 9
    OUTPUT "Average" Average
    

    The division should be by 10, not 9 (a logic error); the output line needs a comma or an & between the string and the value (a syntax error); and Average is never declared as REAL (a syntax or run-time error, depending on the language). Say which line and what the corrected line is: Average <- Total / 10.

    Vocabulary Train
    English Chinese Pinyin
    syntax error 语法错误 yǔ fǎ cuò wù
    run-time error 运行时错误 yùn xíng shí cuò wù
    logic error 逻辑错误 luó jí cuò wù
    Watch lesson Exercise sheet
    12.3

    Testing methods

    • dry run 手工跟踪 — trace the code on paper, writing each variable's value in a table.
    • walkthrough 走查 — a team review of the code.
    • white-box testing 白盒测试 — designed from the code's internal structure, covering every statement, branch and loop.
    • black-box testing 黑盒测试 — designed from the specification only: feed inputs, check outputs.
    • integration testing 集成测试 — combine modules and test the interfaces between them.
    • alpha testing α测试 — by the developers/in-house before release; beta testing β测试 — by a limited group of real users in their own environment.
    • acceptance testing 验收测试 — by the customer, to decide if the product is fit for purpose.
    • stub — a placeholder for a module that does not exist yet, so the structure can be tested top-down.
    Black-box testing works from the specification; white-box tests the code's internal paths
    Black-box tests the specification; white-box tests the code paths

    Which method, when. A dry run and a walkthrough need no computer — the dry run is you, tracing the algorithm with a trace table 跟踪表; the walkthrough is a meeting in which the author explains the code line by line and colleagues look for faults, so it also spreads knowledge of the code through the team and checks it against the design. White-box tests are written by someone who can see the code and aims to exercise every path; black-box tests are written from the specification and check only inputs against expected outputs, so a user or a separate tester can do them. Integration testing follows module testing: modules that pass alone can still fail when the data passed between them is the wrong type or in the wrong order. Alpha testing is in-house; beta testing gives a release candidate to a sample of real users, who report faults from real use; acceptance testing is the customer checking the finished product against the requirements before paying for it. A stub lets top-down testing start before every module exists.

    Stub testing: the main program under test calls a finished Module A and a stub standing in for the unwritten Module B, which has the real header but simply returns a fixed value
    A stub stands in for a module that is not written yet, so the modules above it can be tested now

    Worked example. After the program passed its in-house tests it was given to a group of users to try before release. Name this type of testing, and state what happens next.

    Beta testing — real users in their own environment, reporting faults the developers did not find. The faults are corrected, then the customer carries out acceptance testing against the requirements and the program is released; faults found in live use are then handled by corrective maintenance.

    Worked example. Give three benefits of testing a program by walkthrough.

    Errors are found by people who did not write the code and so read it without assumptions; the logic is checked against the design and specification, not only against test data; several people learn how the code works, which helps later maintenance; and no test data or working computer is needed, so it can be done early.

    Vocabulary Train
    English Chinese Pinyin
    acceptance testing 验收测试 yàn shōu cè shì
    dry run 手工跟踪 shǒu gōng gēn zōng
    trace table 跟踪表 gēn zōng biǎo
    walkthrough 走查 zǒu chá
    white-box testing 白盒测试 bái hé cè shì
    black-box testing 黑盒测试 hēi hé cè shì
    integration testing 集成测试 jí chéng cè shì
    alpha testing α测试 α cè shì
    beta testing β测试 β cè shì
    stub zhuāng
    12.3

    Test strategy and test plan

    A test strategy 测试策略 is the high-level approach — which kinds of testing, who does them, when, and the criteria to move on. A test plan 测试计划 is the detailed list of tests — each with input data, expected output, and a column for the actual output.

    What each contains. A test strategy states which testing methods will be used at which stage (module testing by the programmer, then integration, alpha, beta, acceptance), who is responsible for each, what test data is required, and the criteria for passing to the next stage. A test plan lists the individual tests: for each, the module or feature under test, the input data, the reason the data was chosen (normal, abnormal, extreme, boundary), the expected result, a space for the actual result, and what to do if they differ. The plan is written at the design stage, from the specification, so that it tests what the program should do rather than what it happens to do.

    Choosing test data

    For each field or condition, include three kinds:

    • normal data 正常数据 — typical values inside the valid range (for marks 0–100: 50, 75).
    • abnormal data 异常数据 — values that should be rejected (-10, 200, "abc").
    • extreme data 极端数据 — the largest and smallest values still accepted (0 and 100).
    • boundary data 边界数据 — values at the edges, where off-by-one errors hide (each accepted extreme and the rejected value just outside it: 0/-1, 100/101).
    A number line for a mark field 0 to 100: normal values 50 and 75 inside, the extremes 0 and 100 at the accepted boundaries, and abnormal values -1, 101, -10 and 200 rejected outside
    Test data for a 0–100 field: normal inside, extremes at the boundaries, abnormal outside

    Worked example. A field accepts an exam mark from 0 to 100. Give test data of each kind with its expected result. Normal: 50 - accepted, a typical value inside the range. Abnormal: -10, 200, "abc" - all rejected, being out of range or the wrong data type. Extreme: 0 and 100 - the largest and smallest values that are still accepted. Boundary: the pairs straddling each edge - -1 rejected alongside 0 accepted, and 100 accepted alongside 101 rejected. Every value must carry its expected result, or the test plan proves nothing. Extreme and boundary are the pair most often confused: an extreme value sits inside and is accepted, while a boundary test is always a pair either side of the edge - which is exactly where off-by-one errors hide.

    Worked example. A component passes if its weight, measured to the nearest gram, is within 3 g of the target of 50 g, i.e. from 47 g to 53 g inclusive. Draw up the test-plan rows for the check.

    Test data Type Reason Expected result
    50 normal a typical value well inside the range accepted
    47, 53 extreme (boundary) the smallest and largest values that must still be accepted accepted
    46, 54 boundary the values just outside the range, where an off-by-one error would accept them rejected
    20, 90 abnormal values far outside the range rejected
    "abc", −5 abnormal the wrong type, a negative weight rejected

    Each row must say why the value was chosen and what should happen; a bare list of numbers earns nothing.

    Vocabulary Train
    English Chinese Pinyin
    test plan 测试计划 cè shì jì huà
    boundary data 边界数据 biān jiè shù jù
    test strategy 测试策略 cè shì cè lüè
    normal data 正常数据 zhèng cháng shù jù
    abnormal data 异常数据 yì cháng shù jù
    extreme data 极端数据 jí duān shù jù
    12.3

    Maintenance

    Most of a program's lifetime cost is in maintenance. Three kinds:

    The three kinds of maintenance: perfective, adaptive and corrective
    Three kinds of maintenance: perfective, adaptive and corrective
    • perfective maintenance 完善性维护 — improving performance or features even though it works (a faster query, a new option).
    • adaptive maintenance 适应性维护 — keeping it working in a changing environment (a new OS, a new API, a legal change).
    • corrective maintenance 纠正性维护 — fixing bugs found in use.

    A program may need all three throughout its life.

    Why each is needed — the reasons the mark scheme lists. Corrective: a fault is reported by a user after release, or an incorrect output is noticed in particular circumstances that testing did not cover. Adaptive: the operating system, hardware or browser is upgraded; a law or company rule changes (tax rates, data-protection requirements); the program must work with a new external system or file format. Perfective: users ask for extra features or a better interface; the program is made faster or made to use less memory; the code is tidied to make future changes easier.

    Worked example. (a) A released program outputs a wrong value under certain circumstances. (b) The hardware that runs a program is replaced. (c) Customers ask for the coffee-shop loyalty program to send a message on a customer's birthday. Name the maintenance type in each case.

    (a) Corrective — a fault in the delivered program is being fixed. (b) Adaptive — the program is changed to run in its new environment. (c) Perfective — a feature is added to a program that already works.

    Vocabulary Train
    English Chinese Pinyin
    corrective maintenance 纠正性维护 jiū zhèng xìng wéi hù
    perfective maintenance 完善性维护 wán shàn xìng wéi hù
    adaptive maintenance 适应性维护 shì yìng xìng wéi hù
    12.3

    Amending an existing program

    When asked to add a feature or fix a bug:

    1. read the existing code until you understand the algorithm and data flow.
    2. find where the change goes — which subroutine, which lines.
    3. make the change as small as possible — don't rewrite working code.
    4. update related parts — every caller of a changed parameter list, every routine using a changed data structure.
    5. test the new behaviour and the old (regression testing 回归测试 — check you broke nothing).
    6. document the change.

    Clear comments, meaningful names, decomposed subroutines and a structure chart make a program much easier to amend — which is why the design tools matter even after the first release.

    Analysing a program you did not write. Start from the identifier table and the module headers: they tell you what each module receives and returns before you read a line of its body. Then trace the algorithm with a trace table for one small input, noting where each output value comes from. Only then decide where the enhancement goes — usually a new module called from the existing one, so the working code is disturbed as little as possible — and write the pseudocode for the change and the test data that proves it.

    Vocabulary Train
    English Chinese Pinyin
    regression testing 回归测试 huí guī cè shì
    12.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    development life cycle the sequence of stages, from analysis to maintenance, followed to produce and support a program
    waterfall model a life cycle in which the stages are carried out in a fixed order, each completed before the next begins
    iterative model a life cycle in which a working version is produced and then repeatedly refined until it is complete
    rapid application development a life cycle that builds prototypes quickly, refining them with user feedback until they are accepted
    structure chart a diagram that shows how a program is decomposed into modules, the order in which they are called and the parameters passed between them
    state-transition diagram a diagram that shows the states a system can be in and the inputs that cause it to move between them
    syntax error an error in the way a statement is written, so it breaks the rules of the language and cannot be translated
    logic error an error in the algorithm, so the program runs but produces the wrong result
    run-time error an error that occurs while the program is running, such as division by zero, and stops it
    dry run working through the algorithm by hand, recording the values of the variables in a trace table
    walkthrough a review in which the author steps through the code with colleagues who look for errors
    stub a placeholder module with the correct header that returns a fixed value, used so the modules that call it can be tested
    test plan a list of the tests to be carried out, each with its test data, the reason for the data and the expected result
    boundary data values at each edge of the valid range, both the last value accepted and the first value rejected
    corrective / adaptive / perfective maintenance fixing faults found in use / changing the program to suit a changed environment / improving a program that already works
    12.3

    Exam tips

    • Compare development models (waterfall, iterative, RAD) by principle, benefit, drawback, and know the five stages of the program development life cycle and what each produces.
    • Distinguish syntax, logic and run-time errors by when each shows itself: at translation, in the output, during the run.
    • Choose test data of every kind — normal, abnormal, extreme and boundary — and give each value with its reason and expected result.
    • Distinguish the types of maintenance (corrective, adaptive, perfective) by why the change is being made.
    • On a structure chart, name every symbol: box, calling line, data couple, control couple, selection diamond, iteration arrow. Reading module headers off a chart, remember a function has RETURNS.

    Common mistakes

    • Describing a life cycle stage by its name only ("in the design stage the program is designed"). Say what is produced: structure chart, pseudocode, test plan.
    • Calling a wrong output a "run-time error". If the program runs to the end, it is a logic error.
    • Giving boundary data as just the extremes. The mark needs the values on both sides of the edge.
    • Treating alpha and beta testing as the same. Alpha is in-house by the developers; beta is by real users outside.
    • Confusing adaptive and perfective maintenance. Adaptive responds to a change outside the program; perfective improves a program nobody had to change.
    • Drawing a structure chart with the modules in any order. They read left to right in the order they are called, and each parameter needs its arrow.
  • 13

    Data Representation

    13.1

    User-defined data types

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of why user-defined types are necessary
    Define and use non-composite types Including enumerated, pointer
    Define and use composite data types Including set, record and class/object
    Choose and design an appropriate user-defined data type for a given problem

    Source: Cambridge International syllabus

    The built-in types (INTEGER, REAL, STRING, CHAR, BOOLEAN) cover the simplest cases. For richer problems you can define user-defined types 用户定义类型, making the code clearer and the compiler stricter.

    Why they are needed

    A built-in STRING lets you store nonsense in a field that should hold one of a few legal values; a user-defined type can restrict it. Real entities are usually a collection of values of different types. And DECLARE Taxi : Vehicle is clearer (self-documenting) than DECLARE Taxi : STRING.

    "Describe the purpose of a user-defined data type" (two marks). A data type defined by the programmer, built from existing (built-in) types, so that data specific to the problem can be represented when no built-in type fits. Both halves score: defined by the programmer and based on existing types. The examiner also accepts "to make the program easier to read and maintain" as a supporting point, never on its own.

    "Explain what is meant by non-composite and composite data types" (four marks). A non-composite type is defined without reference to another type: it holds a single value, for example an integer, a real, or an enumerated value. A composite type is a collection of other types (which may themselves be composite): it holds several values under one identifier, for example a record, a set, an array or a class. Give an example with each definition; the exam asks for one.

    Non-composite types

    Enumerated type

    An enumerated type 枚举类型 has values that are a fixed list of named constants:

    TYPE Vehicle = (M100, M230, T101, T102, T120, T150)
    DECLARE MyTaxi : Vehicle
    MyTaxi ← T102
    

    The names are values of the new type (stored internally as small integers); you cannot assign anything outside the list. Uses: days of the week, colours, status codes.

    "State what is meant by an enumerated data type." A non-composite user-defined type defined by listing all its possible values (in order). Because the values are ordered, they can be compared and stepped through: with TYPE Month = (January, February, ..., December), the test IF ThisMonth > June is legal, and the values are stored internally as integers. The pseudocode has three parts and the exam marks each: the keyword TYPE, the identifier with =, and the list in brackets separated by commas.

    Worked example. Write pseudocode to define an enumerated type for the days on which a school is open (Monday to Friday), and declare a variable of that type set to Wednesday.

    TYPE SchoolDay = (Monday, Tuesday, Wednesday, Thursday, Friday)
    DECLARE Today : SchoolDay
    Today ← Wednesday
    

    A variable of an enumerated type cannot be given a value outside the list, which is the whole point: Today ← Saturday is a compile-time error, whereas a STRING would have accepted "Saturdy".

    An enumerated type Vehicle with the fixed named values M100, M230, T101, T102, T120 and T150; a variable of this type may only hold one of them
    An enumerated type is a fixed list of named values

    Pointer type

    A pointer 指针 holds the memory address of another variable (or NULL for "no target"). Pointers build dynamic structures (linked lists, trees) and pass references without copying.

    TYPE PNode = ^TNode    // pointer to a TNode
    DECLARE p : PNode
    p ← NEW TNode
    p^.Value ← 42          // dereference to reach the fields
    

    To dereference 解引用 (p^) means to reach the variable it points to.

    "State what is meant by a pointer data type." A non-composite type whose value is the memory address of (a reference to) a variable of a given type. The pseudocode declares the type with a caret before the type it points to, and the exam asks for exactly that line:

    TYPE SelectParts = ^Parts        // a pointer to a value of type Parts
    DECLARE Chosen : SelectParts
    Chosen ← ^Keyboard               // Chosen now holds the address of Keyboard
    OUTPUT Chosen^                   // dereference: the value stored at that address
    

    Pointers are what a dynamic linked list or binary tree (Topic 19) is built from: each node holds a pointer to the next. Two marks are commonly lost here: writing the pointer type as if it held the value itself, and forgetting the caret when reading through the pointer.

    A pointer p holds an address and points to a TNode holding Value = 42 and a Next field; p^ dereferences to reach the node's fields, such as p^.Value
    A pointer holds an address; p^ dereferences it to reach the node's fields

    Composite types

    A composite type 复合类型 (one of the composite data types) groups several values under one name.

    A set: an unordered collection where every value is unique
    A set is an unordered collection of unique values
    A record Student with fields Name, Age, Grade and Enrolled, each of a different type
    A record groups fields of different types under one name
    • record 记录 (Topic 10) — fields of different types in a TYPE ... ENDTYPE block.
    • set 集合 — an unordered collection of unique values, with operations add, remove, membership test, union, intersection:
    DECLARE Available : SET OF Colour
    Available ← {Red, Blue}
    IF Green IN Available THEN ...
    
    • class / object 对象 — the OOP composite type, combining data fields (attributes 属性) with operations on them (methods 方法). An object is an instance of a class:
    CLASS Taxi
        PRIVATE Capacity : INTEGER
        PUBLIC FUNCTION GetCapacity() RETURNS INTEGER
            RETURN Capacity
        ENDFUNCTION
    ENDCLASS
    

    Choosing a type

    Use enumerated for a value from a fixed list, pointer for indirection, record for a group of fields, set for an unordered unique collection, and class when you need state and behaviour together.

    "Describe the user-defined data type set" (three marks). A composite type that holds a collection of values of the same type, in no particular order and with no duplicates; values can be added and removed, and a value can be tested for membership. Declare the type with SET OF, then define a set constant with its values in brackets:

    TYPE EvenNumbers = SET OF INTEGER
    DEFINE Evens (2, 4, 6, 8, 10, 12) : EvenNumbers
    TYPE SymbolSet = SET OF CHAR
    DEFINE Operators ('+', '-', '*', '/') : SymbolSet
    

    "Describe the user-defined data type record" (three marks). A composite type made up of a fixed number of fields (items), each with its own identifier and its own type, referred to under a single identifier; the fields are accessed with dot notation.

    Worked example. Write pseudocode to declare a record type ClubMember for a club member's first name, last name, membership code (an integer), date of joining and whether fees have been paid; then declare a variable and set two of its fields.

    TYPE ClubMember
        DECLARE FirstName : STRING
        DECLARE LastName : STRING
        DECLARE Code : INTEGER
        DECLARE DateJoined : DATE
        DECLARE FeesPaid : BOOLEAN
    ENDTYPE
    
    DECLARE NewMember : ClubMember
    NewMember.LastName ← "Chen"
    NewMember.FeesPaid ← TRUE
    

    Every field needs its own DECLARE line with an appropriate type, the block ends with ENDTYPE, and a field 字段 is reached as variable.field. Asked to choose a type for each field, match it to the data: a code that is only ever compared is a STRING if it can contain letters, an INTEGER if arithmetic or ordering is needed; a yes/no is BOOLEAN; a date is DATE. A field that can take one of a few named values (a pet's species, a colour) is the one to make an enumerated type.

    An array of four ClubMember records drawn as rows of fields, with the callout Members[3].LastName picking out one field of one element, and an assignment writing one field of another element
    An array of records: each element is a whole record, an index chooses the element, and a dot chooses the field

    Records in arrays and files. A table of many members is DECLARE Members : ARRAY[1:100] OF ClubMember; then Members[3].LastName is one field of one element, and a loop over the index processes every record. A record is also the natural unit written to and read from a file (below), one record per PUTRECORD or WRITEFILE.

    Worked example. A composite type Pet stores each pet's name (string), species (one of dog, cat, rabbit or hamster) and weight in kilograms (real). Define the types and declare a variable.

    TYPE Species = (Dog, Cat, Rabbit, Hamster)
    TYPE Pet
        DECLARE Name : STRING
        DECLARE Kind : Species
        DECLARE Weight : REAL
    ENDTYPE
    DECLARE MyPet : Pet
    MyPet.Kind ← Rabbit
    

    The enumerated type is defined first, because the record uses it: order matters in pseudocode as it does in a compiler.

    Classes in pseudocode. A class is the composite type that also carries behaviour. The exam asks for the declaration with its attributes marked PRIVATE, a constructor 构造函数 named NEW that sets them, and PUBLIC methods to get or change them:

    CLASS Appointment
        PRIVATE PatientName : STRING
        PRIVATE Treatment : STRING
        PRIVATE Medication : STRING
        PUBLIC PROCEDURE NEW(Name : STRING, Treat : STRING, Med : STRING)
            PatientName ← Name
            Treatment ← Treat
            Medication ← Med
        ENDPROCEDURE
        PUBLIC FUNCTION GetTreatment() RETURNS STRING
            RETURN Treatment
        ENDFUNCTION
    ENDCLASS
    
    DECLARE Visit : Appointment
    Visit ← NEW Appointment("A. Chen", "filling", "none")
    OUTPUT Visit.GetTreatment()
    

    Attributes are private so that they can only be changed through methods (encapsulation, Topic 20); the constructor is a procedure called NEW with one parameter per attribute; a getter is a function that returns the attribute. Each of these is a separate mark.

    Explore

    Programming concept lab

    Connect examples to the programming idea they show.

    Vocabulary Train
    English Chinese Pinyin
    user-defined types 用户定义类型 yòng hù dìng yì lèi xíng
    user-defined type 用户定义类型 yòng hù dìng yì lèi xíng
    field 字段 zì duàn
    record 记录 jì lù
    set 集合 jí hé
    class lèi
    composite type 复合类型 fù hé lèi xíng
    enumerated type 枚举类型 méi jǔ lèi xíng
    pointer 指针 zhǐ zhēn
    dereference 解引用 jiě yǐn yòng
    object 对象 duì xiàng
    attributes 属性 shǔ xìng
    methods 方法 fāng fǎ
    constructor 构造函数 gòu zào hán shù
    Exercise sheet
    13.2

    File organisation and access

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of the methods of file organisation and select an appropriate method of file organisation and file access for a given problem Including serial, sequential (using a key field), random (using a record key)
    Show understanding of methods of file access Including Sequential access for serial and sequential files Direct access for sequential and random files
    Show understanding of hashing algorithms Describe and use different hashing algorithms to read from and write data to a random/sequential file

    Source: Cambridge International syllabus

    File organisation 文件组织 is how the data is laid out; file access is how the program reaches a record.

    • serial file 串行文件 — records in the order added, no sorting. Access is sequential only; appending is fast; searching is slow. Used for logs and audit trails.
    • sequential file 顺序文件 — records sorted by a key. Searching is faster (you can stop early or binary-search); inserting is slow (records must shift). Used for master files updated in batch.
    • random file 随机文件 (direct-access file) — records at positions computed from the key (often by a hash). Direct access by key is very fast; reading in key order is harder. Used for large lookup tables and customer accounts.
    A row of record boxes from first to sixth in the order they were added, with an append arrow and a Start of file marker
    Serial file: records are kept in the order they were added
    A row of customer record boxes with ascending key values, showing the records sorted into key order
    Sequential file: records are sorted by a key field
    A record key passing through a hash function to compute a slot number, with the record placed in that slot of the file
    Random file: records sit at positions computed from the key

    The two access methods are sequential access 顺序存取 (read from start to end) and direct access 直接存取 (jump straight to a known position). Match the structure to the dominant operation: single-key lookups favour random; in-order reports favour sequential.

    Describing each organisation (the wording that scores). Serial: records are stored one after another in the order in which they were added, with no ordering by key. Sequential: records are stored in order of a key field (sorted). Random: each record is stored at an address calculated from its key by a hashing algorithm, so the records are not in any order. Comparing serial and sequential: both store records one after another and both are read sequentially, but a sequential file is ordered by key, so a search can stop as soon as a key larger than the target is read, and a new record must be inserted in its correct position (usually by rewriting the file), whereas a serial file is simply appended to.

    Two chains of steps: direct access hashes the key to an address, seeks straight to it and reads or writes the record; sequential access opens the file, reads records one at a time from the start and compares keys until the record is found or the end of the file is reached
    The two access methods as procedures: direct access computes where to look; sequential access looks everywhere in turn

    Describing each access method. Sequential access: start at the beginning of the file and read the records one after another (in the order stored) until the required record is found or the end of the file is reached. Applied to a serial file this means reading every record up to the match, and reading the whole file to establish that a record is absent; applied to a sequential file the search can stop early, as soon as a key greater than the target is read. Direct access: the address of the record is calculated from its key (by a hashing algorithm, or from an index), and the program goes straight to that position without reading the records before it; this is the access method for random files, and for a record referenced by a unique address on a disk.

    Choosing. A payroll or utility-billing master file processed in batch, every record in turn, suits a sequential file; a log of transactions in the order they happened suits a serial file; a stock or customer file where single records are looked up and updated by key while the program runs suits a random file with direct access.

    File handling in pseudocode. The exam expects the standard statements, and Paper 3 sets algorithms that use them:

    Task Statements
    open a text file OPENFILE "Scores.txt" FOR READ (or FOR WRITE, which creates or overwrites, or FOR APPEND)
    read or write a line READFILE "Scores.txt", Line and WRITEFILE "Scores.txt", Line
    test for the end WHILE NOT EOF("Scores.txt")
    close CLOSEFILE "Scores.txt"
    open a random file OPENFILE "Stock.dat" FOR RANDOM
    move to a record position SEEK "Stock.dat", Address
    read or write a whole record GETRECORD "Stock.dat", Item and PUTRECORD "Stock.dat", Item

    Worked example. A random file Stock.dat holds records of type StockItem, stored at the address given by ItemID MOD 100. Write pseudocode that stores a new item at its hashed address if that position is empty, reporting the position if it is already in use.

    DECLARE Item, Existing : StockItem
    DECLARE Address : INTEGER
    INPUT Item.ItemID, Item.Description, Item.Quantity
    Address ← Item.ItemID MOD 100
    OPENFILE "Stock.dat" FOR RANDOM
    SEEK "Stock.dat", Address
    GETRECORD "Stock.dat", Existing
    IF Existing.ItemID = 0 THEN        // 0 marks an empty position
        SEEK "Stock.dat", Address
        PUTRECORD "Stock.dat", Item
        OUTPUT "Stored at ", Address
    ELSE
        OUTPUT "Position ", Address, " is in use"
    ENDIF
    CLOSEFILE "Stock.dat"
    

    Two details the mark scheme checks: SEEK before each GETRECORD or PUTRECORD (reading moves the position on, so seek again before writing), and the file opened FOR RANDOM and closed at the end. To copy every record of a random file to another, loop over the addresses with SEEK, GETRECORD from one file and PUTRECORD to the other, skipping empty positions.

    Explore

    File access route

    Follow a file from storage to program and back safely.

    Vocabulary Train
    English Chinese Pinyin
    File organisation 文件组织 wén jiàn zǔ zhī
    serial file 串行文件 chuàn xíng wén jiàn
    sequential file 顺序文件 shùn xù wén jiàn
    random file 随机文件 suí jī wén jiàn
    direct access 直接存取 zhí jiē cún qǔ
    sequential access 顺序存取 shùn xù cún qǔ
    Watch lesson Exercise sheet
    13.2

    Hashing

    A hash function 散列函数 (a hashing algorithm) takes a record key and produces an address where the record is stored. A good one is fast, deterministic 确定性, and spreads keys evenly.

    Common hashing algorithms for $N$ slots: modulo hash address ← key MOD N; folding (split the key, add the pieces, MOD N); a string hash (sum the character codes, MOD N).

    A collision 冲突 is when two keys hash to the same address. Three ways to resolve it:

    Strategy How it works Trade-off
    linear probing 线性探测 use the next free slot (wrapping around) simple, but keys cluster
    chaining 链接法 each slot points to a linked list 链表 of records no clustering, but uses more memory
    rehashing apply a second hash function spreads keys, but more work
    Resolving a collision where keys A and B both hash to slot 2. Linear probing puts B in the next free slot (3); chaining keeps slot 2 pointing to a linked list of A then B
    Resolving a hash collision: linear probing uses the next free slot; chaining keeps a linked list per slot

    To search: hash the key, read that slot; if the keys match you are done, else follow the resolution strategy until a match or an empty slot. To insert: hash the key, write to that slot or the next free one. Keep the load factor 装填因子 (records ÷ slots) below about 70% for near-O(1) lookups.

    "Explain what is meant by a hashing algorithm in the context of file access" (three marks). A calculation (function) performed on the key field of a record that produces a value, which is used as the address (location) at which the record is stored in the file and from which it is retrieved. The same calculation on the same key always gives the same address, which is why the record can be found again without searching.

    "Outline two methods of overcoming a collision." (1) Linear probing (open addressing): store the record in the next free location after the calculated address, wrapping round to the start if necessary; to retrieve, start at the hashed address and read forward until the key matches. (2) An overflow area 溢出区 or chaining: store the colliding record in a separate overflow area (or a linked list attached to the address), which is searched sequentially after the main address fails to match. Either scores; describe the retrieval as well as the storage.

    Worked example. A random file has 11 record positions, numbered 0 to 10, and the hashing algorithm is Address ← Key MOD 11. Records with keys 1250, 1381, 1452, 1613 and 1470 are stored in that order, using linear probing. Show where each record goes, and describe how key 1470 is retrieved.

    $1250 \bmod 11 = 7$; $1381 \bmod 11 = 6$; $1452 \bmod 11 = 0$; $1613 \bmod 11 = 7$, a collision with 1250, so 1613 takes the next free position, 8; $1470 \bmod 11 = 7$ again, and positions 7 and 8 are full, so 1470 goes to 9. To retrieve 1470: calculate $7$, read position 7 (key 1250, no match), read 8 (1613, no), read 9 (1470, found). If an empty position is reached before a match, the record is not in the file. Collisions are the price of a small file: a good hashing algorithm spreads the keys evenly, and the file is kept well below full so that probes stay short.

    Explore

    A hash table

    Watch each key get hashed to a bucket. A good hash spreads keys out so lookups stay fast.

    Vocabulary Train
    English Chinese Pinyin
    linked list 链表 liàn biǎo
    hash function 散列函数 sàn liè hán shù
    deterministic 确定性 què dìng xìng
    collision 冲突 chōng tū
    linear probing 线性探测 xiàn xìng tàn cè
    chaining 链接法 liàn jiē fǎ
    load factor 装填因子 zhuāng tián yīn zi
    overflow area 溢出区 yì chū qū
    13.3

    Floating-point numbers

    Syllabus
    Candidates should be able to: Notes and guidance
    Describe the format of binary floating-point real numbers Use two's complement form Understand of the effects of changing the allocation of bits to mantissa and exponent in a floating-point representation
    Convert binary floating-point real numbers into denary and vice versa
    Normalise floating-point numbers Understand the reasons for normalisation
    Show understanding of the consequences of a binary representation only being an approximation to the real number it represents (in certain cases) Understand how underflow and overflow can occur
    Show understanding that binary representations can give rise to rounding errors

    Source: Cambridge International syllabus

    To store real numbers of very different sizes, computers use a floating-point 浮点 format — a binary form of scientific notation, with two fields:

    • a mantissa 尾数 — the significant digits.
    • an exponent 指数 — the power of 2 to multiply by.

    Both are stored as two's complement 补码 integers. The value is

    $$\text{number} = \text{mantissa} \times 2^{\text{exponent}}.$$

    Read the mantissa as a binary fraction — the first bit after the point is worth $1/2$, the next $1/4$, then $1/8$, and so on. So 0.1010000 is $1/2 + 1/8 = 0.625$; with exponent 00000010 (= 2) the value is $0.625 \times 2^{2} = 2.5$.

    Two bytes of place values: an 8-bit mantissa with a sign bit and fractions from one half to one over 128, and an 8-bit two's-complement exponent from minus 128 to 1
    The place values of an 8-bit mantissa and an 8-bit exponent

    Converting

    • binary → denary: read the mantissa (use two's-complement rules if negative) as a fraction, read the exponent as a signed integer, then multiply mantissa by $2^{\text{exponent}}$.
    • denary → binary: write the number as a binary fraction × a power of 2, then store the mantissa and exponent in the agreed formats.

    Worked example. A number has mantissa 10110000 and exponent 00000011. Find its denary value.

    The exponent 00000011 is $+3$. The mantissa begins with a 1, so it is negative. Read as 1.0110000 in two's complement, the sign bit is worth $-1$ and the fraction bits add $\tfrac{1}{4} + \tfrac{1}{8} = 0.375$, so the mantissa is $-1 + 0.375 = -0.625$. Then

    $$\text{number} = -0.625 \times 2^{3} = -5.0.$$

    Worked example. Store $+2.5$ in this format.

    In binary $2.5 = 10.1$. Written as a normalised fraction, $2.5 = 0.101 \times 2^{2}$. So the mantissa is 01010000 (sign bit 0, then .101) and the exponent is 00000010 ($= 2$).

    The exam's format: two's complement, a mantissa and an exponent

    The exam states a format such as 10 bits for the mantissa and 6 bits for the exponent, both in two's complement. The mantissa's binary point sits after its first (sign) bit, so a positive mantissa is 0.xxxxxxxxx and a negative one 1.xxxxxxxxx; the exponent is an ordinary signed integer. Every conversion uses the same three moves: read the mantissa as a fraction (two's-complement rules if it starts with 1), read the exponent as an integer, multiply by $2^{\text{exponent}}$.

    Worked example (binary to denary). Mantissa 0101100000, exponent 000011.

    Mantissa: $0.101100000_2 = \tfrac{1}{2} + \tfrac{1}{8} + \tfrac{1}{16} = 0.6875$. Exponent: $000011_2 = 3$. Value: $0.6875 \times 2^{3} = 5.5$.

    Worked example (negative mantissa). Mantissa 1011000000, exponent 000010.

    The mantissa starts with 1, so it is negative. Its value is $-1 + 0.011000000_2 = -1 + (\tfrac{1}{4} + \tfrac{1}{8}) = -0.625$; exponent $= 2$; value $-0.625 \times 4 = -2.5$. (Alternatively, take the two's complement of the mantissa, 0101000000 $= 0.625$, and attach the minus sign.) A negative exponent such as 111110 $= -2$ divides instead: a mantissa of $0.5$ with that exponent is $0.5 \times 2^{-2} = 0.125$.

    Worked example (denary to binary). Store $+6.5$ and $-6.5$ in the 10-bit and 6-bit format, normalised.

    $6.5 = 110.1_2 = 0.1101_2 \times 2^{3}$, so the mantissa is 0110100000 and the exponent 000011. For $-6.5$, take the two's complement of the mantissa: 1001100000 (check: $-1 + 0.0011_2 = -1 + 0.1875 = -0.8125$, and $-0.8125 \times 8 = -6.5$), exponent 000011 unchanged. The sign never goes into the exponent; a negative number has a negative mantissa.

    Normalisation

    A number is normalised 规格化 when the first significant bit is immediately after the binary point (no wasted leading zeros). This maximises precision, because every mantissa bit carries information. To normalise, shift the mantissa left and decrease the exponent (or shift right and increase it) until the first significant bit is in place; the value is unchanged. For negative (two's-complement) mantissas, the sign bit (1) is followed immediately by a 0.

    Recognising and producing normalised form. A positive normalised mantissa begins 01; a negative one begins 10. So 0011000000 is not normalised (shift left one place and subtract one from the exponent: 0110000000, exponent one less) and 1100000000 is not either (shift left until the pattern is 10...). Each shift left of the mantissa must be matched by subtracting one from the exponent, or the value changes.

    "Explain why numbers are stored in normalised form" (two marks). (1) It gives the maximum precision (accuracy) for the number of bits available, because no bits are wasted on leading zeros (or leading ones for a negative number); (2) each number then has a unique representation, so numbers can be compared; and (3) it makes the best use of the available range. Any two of these score.

    Normalising 0.0011010 with exponent 4: shift the mantissa left two places and decrease the exponent by 2, giving 0.1101000 with exponent 2 — the same value, with no wasted leading zeros
    Normalising: shift the mantissa left to remove leading zeros, lowering the exponent by the same amount

    Approximation and rounding errors

    Many denary reals cannot be stored exactly in binary — e.g. $0.1_{10}$ is the repeating binary fraction $0.000110011\ldots_{2}$, which must be truncated. Consequences:

    • rounding errors 舍入误差 build up over many operations (0.1 + 0.2 is not exactly 0.3).
    • comparisons fail — test ABS(x - 0.3) < 1e-9 instead of x = 0.3.
    • subtracting two nearly-equal values loses precision.
    • overflow 溢出 (a result too large for the exponent's range) and underflow 下溢 (a result too small, rounding to zero) occur when the exponent runs out of range.

    For exact needs (currency), use fixed-point 定点 or BCD 二进码十进数 instead of floating-point.

    Three 16-bit words split differently between mantissa and exponent: twelve and four bits for precision with a small range, eight and eight for balance, four and twelve for a huge range with coarse values
    The same total of bits shared two ways: mantissa bits buy precision, exponent bits buy range, and one can only grow at the other's expense

    "Describe the effect of changing the allocation of bits" (three marks). With a fixed total number of bits, increasing the mantissa and reducing the exponent gives greater precision 精度 (more significant figures, smaller rounding errors) but a smaller range 范围 (the largest and smallest magnitudes that can be stored shrink); increasing the exponent does the opposite: a larger range at the cost of precision. Name both effects and both directions.

    Largest and smallest. In the 10-bit mantissa, 6-bit exponent format the largest positive number has mantissa 0111111111 ($= 1 - 2^{-9}$) and exponent 011111 ($= 31$): about $2^{31}$. The smallest positive normalised number has mantissa 0100000000 ($= 0.5$) and exponent 100000 ($= -32$): $0.5 \times 2^{-32} = 2^{-33}$. The most negative number has mantissa 1000000000 ($= -1$) and exponent $31$: $-2^{31}$.

    "Explain what is meant by overflow and underflow." Overflow occurs when the result of a calculation is larger than the largest number that can be represented, so the exponent would need more bits than it has; underflow occurs when a result is smaller than the smallest (non-zero) number that can be represented, too close to zero for the exponent to express, so it is stored as zero. Both come from the exponent's range, not the mantissa's.

    Why a binary representation is only an approximation. A binary fraction can only represent sums of $\tfrac{1}{2}, \tfrac{1}{4}, \tfrac{1}{8}, \ldots$ exactly; a value such as $0.1$ or $\tfrac{1}{3}$ has an infinite binary expansion, and the mantissa has a fixed number of bits, so the stored value is the nearest one that fits. The difference is a rounding error; it is small for one number but accumulates over repeated calculations (adding $0.1$ ten times may not give exactly $1$), which is why real numbers should never be tested for exact equality.

    Explore

    Build a floating-point number

    Flip the mantissa and exponent bits to make a value, and check whether it is normalised.

    Explore

    Normalising a floating-point number

    Step through normalisation. Shifting the mantissa to remove wasted leading zeros — and adjusting the exponent to match — keeps the value the same but spends every bit on precision.

    Vocabulary Train
    English Chinese Pinyin
    overflow 溢出 yì chū
    floating-point 浮点 fú diǎn
    mantissa 尾数 wěi shù
    exponent 指数 zhǐ shù
    two's complement 补码 bǔ mǎ
    normalised 规格化 guī gé huà
    rounding errors 舍入误差 shě rù wù chā
    underflow 下溢 xià yì
    fixed-point 定点 dìng diǎn
    BCD 二进码十进数 èr jìn mǎ shí jìn shù
    precision 精度 jīng dù
    range 范围 fàn wéi
    Watch lesson Exercise sheet
    13.3

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    user-defined data type a data type defined by the programmer, based on existing types, to represent data specific to the problem
    non-composite type a type defined without reference to another type; it holds a single value (integer, real, enumerated, pointer)
    composite type a type made up of other types; it holds several values under one identifier (record, set, array, class)
    enumerated type a non-composite type defined by listing all its possible values, in order
    pointer type a non-composite type whose value is the memory address of a variable of a given type
    set a composite type holding a collection of values of one type, unordered and without duplicates
    record a composite type with a fixed number of fields, each with its own identifier and type, accessed by dot notation
    class a composite type combining attributes (data) with the methods (procedures and functions) that act on them; an object is an instance of a class
    serial file records stored one after another in the order in which they were added
    sequential file records stored one after another in order of a key field
    random file records stored at addresses calculated from their keys by a hashing algorithm
    sequential access reading the records in turn from the start of the file until the one required is found
    direct access calculating the address of a record from its key and going straight to that position
    hashing algorithm a calculation on the key of a record that gives the address at which the record is stored and found
    collision two different keys producing the same address
    mantissa the part of a floating-point number that holds its significant bits, as a two's-complement fraction
    exponent the two's-complement integer giving the power of two by which the mantissa is multiplied
    normalised a floating-point number whose mantissa begins 01 (positive) or 10 (negative), so no bits are wasted on leading zeros or ones
    overflow a result too large to be represented in the number of bits available
    underflow a non-zero result too small to be represented, so it is stored as zero
    rounding error the difference between a real number and the nearest value that the binary representation can hold
    13.3

    Exam tips

    • Pseudocode declarations are marked line by line: TYPE ... = (...) for enumerated, TYPE ... = ^... for pointer, TYPE ... = SET OF ... then DEFINE ... (...) : ... for a set, TYPE ... DECLARE ... ENDTYPE for a record, CLASS ... PRIVATE ... PUBLIC PROCEDURE NEW ... ENDCLASS for a class.
    • Match the type to the data: fixed named values, enumerated; a group of different fields, record; a collection of unique values, set; data plus behaviour, class; an address, pointer.
    • File organisation is how records are stored; file access is how they are found. Serial and sequential are read sequentially; random files use direct access via a hash of the key. Sequential search of a sequential file can stop early; of a serial file it cannot.
    • Random-file pseudocode: OPENFILE ... FOR RANDOM, SEEK before every GETRECORD or PUTRECORD, CLOSEFILE at the end. Say how a collision is resolved when you describe hashing.
    • Floating point: mantissa as a two's-complement fraction (point after the sign bit), exponent as an integer, multiply by $2^{\text{exponent}}$; shift left and subtract one from the exponent to normalise; the mantissa buys precision, the exponent buys range.
    • The three "explain" stock answers: why normalise (precision, unique form, range), the effect of re-allocating bits (precision against range), and why $0.1$ cannot be stored exactly (an infinite binary fraction in a finite mantissa).

    Common mistakes

    • Writing DECLARE instead of TYPE for a new type, or leaving out ENDTYPE; declaring a set without SET OF, or an enumerated type with quotation marks round its values.
    • Putting the sign of a floating-point number in the exponent; the sign is the first bit of the mantissa.
    • Reading a negative mantissa as if it were sign-and-magnitude; it is two's complement, so 1011000000 is $-0.625$, not $-0.375$.
    • Shifting the mantissa to normalise without changing the exponent, or changing it the wrong way (shift left, exponent down).
    • Describing a random file as "in random order"; the records are at addresses computed from their keys.
    • Saying sequential access reads "the whole file" for a sequential file; it stops when a larger key is met.
    • Explaining hashing without saying what the calculated value is used for (the address to store and retrieve the record), or without a way of handling collisions.
    • Defining overflow as "too many digits" instead of a result beyond the largest representable value, or blaming the mantissa for it.
  • 14

    Communication and internet technologies

    14.1

    Why protocols are needed

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of why a protocol is essential for communication between computers
    Show understanding of how protocol implementation can be viewed as a stack, where each layer has its own functionality
    Show understanding of the TCP/IP protocol suite Four Layers (Application, Transport, Internet, Link) Purpose and function of each layer Application when a message is sent from one host to another on the internet
    Show understanding of protocols (HTTP, FTP, POP3, IMAP, SMTP, BitTorrent) and their purposes BitTorrent protocol provides peer-to-peer file sharing

    Source: Cambridge International syllabus

    A protocol 协议 is a set of rules for how devices communicate. Both ends must follow the same rules, or one side's signals are meaningless to the other. Protocols define the format of the data (where addresses and payload sit), the order of messages (who speaks first, when to acknowledge), the meaning of each message, the timing (timeouts, retransmits), and what to do on error. Without an agreed protocol, communication fails — like two people speaking different languages with no translator.

    "Explain why protocols are essential for communication between computers" (three marks). (1) A protocol is a set of rules agreed by both the sender and the receiver; (2) without it the two computers would interpret the data differently (format, order, meaning of each part), so the message could not be understood; (3) it allows computers of different types and manufacturers to communicate, because everyone implements the same standard. Mention what the rules cover: the format of the data, the order of messages, error detection and recovery, and speed or timing.

    Two devices following the same rules: format, order, timing and what to do on error
    A protocol is the shared rules: format, order, timing and errors
    Vocabulary Train
    English Chinese Pinyin
    protocol 协议 xié yì
    Exercise sheet
    14.1

    Layered protocols

    Networking is complex, so it is split into layers, each with one focused job, talking only to the layer above and below. Benefits: modularity 模块化 (replace one layer — say Ethernet with Wi-Fi — without touching the others), standardisation (vendors interoperate), and abstraction 抽象 (you ignore details handled elsewhere). The internet uses the TCP/IP protocol suite 协议栈 (4 layers).

    Vocabulary Train
    English Chinese Pinyin
    layers céng
    modularity 模块化 mó kuài huà
    abstraction 抽象 chōu xiàng
    protocol suite 协议栈 xié yì zhàn
    14.1

    TCP/IP protocol suite

    Layer Purpose Examples
    Application what the user program does HTTP, FTP, SMTP, IMAP
    Transport end-to-end delivery between processes TCP, UDP
    Internet routing packets between networks IP
    Link sending bits over the physical medium Ethernet, Wi-Fi
    A four-row stack: Application, Transport, Internet, Link, with sending going down the left and receiving going up the right, and example protocols on each layer
    The four layers of the TCP/IP protocol suite

    The purpose of each layer, as the mark scheme words it. Application layer: provides the protocols that user applications use (HTTP for the web, SMTP for email) and the interface between the application and the network; it produces the data to be sent and passes it to the transport layer. Transport layer: establishes the end-to-end connection, splits the data into packets (segments) and adds port numbers and sequence numbers; on receipt it reassembles the packets in order and requests any that are missing (TCP), or sends without those guarantees (UDP). Internet layer: adds the source and destination IP addresses to form IP packets (datagrams) and routes them across networks via routers; it does not guarantee delivery. Link layer: adds the MAC addresses and error-check bits to form a frame and transmits the bits over the physical local network (Ethernet or Wi-Fi) through the network interface card. "Complete the stack" means these four, in this order, from the top: Application, Transport, Internet, Link.

    Sending a message down the TCP/IP stack: the application's message is wrapped by a TCP header carrying ports and a sequence number, then by an IP header carrying the source and destination IP addresses, then by a frame header carrying MAC addresses and a check field; the receiver strips them in the reverse order
    Encapsulation: each layer adds its own header 首部 to what it receives from the layer above, so the bits on the wire carry four sets of information; the receiver removes them one layer at a time

    "Describe how the TCP/IP suite is applied when a message is sent from one host to another" (five marks). At the sender the message passes down the stack: (1) the application layer produces the data using a protocol such as HTTP or SMTP; (2) the transport layer splits it into packets and adds a header with the port numbers and a sequence number; (3) the internet layer adds a header with the source and destination IP addresses and chooses the route; (4) the link layer adds the MAC addresses of the next device and sends the frame over the physical link. Routers along the way read the internet-layer header and forward each packet. At the receiver the frame passes up the stack: each layer removes and acts on its own header, the transport layer reassembles the packets in sequence-number order and asks for any that are missing, and the application layer presents the message. The same protocol at each layer at both ends is what makes the exchange work.

    Application layer

    The application layer 应用层 gives services to user programs and defines the protocols they speak (HTTP for web, SMTP for email). This is where a programmer most often works.

    Transport layer

    The transport layer 传输层 delivers data end-to-end between processes, identified by port numbers 端口号. Two protocols:

    TCP sets up a connection and delivers all data in order; UDP sends and forgets
    TCP connects and delivers in order; UDP sends and forgets
    • TCP 传输控制协议connection-oriented 面向连接: sets up a connection, ensures all data arrives in order, retransmits lost packets 数据包, controls flow. Reliable but with overhead. Used by HTTP, HTTPS, SMTP, FTP.
    • UDP 用户数据报协议connectionless 无连接: sends and forgets, with no acknowledgements or ordering. Low overhead, no guarantees. Used for streaming, DNS and gaming, where speed beats reliability.

    Internet layer

    The internet layer 网络层 carries packets between hosts using IP. Each packet has a source and destination IP address IP地址, and routers 路由器 forward it onward. It does not guarantee delivery — that is TCP's job.

    A home router does this job for your house: it reads each packet's destination address and sends it on towards the internet, and back to the right device.

    A black home Wi-Fi router with four upright antennas and a row of status lights along the front
    A home Wi-Fi router: it forwards packets between your devices and the internet

    Before the router reaches the wider internet, a modem 调制解调器 connects the home to the internet provider over the provider's cable or phone line. Its lights show the link is up and online.

    A tall black cable modem standing upright on a plain background, with a column of status lights down its front
    A cable modem connects a home network to the internet provider

    Link layer

    The link layer 链路层 sends bits over one physical link (Ethernet, Wi-Fi). It adds a frame header with MAC addresses MAC地址 and handles medium access (e.g. CSMA/CD 载波侦听多路访问/冲突检测 on Ethernet).

    An Ethernet frame split into preamble, start of frame, Ethernet data and interpacket gap, with the data part expanded into destination and source MAC addresses, type/length, payload message and frame check sequence, each with its size in bytes
    The parts of a typical Ethernet frame

    On a wired local network, a switch 交换机 joins many devices together. Each device plugs into a port with an Ethernet cable (an RJ45 plug), and the switch uses the MAC addresses in each frame to send it only to the correct port.

    A small black 8-port Gigabit Ethernet switch on a plain background, its numbered RJ45 ports in a row along the front, each with a status light
    A network switch connects many wired devices on a local network

    The physical link can be a copper wire, a radio signal (Wi-Fi), or a fibre-optic cable 光纤. In a fibre-optic cable, the bits travel as flashes of light through very thin strands of glass, which is fast and carries data a long way.

    A bundle of fibre-optic strands fanning out against a dark background, each thin glass strand glowing with a point of blue-white light at its tip
    A fibre-optic cable: data travels as light through thin glass strands

    A radio link can reach much further. A satellite dish 卫星天线 sends and receives radio signals to and from a satellite, carrying data to places that wired links cannot easily reach.

    A round grey home satellite dish mounted on a house wall beside a window, with its feed arm reaching out to the front
    A satellite dish sends and receives data by radio over a long distance
    Explore

    Tap the four layers of the TCP/IP model

    Explore each layer. Data travels DOWN the stack as it's sent (each layer adds its header) and back UP as it's received — and any layer can be swapped without touching the others.

    Vocabulary Train
    English Chinese Pinyin
    application layer 应用层 yìng yòng céng
    transport layer 传输层 chuán shū céng
    port numbers 端口号 duān kǒu hào
    TCP 传输控制协议 chuán shū kòng zhì xié yì
    connection-oriented 面向连接 miàn xiàng lián jiē
    packets 数据包 shù jù bāo
    UDP 用户数据报协议 yòng hù shù jù bào xié yì
    connectionless 无连接 wú lián jiē
    internet layer 网络层 wǎng luò céng
    routers 路由器 lù yóu qì
    modem 调制解调器 tiáo zhì jiě tiáo qì
    link layer 链路层 liàn lù céng
    CSMA/CD 载波侦听多路访问/冲突检测 zài bō zhēn tīng duō lù fǎng wèn / chōng tū jiǎn cè
    switch 交换机 jiāo huàn jī
    fibre-optic cable 光纤 guāng xiān
    satellite dish 卫星天线 wèi xīng tiān xiàn
    IP address IP地址 IP dì zhǐ
    MAC addresses MAC地址 MAC dì zhǐ
    header 首部 shǒu bù
    14.1

    Common application-layer protocols

    • HTTP 超文本传输协议 — browsers fetch web pages from servers (over TCP, port 80). HTTPS is HTTP over TLS — encrypted, port 443.
    • FTP 文件传输协议 — transfer files between client and server.
    • SMTP 简单邮件传输协议send email between client and server, and between servers. Receiving uses POP3 or IMAP.
    • POP3 — downloads email and usually deletes it from the server. IMAP — leaves email on the server and syncs across devices, so the same inbox appears everywhere.
    • BitTorrent — a peer-to-peer 对等网络 protocol; a file is split into pieces downloaded from many peers in parallel, so no single server carries all the load.
    A tracker in the centre with peers around it — seeds, leeches and new peers — exchanging file pieces, with a key
    BitTorrent: a tracker helps peers find each other, then they share file pieces directly

    The purpose of each protocol, in the words that score.

    Protocol Purpose (state this)
    HTTP transfers web pages (hypertext) between a web server and a browser; HTTPS is the encrypted version
    FTP transfers files between a client and a server (uploading to and downloading from a file server)
    SMTP sends email from a client to a mail server, and between mail servers (a "push" protocol)
    POP3 downloads email from the server to the client, usually deleting it from the server, so it is read on one device
    IMAP lets the client read and manage email that stays on the server, so the same mailbox is seen on every device
    BitTorrent shares files peer-to-peer: pieces of a file are downloaded from, and uploaded to, many other users at once

    Asked for the two email protocols, give SMTP for sending and POP3 or IMAP for receiving; asked to describe IMAP, say that the messages remain on the server and are synchronised across devices, which is the difference from POP3.

    "Describe how files are shared using the BitTorrent protocol" (four marks). (1) The file is split into pieces (typically 256 KB each), and a small torrent file describes them (their hashes) and names a tracker 追踪器. (2) A peer wanting the file contacts the tracker, which keeps a list of the peers in the swarm currently sharing that file. (3) The peer downloads different pieces from many peers at the same time, and as soon as it holds a piece it uploads it to others; a peer with the whole file is a seed 种子, one still downloading a leech. (4) When all pieces are in, they are reassembled and checked against the hashes. "Explain what peer-to-peer file sharing means": there is no central server holding the file; every computer is both a client and a server, downloading from and uploading to the others, so the load and the bandwidth are spread across the swarm and the more peers there are, the faster it gets.

    Explore

    Network route lab

    Follow data from a device through network hardware and protocols.

    Vocabulary Train
    English Chinese Pinyin
    HTTP 超文本传输协议 chāo wén běn chuán shū xié yì
    FTP 文件传输协议 wén jiàn chuán shū xié yì
    SMTP 简单邮件传输协议 jiǎn dān yóu jiàn chuán shū xié yì
    peer-to-peer 对等网络 duì děng wǎng luò
    tracker 追踪器 zhuī zōng qì
    swarm qún
    seed 种子 zhǒng zi
    bandwidth 带宽 dài kuān
    14.2

    Circuit switching vs packet switching

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of circuit switching Benefits, drawbacks and where it is applicable
    Show understanding of packet switching Benefits, drawbacks and where it is applicable Show understanding of the function of a router in packet switching Explain how packet switching is used to pass messages across a network, including the internet

    Source: Cambridge International syllabus

    Circuit switching

    A dedicated path is set up between the two ends before any data is sent (circuit switching 电路交换), reserved for the whole conversation, then released. It gives reserved bandwidth 带宽 and in-order delivery, but is inefficient during silences and slow to set up. Classic example: the traditional telephone network.

    A mesh of routers between device A and device B, with one path highlighted and reserved end-to-end for the whole call
    Circuit switching: one dedicated path is reserved end to end

    "Describe circuit switching as a method of data transmission" (three marks). (1) A dedicated path (circuit) is set up between the sender and the receiver before any data is sent; (2) the whole message is sent along that path, in order, as one continuous stream; (3) the circuit is reserved for the duration of the communication and released afterwards.

    Benefits and drawbacks. Benefits: the full bandwidth of the circuit is available and guaranteed; data arrives in order with no reassembly and no delay once the circuit is up; the route does not change, so timing is predictable (good for real-time voice and video). Drawbacks: time is spent setting up the circuit before anything is sent; the circuit is reserved even while no data is flowing, so bandwidth is wasted and other users cannot share it; both ends must be free at the same time; a failure anywhere on the path breaks the whole call, and there is no automatic alternative route. Where it is appropriate: a telephone call or a live video link, where a steady, uninterrupted stream matters more than efficiency.

    Packet switching

    The data is split into packets, each sent independently (packet switching 分组交换). Each packet carries the destination address; routers make per-packet decisions, so packets may take different routes and arrive out of order, and the destination reassembles them. It is efficient (one link is multiplexed 多路复用 across many conversations), robust (reroute around a failure), but has variable latency 延迟 and possible loss (TCP handles reliability). Used by the internet.

    The same router mesh with packets shown as numbered coloured squares taking different routes from computer A to computer B, then reassembled in order at B
    Packet switching: packets travel independently and may take different routes
    The parts of a packet: a header holding the source and destination addresses, the sequence number, the packet count and a checksum, followed by the payload that carries this packet's share of the data
    What lets a packet travel on its own: the addresses say where, the sequence number says which part of the message it is, and the checksum shows whether it arrived undamaged

    "Describe how packet switching is used to pass messages across a network" (four marks). (1) The message is split into packets of a fixed maximum size; (2) each packet is given a header containing the source and destination addresses, a sequence number 序号 and an error check; (3) each packet is sent independently and may take a different route, chosen by the routers it meets; (4) at the destination the packets are reassembled in order using the sequence numbers, and any missing packet is requested again. If the question excludes checking and resending, leave out the last clause.

    "Describe the function of a router in packet switching" (three marks). A router receives a packet, reads the destination IP address in its header, and consults its routing table 路由表 to decide the best next hop towards that destination, taking account of the traffic (congestion) and failed links; it then forwards the packet onto that link. Packets of the same message may leave by different routes; the router holds packets in a queue when a link is busy.

    "Describe two ways packet switching ensures the complete message is received." (1) Each packet carries a sequence number, so the receiver can put the packets in order and can tell that one is missing, and (2) the receiver sends an acknowledgement 确认 for packets that arrive; a packet not acknowledged within a time limit is retransmitted by the sender. A checksum 校验和 in each packet lets the receiver detect a corrupted packet and discard it, which then triggers the resend.

    Benefits and drawbacks. Benefits: no circuit to set up; the network's links are shared by many messages, so bandwidth is used efficiently; packets can be rerouted around a failed or congested link, so transmission is robust; a lost or damaged packet means resending only that packet, not the whole message. Drawbacks: packets may arrive out of order and must be reassembled, and some may be lost or delayed; the headers add overhead; the variable delay makes it less suitable for real-time voice and video without extra measures; a heavily loaded network drops packets. Where it is appropriate: email, web pages, file downloads and any "bursty" traffic, and the internet in general.

    Aspect Circuit switching Packet switching
    Path dedicated, reserved shared, per-packet
    Setup time slow none
    Bandwidth use inefficient efficient
    Order in order may be out of order
    Robustness one failure cuts the circuit reroute around failures
    Suits constant-rate flows (voice) bursty flows (web, email)

    Modern networks use packet switching for its efficiency and resilience.

    Four differences, stated as pairs. (1) Circuit switching sets up a dedicated path before sending; packet switching sends without setting up a path. (2) In circuit switching the whole message follows one route; in packet switching the packets may take different routes. (3) Circuit switching delivers the data in order without reassembly; packet switching needs sequence numbers to reassemble it. (4) Circuit switching reserves bandwidth for one conversation even when idle; packet switching shares the links between many messages. (Also acceptable: a failed link breaks a circuit but packets are rerouted; circuit switching suits real-time streams, packet switching suits bursty data.) Write each difference as both halves; one side alone earns nothing.

    Describing packet switching in a few sentences

    A good exam answer: "The message is broken into small packets. Each packet carries the destination and source addresses and a sequence number. Each packet travels through the network independently, with routers choosing the next hop per packet. Packets may take different paths and arrive out of order. The destination uses the sequence numbers to reassemble the message, and missing packets can be requested again."

    Worked example. A phone call and a large file download share a network. Which switching method suits each, and why? A phone call needs a steady stream with low delay, and it would suffer badly if pieces arrived late or out of order - so circuit switching suits it: a dedicated path is set up for the whole call and its capacity is reserved for the duration. A file download does not care about timing or arrival order, because the receiver reassembles it, and it benefits from using whatever capacity happens to be spare - so packet switching suits it: the file is split into packets that travel independently, each carrying source and destination addresses and a sequence number, with routers choosing a next hop per packet. Name the property of the traffic that decides it: reserved capacity and low delay for the call, efficiency and resilience for the download.

    Explore

    A packet's journey across the internet

    Step through packet switching. The message is split up, each packet finds its own way, and the destination puts them back together — which is why the internet is so efficient and hard to break.

    Vocabulary Train
    English Chinese Pinyin
    circuit switching 电路交换 diàn lù jiāo huàn
    reserved bandwidth 带宽 dài kuān
    packet switching 分组交换 fēn zǔ jiāo huàn
    multiplexed 多路复用 duō lù fù yòng
    variable latency 延迟 yán chí
    sequence number 序号 xù hào
    routing table 路由表 lù yóu biǎo
    acknowledgement 确认 què rèn
    checksum 校验和 jiào yàn hé
    latency 延迟 yán chí
    Watch lesson Exercise sheet
    14.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    protocol a set of rules governing how data is transmitted, agreed by sender and receiver so that both interpret it the same way
    protocol stack the layers of protocols, each with its own function, that together carry out communication; each layer communicates only with the layers above and below
    application layer provides the protocols used by applications to exchange data (HTTP, SMTP, FTP, IMAP, POP3)
    transport layer establishes end-to-end communication, splits data into packets with port and sequence numbers, reassembles them and requests missing ones (TCP), or sends without guarantees (UDP)
    internet layer adds IP addresses to form packets and routes them between networks via routers
    link layer adds MAC addresses to form frames and transmits the bits over the physical local network
    router a device that reads a packet's destination address and forwards it along the best available route towards that destination
    circuit switching a dedicated communication path is established between the two ends before data is sent and held for the whole transmission
    packet switching the message is split into packets, each with a header, sent independently over possibly different routes and reassembled at the destination
    packet a unit of data carrying a header (addresses, sequence number, error check) and a payload
    peer-to-peer file sharing without a central server, each computer acting as both client and server
    14.2

    Exam tips

    • Why protocols: shared rules, same interpretation, any make of computer. Why layers: each layer has one job and can be changed independently.
    • The four layers in order, top to bottom: Application, Transport, Internet, Link. Give each layer's job in one sentence, and the "message from host to host" answer as a walk down the stack and back up.
    • Protocol purposes are one-liners: HTTP web pages, FTP files, SMTP sending mail, POP3 downloading mail, IMAP mail kept on the server, BitTorrent peer-to-peer pieces from a swarm.
    • Circuit switching: dedicated path first, whole message, held for the duration. Packet switching: split, header with addresses and sequence number, independent routes, reassemble. Benefits and drawbacks come in pairs of opposites.
    • A router reads the destination address, consults its routing table, forwards along the best route; it is the packet-switching question the exam asks most.
    • "Where appropriate": circuit switching for a phone or live video call; packet switching for email, the web and downloads.

    Common mistakes

    • Defining a protocol as "a language" or "software"; it is a set of rules.
    • Putting the layers in the wrong order, or giving the OSI seven layers instead of the four of TCP/IP.
    • Describing the transport layer as "routing" or the internet layer as "splitting into packets"; ports and splitting are transport, IP addresses and routing are internet.
    • Confusing POP3 with IMAP, or saying SMTP receives email.
    • Describing packet switching without the header (addresses and sequence number) or without reassembly.
    • Saying a router "sends the packet everywhere"; it chooses one next hop from its routing table.
    • Giving a benefit of packet switching as a drawback of circuit switching without stating the circuit-switching side; each difference needs both halves.
    • Claiming packet switching guarantees delivery by itself; the transport layer's sequence numbers and acknowledgements do that.
  • 15

    Hardware and Virtual Machines

    15.1

    RISC vs CISC processors

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of Reduced Instruction Set Computers (RISC) and Complex Instruction Set Computers (CISC) processors Differences between RISC and CISC Understand interrupt handling on CISC and RISC processors
    Show understanding of the importance/use of pipelining and registers in RISC processors
    Show understanding of the four basic computer architectures SISD, SIMD, MISD, MIMD
    Show understanding of the characteristics of massively parallel computers
    Show understanding of the concept of a virtual machine Give examples of the role of virtual machines Understand the benefits and limitations of virtual machines

    Source: Cambridge International syllabus

    Two styles of CPU design. The CPU itself plugs into the motherboard 主板, the main board that links the processor, the memory and every other part of the computer together.

    CISC has many complex variable-length instructions; RISC has few simple fixed-length ones
    CISC has many complex instructions; RISC has few simple ones
    A computer motherboard on a white background, showing the square CPU socket in the middle, the long memory slots, several expansion slots and the rows of I/O ports along one edge
    A motherboard links the CPU, memory and other parts together

    CISC

    A CISC 复杂指令集 (Complex Instruction Set Computers) has many, often complex instructions (one may do several memory accesses and operations), of variable length, so decoding is intricate. It does more per instruction in hardware. Examples: Intel x86.

    RISC

    A RISC 精简指令集 (Reduced Instruction Set Computers) has a small set of simple instructions, each doing one basic operation, all of fixed length (fast to decode). Only load and store touch memory; everything else is register 寄存器 to register. Programs are longer but each instruction is quick and predictable, which suits pipelining. Examples: ARM, RISC-V.

    Feature CISC RISC
    Instruction set many few
    Instruction length variable fixed
    Memory access many instructions only load/store
    Pipeline-friendly harder naturally
    Per-instruction cycles varies usually 1

    The trade-off is doing more per instruction (CISC) vs doing each instruction faster and more predictably (RISC). Modern Intel chips translate CISC instructions into simpler RISC-like micro-ops internally.

    "Identify four features of a RISC processor." Any four of: a small set of simple instructions; instructions of fixed length (one word); most instructions complete in one clock cycle; many general-purpose registers; only load and store instructions access memory (all arithmetic is register to register); hard-wired control (no microcode); designed for pipelining; the compiler does more of the work, so programs contain more instructions and need more memory. "Identify four features of a CISC processor." Any four of: a large set of instructions, many of them complex (one instruction may do several operations); instructions of variable length; instructions that take several clock cycles; fewer registers; instructions that can access memory directly; microprogrammed control; less suited to pipelining; shorter programs, so a simpler compiler and less memory. "Describe what is meant by RISC and CISC" (two marks each): name the expansion and give the defining idea (few simple single-cycle instructions; many complex multi-cycle instructions).

    Interrupt handling on the two designs. On a CISC processor the current instruction, however complex, is completed before the interrupt is serviced; the processor then saves the contents of its registers (including the program counter) on the stack, jumps to the interrupt service routine, and restores the registers afterwards. On a RISC processor with a pipeline, several instructions are part-way through at the moment the interrupt 中断 arrives, so the processor must either let every instruction in the pipeline finish, or discard (flush) the partly executed instructions and restart them after the interrupt; either way the pipeline is emptied, the registers are saved, and the service routine runs. The exam phrasing: "pipelining makes interrupt handling more complex, because the contents of the pipeline must be dealt with before the interrupt can be serviced".

    Vocabulary Train
    English Chinese Pinyin
    motherboard 主板 zhǔ bǎn
    CISC 复杂指令集 fù zá zhǐ lìng jí
    RISC 精简指令集 jīng jiǎn zhǐ lìng jí
    register 寄存器 jì cún qì
    interrupt 中断 zhōng duàn
    Exercise sheet
    15.1

    Pipelining

    A pipeline 流水线 processes instructions in overlapping stages, like an assembly line: Fetch → Decode → Execute (in the ALU 算术逻辑单元) → Memory access → Write back. Each stage works on a different instruction at once, so once the pipeline is full, one instruction completes per cycle. RISC's fixed-length, simple instructions make every stage take the same time. A pipeline can stall on a hazard 冒险 — a data hazard (an instruction needs a result not ready yet) or a control hazard (a branch makes the next address unknown).

    A Gantt chart of the five pipeline stages IF, ID, EX, MEM, WB across ten clock cycles, with six instructions A to F each shifted one cycle later so they overlap diagonally
    Pipelining overlaps the stages of six instructions, so one finishes each cycle

    RISC chips keep data in many registers because memory is slow and registers are fast; the compiler allocates values to registers wisely.

    "Describe the use of pipelining in RISC processors" (three marks). (1) The fetch–execute cycle is divided into stages (fetch, decode, execute, memory access, write back); (2) several instructions are in the pipeline at once, each at a different stage, so while one is being executed the next is being decoded and the one after fetched; (3) a new instruction is started, and one completed, in every clock cycle once the pipeline is full, which increases throughput 吞吐量 (the number of instructions completed per second), although each instruction still takes the same time on its own. Fixed-length single-cycle RISC instructions are what make the stages equal and the pipeline possible.

    Worked example. A processor uses five pipeline stages (IF, ID, OF, EX, WB). Four instructions enter the pipeline one after another. In which cycle does the last instruction complete, and how many cycles would the four take without pipelining?

    Instruction 1 occupies IF in cycle 1, ID in 2, OF in 3, EX in 4 and WB in 5; instruction 2 starts one cycle later and finishes in cycle 6; instruction 3 in cycle 7; instruction 4 in cycle 8. In general $n$ instructions through $k$ stages take $n + k - 1$ cycles, here $4 + 5 - 1 = 8$. Without pipelining each instruction takes all five cycles before the next starts: $4 \times 5 = 20$ cycles. The exam's table is filled by writing each instruction's stages diagonally, one column to the right of the previous instruction.

    A processor running this fast gives off a lot of heat, so a heat-sink 散热器 and fan sit on top of it. The metal fins spread the heat and the fan blows it away, keeping the CPU cool enough to work.

    A tower CPU cooler with a black fan in front, a tall stack of thin metal cooling fins, and copper heat-pipes running up from the flat base that touches the processor
    A CPU heat-sink and fan carry heat away from the processor
    Explore

    How pipelining fills up

    Step through the clock cycles. Once the pipeline is full, a new instruction finishes every cycle — even though each one still takes several stages — because the stages of different instructions overlap.

    Vocabulary Train
    English Chinese Pinyin
    pipeline 流水线 liú shuǐ xiàn
    ALU 算术逻辑单元 suàn shù luó jí dān yuán
    hazard 冒险 mào xiǎn
    throughput 吞吐量 tūn tǔ liàng
    heat-sink 散热器 sàn rè qì
    15.1

    Flynn's taxonomy

    Flynn's taxonomy 弗林分类 sorts computers by the number of instruction and data streams:

    • SISD — one instruction, one data stream (a traditional single core).
    • SIMD 单指令多数据 — one instruction works on many data items at once (GPUs, CPU vector extensions). Great for images, video, scientific arrays.
    • MISD — several operations on the same data; rare, mostly theoretical.
    • MIMD 多指令多数据 — many processors run different instructions on different data (multi-core CPUs, clusters). The most general.

    Describing the four architectures (two marks each). SISD: a single processor executes one instruction at a time on one item of data; no parallelism, the traditional von Neumann machine. SIMD: one instruction is applied simultaneously to many data items, by many processing elements acting in step; used for array and graphics processing. MISD: several processors apply different instructions to the same data; rarely used, for example a fault-tolerant system where several processors check one stream. MIMD: many processors, each executing its own instructions on its own data, independently; the multi-core computer and the cluster.

    A single control unit broadcasting one instruction stream to four processing units, each of which works on its own data item
    SIMD: many processors run the same instruction on different data

    A graphics card 显卡 (with its GPU) is a real example of SIMD hardware: it has thousands of small cores that run the same instruction on many pixels or numbers at once, which is why GPUs are so fast for images, video and machine learning.

    A graphics card on a white background, showing the large cooling fan over the GPU and the gold edge connector that plugs into the motherboard
    A graphics card: its GPU runs the same instruction on many data items at once (SIMD)
    Four independent processors, each fed by its own separate instruction stream from above and its own data item from below
    MIMD: each processor runs its own instructions on its own data
    Vocabulary Train
    English Chinese Pinyin
    Flynn's taxonomy 弗林分类 fú lín fēn lèi
    SIMD 单指令多数据 dān zhǐ lìng duō shù jù
    MIMD 多指令多数据 duō zhǐ lìng duō shù jù
    graphics card 显卡 xiǎn kǎ
    15.1

    Massively parallel computers

    A massively parallel 大规模并行 system uses thousands of processors on a fast network, each with its own memory (distributed memory 分布式内存), exchanging data by messages. It is MIMD, needs specially-written software (MPI, CUDA), and suits climate simulation, large machine learning 机器学习 training, and astrophysics. The largest supercomputers 超级计算机 are massively parallel.

    "Outline the characteristics of massively parallel computers" (three marks). A very large number of processors (thousands), each with its own memory, connected by a network (a high-speed interconnect or bus) so that they can pass messages to one another; they work simultaneously on parts of the same problem, so the problem must be written as a program that can be split into parts that run in parallel and combine their results. It is an MIMD arrangement.

    The processors live in tall server 服务器 racks, often filling a whole room (a data centre 数据中心), wired together so they can work on one big problem at the same time.

    A long row of black server racks on a raised white floor in a data centre, packed with equipment and cables
    Rows of servers in a data centre, like those used for massively parallel computing
    Vocabulary Train
    English Chinese Pinyin
    massively parallel 大规模并行 dà guī mó bìng xíng
    distributed memory 分布式内存 fēn bù shì nèi cún
    machine learning 机器学习 jī qì xué xí
    supercomputers 超级计算机 chāo jí jì suàn jī
    server 服务器 fú wù qì
    data centre 数据中心 shù jù zhōng xīn
    15.1

    Virtual machines

    A virtual machine 虚拟机 (VM) is a software emulation of a whole computer — the software inside sees a CPU, memory and disks that look real but are managed by host software.

    • a system VM runs a complete OS. A hypervisor 虚拟机监控器 creates and manages VMs, each booting its own guest OS. Uses: run different OSes on one machine; server consolidation; sandboxing 沙箱 (risky software runs isolated); snapshots.
    • a process (language) VM runs one program in portable bytecode 字节码 — the JVM (Java), the CLR (.NET), CPython. Benefits: portability ("write once, run anywhere"), runtime safety checks, and just-in-time compilation 即时编译 for near-native speed. The cost is an extra layer and needing the VM installed.
    A virtual machine stack: the physical hardware at the bottom, the host operating system above it, then the hypervisor, and above that three virtual machines, each holding a guest operating system with its own applications
    One real computer, several apparent ones: the host operating system and hypervisor share the hardware, and each guest operating system runs as if it had a machine of its own

    "Describe what is meant by a virtual machine" (two marks). A software emulation (implementation) of a computer system that runs on a host computer and behaves, to the programs running inside it, like a separate physical computer with its own processor, memory and storage. The host operating system 宿主操作系统 runs on the actual hardware, manages the real resources and (through the hypervisor) creates and controls the virtual machines; each guest operating system 客户操作系统 runs inside a virtual machine, manages the applications in it, and is unaware that its hardware is virtual.

    Benefits (give two). Several different operating systems can run on one machine at the same time; software can be tested on many systems without buying the hardware; a new computer system can be emulated and tried before it is built; each VM is isolated, so a crash or malware in one does not affect the host or the others; VMs can be copied, moved and backed up as files, and a server can be shared between many users, reducing hardware cost. Limitations (give two). A VM runs more slowly than the real hardware because every instruction passes through the emulation layer; it consumes the host's memory and processing power, so the host must be powerful; some hardware features or devices are not emulated exactly, so the tested software may behave differently on the real machine; licences are needed for each guest OS, and setting the system up needs expertise.

    Explore

    Computing concept lab

    Classify concrete examples by the computing idea they demonstrate.

    Vocabulary Train
    English Chinese Pinyin
    virtual machine 虚拟机 xū nǐ jī
    hypervisor 虚拟机监控器 xū nǐ jī jiān kòng qì
    sandboxing 沙箱 shā xiāng
    bytecode 字节码 zì jié mǎ
    just-in-time compilation 即时编译 jí shí biān yì
    host operating system 宿主操作系统 sù zhǔ cāo zuò xì tǒng
    guest operating system 客户操作系统 kè hù cāo zuò xì tǒng
    15.2

    Boolean algebra

    Syllabus
    Candidates should be able to: Notes and guidance
    Produce truth tables for logic circuits including half adders and full adders May include logic gates with more than two inputs
    Show understanding of a flip-flop (SR, JK) Draw a logic circuit and derive a truth table for a flip-flop Understand of the role of flip-flops as data storage elements
    Show understanding of Boolean algebra Understand De Morgan’s laws Perform Boolean algebra using De Morgan’s laws Simplify a logic circuit/expression using Boolean algebra
    Show understanding of Karnaugh maps (K-map) Understand of the benefits of using Karnaugh maps Solve logic problems using Karnaugh maps

    Source: Cambridge International syllabus

    The half adder: XOR + AND add two bits

    Boolean algebra 布尔代数 simplifies Boolean 布尔 expressions, which can equally be described by truth tables 真值表. Symbols: + for OR, · for AND (often omitted), an overbar for NOT.

    Key laws include commutative, associative and distributive (as in ordinary algebra), plus:

    • identity $A + 0 = A$, $A \cdot 1 = A$; null $A + 1 = 1$, $A \cdot 0 = 0$.
    • idempotent $A + A = A$; inverse $A + \overline{A} = 1$, $A \cdot \overline{A} = 0$.
    • De Morgan's laws 德摩根定律: $(A + B)' = A' \cdot B'$; $(A \cdot B)' = A' + B'$ — negate the whole, swap AND/OR, negate each operand.
    • absorption 吸收律: $A + AB = A$.

    Simplifying reduces the number of terms, so the resulting logic circuit has fewer gates. Example: $Z = AB + A\overline{B} = A(B + \overline{B}) = A$.

    The laws with their names (quote the name at each step when "show all working" is asked).

    Law OR form AND form
    identity $A + 0 = A$ $A \cdot 1 = A$
    null (annulment) $A + 1 = 1$ $A \cdot 0 = 0$
    idempotent $A + A = A$ $A \cdot A = A$
    complement (inverse) $A + \overline{A} = 1$ $A \cdot \overline{A} = 0$
    commutative $A + B = B + A$ $A \cdot B = B \cdot A$
    associative $A + (B + C) = (A + B) + C$ $A(BC) = (AB)C$
    distributive $A + BC = (A + B)(A + C)$ $A(B + C) = AB + AC$
    absorption $A + AB = A$ $A(A + B) = A$
    De Morgan $\overline{A + B} = \overline{A} \cdot \overline{B}$ $\overline{A \cdot B} = \overline{A} + \overline{B}$
    double negation $\overline{\overline{A}} = A$

    Worked example. Simplify $X = \overline{\overline{(A \cdot B)} \cdot \overline{(A + B)}}$, showing all working.

    $X = \overline{\overline{(A \cdot B)}} + \overline{\overline{(A + B)}}$ (De Morgan on the outer bar) $= A \cdot B + A + B$ (double negation) $= A + B$ (absorption, $A + AB = A$, applied with $A + B$ absorbing $AB$).

    Worked example. Simplify $(\overline{A + B}) \cdot (\overline{A} + B)$.

    $= \overline{A} \cdot \overline{B} \cdot (\overline{A} + B)$ (De Morgan) $= \overline{A}\,\overline{B}\,\overline{A} + \overline{A}\,\overline{B}\,B$ (distributive) $= \overline{A}\,\overline{B} + 0$ (idempotent, complement) $= \overline{A}\,\overline{B}$.

    Worked example. Simplify $Y = \overline{A}\,\overline{B}\,\overline{C} + \overline{A}\,\overline{B}\,C + A\,\overline{B}\,C$.

    $= \overline{A}\,\overline{B}(\overline{C} + C) + A\,\overline{B}\,C$ (distributive) $= \overline{A}\,\overline{B} + A\,\overline{B}\,C$ (complement, identity) $= \overline{B}(\overline{A} + AC)$ (distributive) $= \overline{B}(\overline{A} + C)$, using $\overline{A} + AC = (\overline{A} + A)(\overline{A} + C) = \overline{A} + C$. Applying De Morgan to a three-input term works the same way: $\overline{A + B + C} = \overline{A} \cdot \overline{B} \cdot \overline{C}$.

    Sum-of-products from a truth table. Take every row whose output is 1, write the AND of its inputs (a variable barred where it is 0), and OR the terms: a row with $A = 1, B = 0, C = 1$ gives $A\,\overline{B}\,C$. This is the sum-of-products 积之和 form the exam asks for, and it is the starting point for both algebraic simplification and the Karnaugh map.

    Explore

    Boolean algebra

    A·B, A+B, Ā …

    Boolean algebra is just these gates written as expressions — compare the truth tables.

    Explore

    Boolean truth tables

    Pick an operator and the inputs to build its truth table — the algebra behind logic circuits.

    Vocabulary Train
    English Chinese Pinyin
    Boolean algebra 布尔代数 bù ěr dài shù
    Boolean 布尔 bù ěr
    truth tables 真值表 zhēn zhí biǎo
    De Morgan's laws 德摩根定律 dé mó gēn dìng lǜ
    absorption 吸收律 xī shōu lǜ
    sum-of-products 积之和 jī zhī hé
    Watch lesson Exercise sheet
    15.2

    Karnaugh maps

    A Karnaugh map 卡诺图 (K-map) simplifies a Boolean expression by grouping adjacent 1s from a truth table. Columns and rows use Gray code 格雷码 order (00, 01, 11, 10) so adjacent cells differ in one variable.

    Place a 1 in each cell where the output is 1. Find rectangular groups of 1s whose sides are powers of 2 (1, 2, 4, 8), wrapping around edges if it makes a bigger group. The larger the group, the simpler the term: a group of 2 drops one variable, a group of 4 drops two, and so on — variables that change within the group disappear. OR the group terms together for the simplified expression. Cover every 1 using as few, as large, groups as possible.

    Worked example. A Karnaugh map for $A$ and $B$ has 1s in the cells $\overline{A}B$ and $AB$. Simplify. The two 1s are adjacent - they share the $B=1$ column - so group them as a rectangle of 2. Inside that group $B$ stays 1 throughout while $A$ changes from 0 to 1, and any variable that changes within a group disappears. So the group leaves simply $X = B$. Compare that with the sum of products read straight off the table, $\overline{A}B + AB$: the same circuit, two gates fewer. Two rules do most of the work - make each group as large as possible (a group of 2 drops one variable, 4 drops two, 8 drops three), and remember the map wraps around its edges, so the leftmost and rightmost columns are adjacent. That wrap is the grouping most candidates miss.

    Two Karnaugh maps: a three-variable map for a six-term expression with a red loop of four down the first two columns giving not A and a blue loop of four wrapping round the outer columns giving not B; and a four-variable map whose four corner ones form one wrap-around loop giving not B and not D
    Loops of 1, 2, 4 or 8 ones; the term for a loop keeps only the variables that do not change inside it. Edges join, so a loop may wrap round, and the four corners count as adjacent

    Building and reading a K-map. Label the columns $AB$ and the rows $C$ (or $CD$) in Gray-code order 00 01 11 10, so that neighbouring cells differ in one variable only. Put a 1 in every cell whose minterm appears in the expression (or whose truth-table row outputs 1). Then draw the fewest, largest loops that cover every 1: each loop must be a rectangle of $1, 2, 4$ or $8$ cells, loops may overlap, may wrap across the left–right and top–bottom edges, and the four corners together make a loop. For each loop write the variables that are constant inside it (barred if 0), and OR the loop terms: that is the optimal sum-of-products. Why use one? It gives the simplest expression without algebra, in a few steps, with less chance of error, and the same map suits three or four variables.

    Worked example. $Z = \overline{A}\,\overline{B}\,\overline{C} + \overline{A}\,\overline{B}\,C + \overline{A}\,B\,\overline{C} + \overline{A}\,B\,C + A\,\overline{B}\,\overline{C} + A\,\overline{B}\,C$.

    On the three-variable map the 1s fill columns 00, 01 and 10 in both rows. The loop of four over columns 00 and 01 has $A = 0$ throughout and $B$, $C$ both varying: term $\overline{A}$. The loop of four over columns 00 and 10 (wrapping round) has $B = 0$ throughout: term $\overline{B}$. So $Z = \overline{A} + \overline{B}$, which Boolean algebra confirms: $\overline{A}(\overline{B} + B) + \ldots = \overline{A} + \overline{B}$. Two loops of two would also be correct but not optimal; a loop is as large as the 1s allow.

    Worked example (four variables). A map has 1s only in its four corners: $\overline{A}\,\overline{B}\,\overline{C}\,\overline{D}$, $A\,\overline{B}\,\overline{C}\,\overline{D}$, $\overline{A}\,\overline{B}\,C\,\overline{D}$ and $A\,\overline{B}\,C\,\overline{D}$. Because the top and bottom rows are adjacent and so are the outer columns, the corners are one loop of four; $B = 0$ and $D = 0$ in all of them while $A$ and $C$ vary, so $Z = \overline{B}\,\overline{D}$.

    Vocabulary Train
    English Chinese Pinyin
    Karnaugh map 卡诺图 kǎ nuò tú
    Gray code 格雷码 gé léi mǎ
    15.2

    Half adder and full adder

    A half adder 半加器 adds two single bits $A$ and $B$, giving a sum $S$ and a carry 进位 $C$:

    A B S C
    0 0 0 0
    0 1 1 0
    1 0 1 0
    1 1 0 1

    So $S = A \text{ XOR } B$ and $C = A \text{ AND } B$. It ignores any carry-in — hence "half".

    A half adder block with inputs A and B and outputs sum and carry, beside its circuit where A and B feed an XOR gate giving the sum and an AND gate giving the carry
    A half adder, as a block and as a circuit of an XOR and an AND gate

    A full adder 全加器 adds three bits ($A$, $B$, carry-in), giving a sum and a carry-out: $S = A \text{ XOR } B \text{ XOR } C_{\text{in}}$. It can be built from two half adders plus an OR gate. Chaining full adders (each carry-out feeding the next carry-in) makes a multi-bit "ripple-carry" adder.

    Two half adders chained with an OR gate to add A, B and a carry-in: the first half adder takes A and B, the second adds the carry-in, and the OR gate combines the two carries into the carry-out
    A full adder is built from two half adders and an OR gate

    The full-adder truth table. With inputs $A$, $B$ and the carry-in $C_{\text{in}}$: the sum $S$ is 1 when an odd number of inputs is 1, and the carry-out is 1 when two or more inputs are 1.

    $A$ $B$ $C_{\text{in}}$ $S$ $C_{\text{out}}$
    0 0 0 0 0
    0 0 1 1 0
    0 1 0 1 0
    0 1 1 0 1
    1 0 0 1 0
    1 0 1 0 1
    1 1 0 0 1
    1 1 1 1 1

    The circuit questions the exam sets. Given a circuit of an XOR and an AND gate sharing two inputs, or two half adders and an OR gate, "complete the truth table (show your working)" means adding a column for every intermediate gate output and filling the rows in order; "state the name of the circuit" is half adder or full adder; "state the purpose of each output" is the sum of the bits and the carry to the next column. Sum-of-products for the half adder: $S = \overline{A}B + A\overline{B}$, $C = AB$. A chain of full adders, each passing its carry-out to the next carry-in, adds two multi-bit numbers.

    Explore

    The gates inside an adder

    A half-adder's sum bit is an XOR gate and its carry is an AND gate — toggle A and B and watch the truth-table row light up.

    Vocabulary Train
    English Chinese Pinyin
    half adder 半加器 bàn jiā qì
    carry 进位 jìn wèi
    full adder 全加器 quán jiā qì
    15.2

    Flip-flops

    A flip-flop 触发器 is a bistable 双稳态 circuit — two stable states (0 and 1) — that remembers its state. It stores one bit and is the basic element of registers and SRAM.

    SR flip-flop

    An SR flip-flop SR触发器 has inputs S (set) and R (reset) and outputs Q and $\overline{Q}$. S=1,R=0 sets Q to 1; S=0,R=1 resets it to 0; S=0,R=0 holds; S=1,R=1 is invalid. Built from two cross-coupled NOR gates.

    An SR flip-flop built from two cross-coupled NOR gates, with S feeding one gate and R the other, each gate's output fed back to the other's input, and its truth table: hold, set, reset and the invalid state
    The SR flip-flop: two NOR gates feeding each other. With both inputs 0 the outputs hold whatever they were, which is the memory; S sets Q to 1, R resets it, and S = R = 1 is not allowed

    "Draw a logic circuit for an SR flip-flop and label the inputs." Two NOR gates (or two NAND gates), the output of each connected back to one input of the other; the free input of one gate is S, of the other R; the outputs are $Q$ and $\overline{Q}$. The feedback is what the marks are for: without it there is no memory. "State the purpose of a flip-flop." To store one bit of data; it is the basic memory element from which registers and static RAM are built, and it holds its value until it is deliberately changed. The invalid input $S = R = 1$ makes both outputs 0, so that $\overline{Q}$ is no longer the complement of $Q$, and the state after both inputs return to 0 is unpredictable, which is the SR flip-flop's weakness.

    JK flip-flop

    A JK flip-flop JK触发器 improves on it by using the previously-invalid 1,1 input as a toggle 翻转 (the output flips). This makes it ideal for building counters 计数器 (a chain of toggling flip-flops). It is usually clocked — inputs act only on a clock edge, keeping flip-flops synchronised.

    A JK flip-flop block symbol with J, K and clock inputs and outputs Q and Q-bar, beside its build from four cross-coupled NAND gates with the Q and Q-bar outputs fed back to the input gates
    A JK flip-flop: its symbol and a build from NAND gates

    Flip-flops are the building blocks of registers (n bits = n flip-flops), counters, and SRAM 静态RAM cells.

    JK flip-flop truth table. The clock 时钟 input decides when the J and K inputs are read, so the output changes only on a clock pulse: with $J = K = 0$ the output is held; $J = 1, K = 0$ sets $Q$ to 1; $J = 0, K = 1$ resets it to 0; $J = K = 1$ toggles it (Q becomes $\overline{Q}$). The last row is exactly the SR flip-flop's forbidden input turned into a useful one, which is why the JK is preferred: every input combination is valid, and the clocked operation makes it the building block of counters and shift registers.

    Vocabulary Train
    English Chinese Pinyin
    flip-flop 触发器 chù fā qì
    bistable 双稳态 shuāng wěn tài
    toggle 翻转 fān zhuǎn
    counters 计数器 jì shù qì
    SRAM 静态RAM jìng tài RAM
    clock 时钟 shí zhōng
    SR flip-flop SR触发器 SR chù fā qì
    JK flip-flop JK触发器 JK chù fā qì
    15.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    RISC a processor with a small set of simple, fixed-length instructions, most executed in one clock cycle, using many registers and pipelining
    CISC a processor with a large set of complex, variable-length instructions, many taking several clock cycles and accessing memory directly
    pipelining dividing the fetch–execute cycle into stages so that several instructions are processed at once, each at a different stage
    SISD / SIMD / MISD / MIMD one instruction on one data item; one instruction on many data items; many instructions on one data item; many instructions on many data items
    massively parallel computer thousands of processors, each with its own memory, connected by a network and working simultaneously on one problem
    virtual machine a software emulation of a computer system running on a host computer and behaving like a separate physical computer
    hypervisor the software that creates virtual machines and shares the host's hardware between them
    truth table a table listing every combination of inputs to a logic circuit with the resulting output(s)
    sum-of-products a Boolean expression written as the OR of AND terms, one term for each input combination giving 1
    Karnaugh map a grid of the truth-table outputs, arranged in Gray-code order, in which loops of adjacent 1s give the simplified expression
    half adder a circuit that adds two bits, producing a sum and a carry
    full adder a circuit that adds two bits and a carry-in, producing a sum and a carry-out
    flip-flop a bistable circuit that stores one bit, holding its output until its inputs change it
    15.2

    Exam tips

    • RISC and CISC are answered as lists of features: simple, fixed, one cycle, many registers, load/store, pipelined against complex, variable, multi-cycle, fewer registers, direct memory access, microcode. Four of each.
    • Pipelining: stages, several instructions at once, one completed per cycle, higher throughput; $n + k - 1$ cycles for $n$ instructions through $k$ stages; interrupts must empty the pipeline.
    • Flynn's four categories are "how many instruction streams" by "how many data streams"; say what runs on what. Massively parallel: many processors, own memory, network, same problem.
    • Virtual machine: emulation of a computer on a host; host OS on the hardware, hypervisor sharing it, guest OS inside. Two benefits and two limitations, each a full sentence.
    • Boolean algebra: name each law as you use it; De Morgan swaps the operator and negates each term; check with a truth table if in doubt.
    • K-map: Gray-code order, largest loops of 1/2/4/8, wrapping allowed, one term per loop with the unchanging variables. State why: simplest expression with no algebra.
    • Half adder gives sum and carry; full adder also takes a carry-in; SR flip-flop is two cross-coupled NOR/NAND gates and stores one bit; JK's 1,1 input toggles.

    Common mistakes

    • Swapping the RISC and CISC feature lists, or offering "faster" as a feature; give the design features, not a verdict.
    • Describing pipelining as "running instructions in parallel on several cores"; it is stages of one processor overlapping.
    • Confusing SIMD (one instruction, many data) with MIMD (many of both), or describing MISD as the common case.
    • Defining a virtual machine as "a copy of a computer" without the word emulation or the host and guest.
    • Applying De Morgan to only part of an expression under a long bar, or dropping the bar without swapping AND for OR.
    • Looping a group of three, or a non-rectangular group, in a K-map; ordering the columns 00, 01, 10, 11 instead of Gray code.
    • Writing the carry of a half adder as XOR and the sum as AND.
    • Drawing an SR flip-flop as two gates with no feedback, or leaving out the invalid state from its truth table.
  • 16

    System Software

    16.1

    How an OS maximises use of resources

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of how an OS can maximise the use of resources
    Describe the ways in which the user interface hides the complexities of the hardware from the user
    Show understanding of process management The concept of multi-tasking and a process The process states: running, ready and blocked The need for scheduling and the function and benefits of different scheduling routines (including round robin, shortest job first, first come first served, shortest remaining time) How the kernel of the OS acts as an interrupt handler and how interrupt handling is used to manage low-level scheduling
    Show understanding of virtual memory, paging and segmentation for memory management The concepts of paging, virtual memory and segmentation The difference between paging and segmentation How pages can be replaced How disk thrashing can occur

    Source: Cambridge International syllabus

    A computer has many resources (CPU time, memory, disk, I/O) and many programs competing for them. The OS shares them fairly and efficiently so each is well used and the system stays responsive:

    The OS shares CPU time, memory, disk and input/output between programs
    The OS shares the CPU, memory, disk and I/O between programs
    • multi-tasking 多任务 — switch the CPU quickly between processes so several seem to run at once.
    • memory management — give each process the memory it needs; use disk paging 分页 when RAM runs out.
    • spooling 假脱机 and buffering — print jobs queue on disk so the CPU never waits for the printer.
    • caching — keep recently-used disk data in cache 高速缓存 / RAM.
    A CPU (central processing unit) chip
    The processor is a key resource the OS shares between competing tasks
    Memory modules (RAM)
    The OS also manages memory (RAM), deciding what to keep in it and what to page out to disk
    Vocabulary Train
    English Chinese Pinyin
    multi-tasking 多任务 duō rèn wù
    paging 分页 fēn yè
    spooling 假脱机 jiǎ tuō jī
    cache 高速缓存 gāo sù huǎn cún
    Exercise sheet
    16.1

    The user interface

    The user interface hides the hardware behind friendly abstractions: the user sees windows, menus and folders, not addresses or sectors. One click on an icon makes the OS find the program on disk, allocate memory, load it and start it. A CLI (command line) is powerful and scriptable for experts; a GUI (graphical) is easier to learn. Most systems offer both.

    "Describe two ways in which the complexities of the hardware are hidden from the user." (1) The user works with files and folders by name, and the OS translates them into the tracks, sectors and blocks of the disk; (2) the user runs a program with a click or a command, and the OS loads it, allocates memory and schedules it without the user knowing any addresses; (3) device drivers let the user print or save without knowing how the printer or disk is controlled; (4) a graphical interface replaces machine-level commands with icons, windows and menus. The benefit to a student, with an example: the OS makes the hardware usable without technical knowledge, for instance saving a document to a USB drive by dragging its icon.

    "Show how an OS maximises the use of resources." It schedules the processor so that it is never idle while a process is ready; it manages memory, allocating it to processes, reclaiming it and extending it with virtual memory; it manages input and output, using buffers and spooling so that fast and slow devices overlap their work; and it manages storage, keeping track of free space and files. Each point names a resource and what the OS does with it.

    16.1

    Process management

    A process 进程 is a program in execution — its code, current state, memory and open files.

    Scheduling

    The scheduler 调度器 chooses which ready process runs next, and for how long:

    • round robin 轮转 — each process gets a fixed time slice 时间片, then goes to the back of the queue.
    • first-come-first-served; shortest job first; shortest remaining time (run the job with the least work left); priority; multilevel feedback queues.

    The trade-off is responsiveness vs throughput vs fairness.

    "Describe what is meant by multi-tasking and how it benefits process management." Several processes are held in memory at the same time and the processor switches between them so quickly that they appear to run simultaneously, each given a share of processor time in turn. The benefit: the processor is never left idle while one process waits for input or output, so throughput is higher and the user can work on several programs at once. "Explain the need for scheduling." There are more processes than processors, so a decision must be made about which process runs next and for how long; scheduling makes sure every process makes progress, that the processor is fully used, that response times are acceptable, and that priorities can be respected.

    Two timelines of the same three jobs: first-come-first-served runs the long job first and the short jobs wait behind it, while shortest-job-first runs the short jobs first and cuts the average waiting time from 6.7 to 2.7 units
    The same work in a different order: shortest-job-first gets the short jobs out of the way, so most jobs wait less, at the risk of a long job waiting for ever

    The scheduling routines, as the exam wants them described.

    Routine Function Benefit Drawback
    first come first served (FCFS) processes run in the order in which they arrive in the ready queue, each to completion simple; every process is dealt with in turn, none is starved a long process holds up all the short ones behind it; poor response
    shortest job first (SJF) the ready process with the shortest estimated run time runs next, to completion minimises the average waiting time; many short jobs finish quickly run times must be known in advance; a long job may never run (starvation)
    shortest remaining time (SRT) pre-emptive 抢占式 version of SJF: if a new process arrives with less time left than the running one, it takes over short processes are served even faster; good throughput more context switches; a long job can be interrupted repeatedly and starve
    round robin (RR) each ready process gets a fixed time slice in turn; when it expires the process goes to the back of the queue fair; every process responds within a bounded time, good for interactive use context-switch overhead; a very short slice wastes time, a long one delays others
    priority the ready process with the highest priority runs first important or time-critical work is done first low-priority processes may starve unless priorities age

    Worked example. Three processes arrive together with CPU times of 8, 4 and 2 ms. Compare the average waiting time under FCFS (in arrival order A, B, C) and under shortest job first.

    FCFS: A waits 0, B waits 8, C waits 12; average $(0 + 8 + 12)/3 = 6.7\ \text{ms}$. SJF runs C, B, A: C waits 0, B waits 2, A waits 6; average $2.7\ \text{ms}$. The total work is the same 14 ms either way; the order decides who waits. Round robin with a 2 ms slice would give A, B and C each a turn in the first 6 ms, so C finishes at 6 ms, B at 12 ms and A at 14 ms: the most responsive, not the fastest on average.

    A Gantt timeline showing P1 then P2, P3, P4 run one after another from time 0 to 39, with a key giving each process's CPU burst time
    First-come-first-served scheduling of four processes
    Round-robin scheduling shown as a timeline: P1, P2, P3 each get a fixed time slice in turn, then the cycle repeats, sharing the CPU between them
    Round-robin: each process gets a fixed time slice in turn, then the next runs (unlike first-come-first-served)

    Process states

    A process is new, ready (waiting for the CPU), running, blocked 阻塞 (waiting for I/O or a lock), or terminated. When its time slice ends it goes running → ready; when it requests I/O it goes running → blocked; when the I/O finishes it goes blocked → ready.

    A state diagram: new to ready (admit), ready to running (dispatch by the scheduler), running to ready (interrupt or time-out), running to blocked (request I/O), blocked back to ready (I/O complete), running to terminated (exit)
    A process moves between the new, ready, running, blocked and terminated states

    The three states and why a process moves. Running: the process has the processor. Ready: it could run but is waiting for the processor. Blocked: it cannot run until something else happens. Reasons for each transition, which the exam asks for one at a time: running to ready when its time slice ends, or when a higher-priority process becomes ready and pre-empts it (an interrupt); running to blocked when it requests input or output or waits for a resource or another process; blocked to ready when the I/O it was waiting for completes (signalled by an interrupt); ready to running when the scheduler dispatches it. A blocked process can never go straight to running: it must become ready first.

    Process control block and context switch

    For each process the OS keeps a process control block 进程控制块 (PCB) — the saved program counter, registers, state and memory info.

    A context switch saves process A's state (its PCB) and loads process B's
    A context switch saves one process's state and loads another's
    • a context switch 上下文切换 suspends one process and starts another: it saves the state into one PCB and restores it from another. This small cost is paid on every switch.
    • the kernel 内核 (the core of the OS) acts as an interrupt handler 中断处理程序. When a device or the timer raises an interrupt, interrupt handling 中断处理 saves the running process and runs the right routine — this is what drives low-level scheduling.

    "Outline how the kernel acts as an interrupt handler" (two marks). When an interrupt is raised, the kernel saves the state of the running process (its registers and program counter, in its process control block), identifies the source and priority of the interrupt, runs the appropriate interrupt service routine, and then restores the interrupted process (or a higher-priority one) so that execution continues. This is how the timer ends a time slice and how a completed I/O operation unblocks a process.

    Inter-process communication

    Processes are isolated, so the OS provides inter-process communication 进程间通信: pipes 管道 (one program's output feeds another's input), shared memory 共享内存 (a region several processes can use), and message passing.

    Explore

    The life of a process

    Tap round the loop a process travels. It only runs when the scheduler picks it; needing I/O sends it to blocked, and finishing its time slice sends it back to ready — round and round until it's done.

    Vocabulary Train
    English Chinese Pinyin
    process 进程 jìn chéng
    scheduler 调度器 diào dù qì
    round robin 轮转 lún zhuàn
    time slice 时间片 shí jiān piàn
    pre-emptive 抢占式 qiǎng zhàn shì
    blocked 阻塞 zǔ sè
    process control block 进程控制块 jìn chéng kòng zhì kuài
    context switch 上下文切换 shàng xià wén qiè huàn
    kernel 内核 nèi hé
    interrupt handler 中断处理程序 zhōng duàn chǔ lǐ chéng xù
    interrupt handling 中断处理 zhōng duàn chǔ lǐ
    inter-process communication 进程间通信 jìn chéng jiān tōng xìn
    pipes 管道 guǎn dào
    shared memory 共享内存 gòng xiǎng nèi cún
    16.1

    Virtual memory, paging, segmentation

    Each process gets its own virtual address space 虚拟地址空间 — a clean, contiguous range of addresses the OS maps to physical memory. This gives each process a simple space, protects processes from each other, and lets the total memory exceed physical RAM.

    In paging, the virtual space is split into fixed-size pages and physical memory into same-sized frames 页框. A page table maps each page to a frame. If an accessed page is not in RAM — a page fault 缺页 — the OS reads it from the swap file 交换文件 into a frame, evicting another page if RAM is full. Frequent faults cause thrashing 抖动 (disk thrashing), where the OS spends most of its time swapping pages instead of doing useful work.

    Logical-memory pages mapped through a page table to non-contiguous physical-memory frames
    Paging maps each page of logical memory to a frame of physical memory

    In segmentation 分段, memory is split into variable-sized logical segments (code, stack, heap), each with its own permissions. Many systems use paging within segments.

    Variable-sized logical segments (code, heap, stack) mapped through a segment table of sizes and start addresses to physical memory
    Segmentation maps variable-sized segments using a segment map table

    "Explain what is meant by virtual memory" (three marks). Secondary storage (disk) is used to extend the RAM, so that the available memory appears larger than the physical memory; the address space of a process is divided into pages, and only the pages currently needed are held in RAM while the rest wait on disk; pages are swapped between RAM and disk as required, and the OS translates each virtual address into a physical one. Why an OS needs it: the programs running may need more memory than the RAM installed; it lets more (or larger) programs run at once; a program can be larger than the physical memory; memory is used efficiently because only the active parts of programs occupy RAM.

    Paging against segmentation: the difference the exam wants. Paging divides memory into blocks of fixed size (pages and frames) chosen by the hardware, with no regard to the program's structure, and the mapping is invisible to the programmer; segmentation divides a program into variable-sized logical units (a procedure, an array, the stack) whose sizes and boundaries follow the program, so a segment can be protected or shared as a unit. "Describe the process of segmentation": the program is split into segments of different sizes, each given a segment number; a segment table records where each segment starts in memory and how long it is; a logical address is a segment number plus an offset, and the OS adds the offset to the segment's base address to find the physical location.

    "Explain what is meant by disk thrashing" and when it occurs. Disk thrashing 磁盘抖动 is the state in which pages are swapped in and out of RAM so frequently that the processor spends more time moving pages than executing instructions, and the system slows almost to a halt. It occurs when the RAM is too small for the pages the running processes need (their working sets): a page just moved out is needed again almost at once, so it is fetched back, which pushes out another page that is soon needed, and so on. Too many processes, or a program that accesses memory unpredictably, brings it on; more RAM or fewer processes cure it.

    Explore

    What happens on a page fault

    Step through a page fault. When the program touches a page that isn't in RAM, the OS quietly fetches it from disk and updates the page table — so the program sees more memory than physically exists.

    Vocabulary Train
    English Chinese Pinyin
    virtual address space 虚拟地址空间 xū nǐ dì zhǐ kōng jiān
    pages
    frames 页框 yè kuāng
    page fault 缺页 quē yè
    swap file 交换文件 jiāo huàn wén jiàn
    thrashing 抖动 dǒu dòng
    segmentation 分段 fēn duàn
    disk thrashing 磁盘抖动 cí pán dǒu dòng
    16.2

    How an interpreter runs a program

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of how an interpreter can execute programs without producing a translated version
    Show understanding of the various stages in the compilation of a program Including lexical analysis, syntax analysis, code generation and optimisation
    Show understanding of how the grammar of a language can be expressed using syntax diagrams or Backus-Naur Form (BNF) notation
    Show understanding of how Reverse Polish Notation (RPN) can be used to carry out the evaluation of expressions

    Source: Cambridge International syllabus

    An interpreter 解释器 translates and runs the source at the same time. For each statement it reads the line, does lexical and syntax analysis, checks types, then executes the action, and moves on. Errors are reported immediately and it usually stops; no executable is produced. The translation is redone every run (slower), but it gives fast development feedback and is portable.

    "Explain how an interpreter executes a program without producing a translated version" (three marks). The interpreter takes one statement (line) at a time, translates (analyses) it, and executes it immediately, before moving to the next; no translated version of the whole program is created or stored, so every statement is translated every time it is executed, including each pass through a loop; if a statement contains an error, execution stops there and the error is reported. This is what makes an interpreter good for developing and testing (errors are found as they are reached, and a change can be tried at once) but slower for running finished programs.

    Vocabulary Train
    English Chinese Pinyin
    interpreter 解释器 jiě shì qì
    Watch lesson Exercise sheet
    16.2

    Stages of compilation

    A compiler 编译器 turns source into machine code 机器码 in phases:

    1. lexical analysis 词法分析 — the lexer groups characters into tokens 词法单元 (keywords, identifiers, operators, literals), discarding whitespace and comments.
    2. syntax analysis (parsing) 语法分析 — check the tokens fit the grammar and build an abstract syntax tree 抽象语法树. A missing bracket gives a syntax error 语法错误.
    3. semantic analysis 语义分析 — check the program makes sense (variables declared, types match).
    4. code generation 代码生成 — walk the tree and emit target code, choosing registers and layouts.
    5. code optimisation 代码优化 — remove redundant work, fold constants, reorder for the pipeline.

    The output is an executable.

    The phases of compilation: source code passes through lexical analysis (tokens), syntax analysis (AST), semantic analysis (checks), code generation and optimisation to produce an executable
    The phases of compilation, from source code to an optimised executable

    The purpose of each stage, in the words that score. Lexical analysis: removes white space and comments; converts the characters of the source code into tokens (keywords, identifiers, operators, constants), checking that each is valid in the language; enters identifiers into the symbol table 符号表. Syntax analysis: checks that the sequence of tokens obeys the grammar (syntax rules) of the language; builds a parse tree (abstract syntax tree); reports syntax errors; type checking and the checking of variable declarations are sometimes counted here as semantic analysis. Code generation: converts the checked tree into object code or machine code (possibly via an intermediate code), allocating memory and registers. Optimisation: makes the code run faster or use less memory, by removing redundant instructions, combining or simplifying calculations, and reorganising loops, without changing what the program does. The matching question pairs each stage with one of these descriptions.

    Explore

    The phases of compilation

    Step through what a compiler does to your source. Each phase hands its output to the next — characters become tokens, tokens become a tree, the tree becomes optimised machine code.

    Vocabulary Train
    English Chinese Pinyin
    compiler 编译器 biān yì qì
    machine code 机器码 jī qì mǎ
    lexical analysis 词法分析 cí fǎ fēn xī
    tokens 词法单元 cí fǎ dān yuán
    syntax analysis (parsing) 语法分析 yǔ fǎ fēn xī
    abstract syntax tree 抽象语法树 chōu xiàng yǔ fǎ shù
    syntax error 语法错误 yǔ fǎ cuò wù
    semantic analysis 语义分析 yǔ yì fēn xī
    code generation 代码生成 dài mǎ shēng chéng
    code optimisation 代码优化 dài mǎ yōu huà
    symbol table 符号表 fú hào biǎo
    16.2

    Grammar: BNF and syntax diagrams

    A grammar 文法 says which token sequences are valid programs.

    Backus-Naur Form 巴科斯-诺尔范式 (BNF) is textual. A production rule 产生式 has the form:

    <symbol> ::= alternative1 | alternative2 | ...
    

    Each alternative is a sequence of terminal 终结符 symbols (literal text) and non-terminal 非终结符 symbols (other rule names):

    <digit>      ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
    <identifier> ::= <letter> | <identifier> <letter> | <identifier> <digit>
    

    The recursive third rule expresses "a letter followed by any number of letters or digits". An IF statement:

    <if-statement> ::= IF <condition> THEN <statement> ENDIF
                     | IF <condition> THEN <statement> ELSE <statement> ENDIF
    

    A syntax diagram 语法图 (railroad diagram) shows the same thing graphically: boxes for non-terminals, rounded boxes for terminals, arrows for valid paths, loops for repetition. The two notations are equivalent. The parser uses the grammar to decide whether a program is valid.

    A railroad diagram for an assignment: a rectangular identifier box, a rounded assignment-symbol box, then a rectangular expression box, connected left to right
    A syntax (railroad) diagram for an assignment statement
    Three syntax diagrams, for a letter, a digit and an identifier that starts with a letter and continues with any number of letters or digits, beside the BNF rules that express exactly the same grammar, with valid and invalid examples
    A syntax diagram and a BNF rule say the same thing: a choice becomes alternatives separated by bars, and a loop becomes a rule that refers to itself

    Reading the exam's diagrams. Each diagram defines one non-terminal; follow the arrows from the entry to the exit, and every path you can trace is a valid string. A choice of boxes side by side is a set of alternatives; a loop back is "repeat as many times as you like"; a box for another non-terminal means "insert anything that rule allows". "State why the string is invalid" wants the rule it breaks, in words: 9K is invalid as a variable because the first character must be a letter, not a digit; JJ90 is an invalid passcode if the rule allows only one letter before the digits, or if J is not in the set of letters listed. Always check the string against the set of characters the diagram actually allows, not against what a real language would accept.

    Writing BNF from a diagram. Each diagram becomes one rule <name> ::= ...; alternatives are separated by |; a sequence is written one symbol after another; and repetition is written with recursion, because BNF has no loop symbol: "one or more letters" is <word> ::= <letter> | <letter><word>, and "zero or more digits after a letter" is <variable> ::= <letter> | <letter><digits> with <digits> ::= <digit> | <digit><digits>.

    Worked example. Complete the BNF for a vehicle registration that must begin with two letters (from A B C) followed by one, two or three digits (from 0 1 2).

    <letter>       ::= A | B | C
    <digit>        ::= 0 | 1 | 2
    <digits>       ::= <digit> | <digit><digit> | <digit><digit><digit>
    <registration> ::= <letter><letter><digits>
    

    AB12 is valid; A12 is not (only one letter); AB1234 is not (four digits); AD1 is not (D is not a listed letter). Asked to add a constraint such as "the third character may also be a symbol", add the extra alternative to the rule for that position only, and define <symbol> with its own rule.

    Worked example. Write BNF for an expression that is a variable, followed by an operator, followed by either a variable or a number, where a variable is a single lower-case letter from a b c and an operator is + or -.

    <variable>   ::= a | b | c
    <operator>   ::= + | -
    <number>     ::= <digit> | <digit><number>
    <expression> ::= <variable><operator><variable> | <variable><operator><number>
    

    The recursive <number> rule allows any number of digits; the two alternatives of <expression> cover both cases named in the definition. Keep every non-terminal in angle brackets and every terminal without them.

    Vocabulary Train
    English Chinese Pinyin
    grammar 文法 wén fǎ
    Backus-Naur Form 巴科斯-诺尔范式 bā kē sī - nuò ěr fàn shì
    production rule 产生式 chǎn shēng shì
    terminal 终结符 zhōng jié fú
    non-terminal 非终结符 fēi zhōng jié fú
    syntax diagram 语法图 yǔ fǎ tú
    16.2

    Reverse Polish Notation (RPN)

    In infix 中缀 notation the operator sits between its operands (3 + 4 * 2), needing brackets and precedence rules. In Reverse Polish Notation 逆波兰表示法 (RPN, postfix 后缀) the operator follows its operands (3 4 2 * +), needing no brackets.

    Converting infix to RPN

    Use an operator stack. Scan left to right: output an operand; for an operator, first pop any stacked operators of higher or equal precedence 优先级 to the output, then push it; push (; on ) pop to output until the matching (. At the end, pop all operators. Example: (3 + 4) * 23 4 + 2 *.

    Evaluating RPN

    Use a stack of operands. Scan left to right: push each operand; on an operator, pop the top two, apply it, and push the result. Evaluating 3 4 2 * +:

    Token Stack
    3 3
    4 3, 4
    2 3, 4, 2
    * 3, 8
    + 11

    Result: 11. RPN needs no brackets at evaluation time and suits a stack machine — which is how the JVM and many bytecode 字节码 interpreters work.

    "Explain why RPN is used to evaluate expressions" (two marks). In RPN the operators appear in the order in which they are applied, so an expression can be evaluated in a single left-to-right pass with no brackets and no precedence rules; it is therefore simpler and faster for the compiler or interpreter to process. "Identify, with reasons, a suitable data structure": a stack, because evaluation needs the most recently pushed operands first (last in, first out): each operand is pushed, and each operator pops the top two, applies itself, and pushes the result. Show the stack contents after every token when asked.

    Converting infix to RPN by hand. (1) Fully bracket the expression using the precedence rules; (2) move each operator to just after the closing bracket of its own pair; (3) remove the brackets. So $(a - b) * (a + c) / 7$ becomes $((a - b) * (a + c)) / 7$, then a b - a c + * 7 /. Note that * and / are applied left to right, so the division is the last operator, not the multiplication. More conversions: $((7 + 3) - (2 * 8)) / 6$ is 7 3 + 2 8 * - 6 /; $(7 - 2 + 8) / (9 - 5)$ is 7 2 - 8 + 9 5 - /; $a * b + b - d + 15$ is a b * b + d - 15 +; $(2 - 6) * (13 + 7) / 5$ is 2 6 - 13 7 + * 5 /.

    Converting RPN back to infix. Work through the RPN with a stack of expressions: push each operand; for each operator pop two, write them either side of it in brackets, and push the result. So a b / 4 * a b + - is $((a / b) * 4) - (a + b)$; 5 2 + 9 3 - / 3 * is $((5 + 2) / (9 - 3)) * 3$; b a c - + d b + * c / is $((b + (a - c)) * (d + b)) / c$; a b - c + c a - * d / is $(((a - b) + c) * (c - a)) / d$. Keep the brackets: dropping them can change the meaning.

    Worked example. Evaluate a b - c d + * e / when $a = 17$, $b = 5$, $c = 7$, $d = 3$ and $e = 10$, showing the stack.

    token action stack (top on the right)
    a push 17 17
    b push 5 17, 5
    - pop 5 and 17, push $17 - 5$ 12
    c push 7 12, 7
    d push 3 12, 7, 3
    + pop 3 and 7, push $7 + 3$ 12, 10
    * pop 10 and 12, push $12 \times 10$ 120
    e push 10 120, 10
    / pop 10 and 120, push $120 / 10$ 12

    Result 12. The order of the pops matters for - and /: the value popped second is the left operand, so a b - is $a - b$, not $b - a$. Two more, in the same way: d a b + * c a - / with $a = 6, b = 12, c = 15, d = 5$ gives $5 \times (6 + 12) / (15 - 6) = 90 / 9 = 10$; c a - b d + * b c + / with $a = 4, b = 12, c = 24, d = 6$ gives $(24 - 4) \times (12 + 6) / (12 + 24) = 360 / 36 = 10$.

    Worked example. Convert $(A + B) \times (C - D)$ to RPN, then evaluate $(3 + 4) \times (5 - 2)$. Scan left to right using an operator stack. Push (; output A; push +; output B; on ) pop back to the matching (, giving A B + so far. Push ×, and the second bracket behaves the same way, giving C D -. At the end pop the ×. Result: A B + C D - ×. To evaluate the numbers, use a stack of operands: push 3, push 4; + pops both and pushes 7; push 5, push 2; - pops both and pushes 3; × pops 7 and 3 and pushes 21. Two things make these reliable: the operands keep their original order through the conversion (only the operators move), and every operator acts on the two values immediately below it on the stack.

    Explore

    Operator precedence — what RPN removes

    In ordinary infix maths × and ÷ bind tighter than + and −, so you must apply rules in the right order. Reverse Polish Notation writes the operands first (3 4 2 × + 1 −), fixing the order so no precedence rules are needed.

    Vocabulary Train
    English Chinese Pinyin
    infix 中缀 zhōng zhuì
    Reverse Polish Notation 逆波兰表示法 nì bō lán biǎo shì fǎ
    postfix 后缀 hòu zhuì
    stack zhàn
    precedence 优先级 yōu xiān jí
    bytecode 字节码 zì jié mǎ
    16.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    multi-tasking several processes held in memory at once, the processor switching between them so that they appear to run simultaneously
    process a program that has been loaded into memory and is being executed (or is ready to be)
    running / ready / blocked has the processor / waiting for the processor / cannot continue until an event such as I/O completes
    scheduling deciding which ready process gets the processor next, and for how long
    pre-emptive scheduling the running process can be interrupted and moved to ready so that another process runs
    virtual memory using secondary storage to extend RAM, holding only the pages currently needed in physical memory
    paging dividing memory and programs into fixed-size pages that are moved between disk and RAM as needed
    segmentation dividing a program into variable-sized logical segments, each mapped to memory by a segment table
    disk thrashing pages being swapped between RAM and disk so often that little useful processing is done
    interpreter translates and executes a program one statement at a time, without producing a translated version
    compiler translates a whole high-level program into machine (object) code before it is run
    lexical analysis converts the source code into tokens, removing white space and comments, and builds the symbol table
    syntax analysis checks that the tokens obey the grammar of the language and builds a parse tree
    Backus–Naur Form a notation for the grammar of a language: rules of the form <name> ::= alternatives built from terminals and non-terminals
    Reverse Polish Notation a way of writing expressions with each operator after its operands, so they can be evaluated with a stack and without brackets
    16.2

    Exam tips

    • The OS questions are marked on named mechanisms: scheduling, memory management, I/O buffering and spooling, file management; for the interface, file names not addresses, clicks not commands, drivers, GUI.
    • Process states with their transitions and the reason for each; scheduling routines as function plus benefit plus drawback; the kernel saves state, identifies the interrupt, services it, restores.
    • Virtual memory: disk extends RAM, pages swapped, address translation; paging is fixed-size and invisible, segmentation is variable-size and logical; thrashing is swapping instead of working.
    • Interpreter: one statement at a time, translated then executed, nothing stored. Compiler stages: tokens and symbol table, grammar and parse tree, code, optimisation.
    • BNF: a rule per diagram, | for choice, recursion for repetition, terminals bare and non-terminals in angle brackets. Say which rule a string breaks.
    • RPN: operators after operands, evaluate with a stack, show every step; convert by fully bracketing; when converting back, keep the brackets.

    Common mistakes

    • Describing multi-tasking as "running several programs at the same time" without saying the processor switches between them.
    • Sending a blocked process straight to running, or giving "time slice ended" as the reason for running to blocked.
    • Confusing shortest job first (non-pre-emptive) with shortest remaining time (pre-emptive), or round robin with priority.
    • Defining virtual memory as "using the hard disk as RAM" with no mention of pages being swapped.
    • Saying an interpreter "converts the program to machine code and then runs it"; that is a compiler.
    • Putting syntax checking in lexical analysis, or optimisation before code generation in the matching question.
    • Writing BNF repetition as <letter>* or with an ellipsis; use recursion. Leaving angle brackets off non-terminals.
    • Reversing the operands of - or / when evaluating RPN, or writing the RPN of $a * b + c$ as a b c + *.
  • 17

    Security

    17.1

    How encryption works

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of how encryption works Including the use of public key, private key, plain text, cipher text, encryption, symmetric key cryptography and asymmetric key cryptography How the keys can be used to send a private message from the public to an individual/organisation How the keys can be used to send a verified message to the public How data is encrypted and decrypted, using symmetric and asymmetric cryptography Purpose, benefits and drawbacks of quantum cryptography
    Show awareness of the Secure Socket Layer (SSL) / Transport Layer Security (TLS) Purpose of SSL/TLS Use of SSL/TLS in client-server communication Situations where the use of SSL/TLS would be appropriate
    Show understanding of digital certification How a digital certificate is acquired How a digital certificate is used to produce digital signatures

    Source: Cambridge International syllabus

    Encryption 加密 turns readable plaintext 明文 (plain text) into unreadable ciphertext 密文 (cipher text) using a maths operation that depends on a key. Only someone with the right key can reverse it — decryption 解密 — to get the plaintext back. An attacker who intercepts the ciphertext without the key sees only meaningless data, because trying every possible key would take far too long. A newer approach, quantum cryptography 量子密码学, uses quantum physics to share a key in a way that reveals any eavesdropper.

    The Enigma cipher machine with its keyboard and rotors
    The Enigma machine encrypted messages in the Second World War — an early, mechanical cipher device
    Plaintext goes through an encryption algorithm with an encryption key to ciphertext, across the internet, then a decryption algorithm with a decryption key back to plaintext
    Encryption scrambles plaintext with a key; decryption reverses it

    Symmetric encryption

    Symmetric encryption 对称加密 (symmetric key cryptography) uses the same key for both encryption and decryption, so sender and receiver must both hold the secret key. It is fast and good for bulk data (a whole disk, a video stream). Its problem is key distribution 密钥分发: how do you share the key safely in the first place? Asymmetric encryption solves this.

    "Describe what is meant by symmetric key encryption" (two marks). The same key is used to encrypt the plaintext and to decrypt the ciphertext, so the key must be shared between sender and receiver and kept secret from everyone else. Two drawbacks. The key has to be exchanged before the message can be sent, and if it is intercepted in transit the interceptor can read every message; a separate key is needed for every pair of correspondents; and it gives no proof of who sent the message, because both ends hold the same key. "Give two reasons for using key cryptography": so that data is unreadable by anyone who intercepts it (confidentiality); so that the receiver can be sure the data came from the claimed sender and was not altered (authenticity and integrity 完整性). The two methods are symmetric and asymmetric key cryptography.

    Symmetric encryption uses the same key at both ends, which must be shared secretly
    Symmetric encryption uses the same secret key at both ends

    Asymmetric encryption (public-key)

    Asymmetric encryption 非对称加密 (asymmetric key cryptography) gives each user a pair of related keys: a public key 公钥 they publish, and a private key 私钥 they keep secret. Data encrypted with the public key can be decrypted only with the matching private key, and vice versa.

    Tom and Meera each have a public key to share and a private key kept secret; Meera sends Tom her public key
    Each user has a public key to share and a private key to keep secret

    To send a secret message to Alice: get her published public key, encrypt with it, and send. Only Alice — holding the matching private key — can decrypt. No prior key exchange is needed. The trade-off is that it is much slower than symmetric, so it is not used for large data.

    "State what is meant by a private key." A key known only to its owner (never transmitted), used to decrypt data that was encrypted with the matching public key, and to create digital signatures. "Describe the process of asymmetric encryption" (four marks): (1) the receiver generates a pair of keys, a public key and a private key, mathematically related; (2) the public key is made available to anyone who wants to send to them; (3) the sender encrypts the plaintext with the receiver's public key; (4) the ciphertext can only be decrypted with the receiver's private key, which never leaves the receiver, so nobody who intercepts the message can read it.

    Worked example. Fred wants to send Sheila a confidential document. Explain how asymmetric encryption is used.

    Sheila has a key pair; she sends Fred her public key (or he obtains it from her certificate). Fred encrypts the document with Sheila's public key and sends the ciphertext. Only Sheila's private key can decrypt it, and only Sheila holds that, so nobody else, including Fred once it is encrypted, can read the document. The keys are used the receiver's way round: her public key to lock, her private key to unlock. An organisation that holds a key pair "to receive secure transmissions" does exactly this: it publishes the public key, keeps the private key, and decrypts what arrives.

    Two differences between symmetric and asymmetric encryption. Symmetric uses one key for both directions; asymmetric uses two related keys, one to encrypt and the other to decrypt. In symmetric encryption the key must be kept secret by both parties and exchanged securely; in asymmetric encryption the public key can be published and only the private key is secret. Symmetric encryption is much faster and suits large amounts of data; asymmetric is slower, so it is used for keys and signatures rather than bulk data.

    A private key must stay secret, so it is sometimes kept on a small hardware security key 硬件安全密钥. You plug it in or tap it to prove who you are, and the secret key never leaves the device.

    A black hardware security key on a white background, with a round gold touch sensor in the middle and a gold USB connector at one end
    A hardware security key stores a secret key to prove who you are

    Hybrid approach (used by almost every real system)

    Use asymmetric encryption to exchange a fresh session key 会话密钥, then use that symmetric key for the data:

    1. the client makes a random session key.
    2. it encrypts the session key with the server's public key.
    3. the server decrypts it with its private key.
    4. both ends now share the session key and use fast symmetric encryption for the rest.

    This is how HTTPS and SSH work.

    The exam's version of the key-exchange problem. "A symmetric key is to be exchanged before the message is sent. Explain how the key can be exchanged securely." The sender encrypts the symmetric key with the receiver's public key and sends it; the receiver decrypts it with their private key; both now hold the symmetric key, which was never exposed in transit, and use it for the messages. Asymmetric encryption solves the distribution problem; symmetric encryption then does the fast work.

    The client encrypts a session key with the server's public key and sends it; only the server's private key can open it; then both ends use fast symmetric encryption with the shared session key
    The hybrid approach: asymmetric crypto shares a session key once, then fast symmetric encryption protects the data

    Hashing (related, not encryption)

    A cryptographic hash 密码散列 function takes any input and gives a fixed-size digest 摘要 such that the same input always gives the same digest, it is infeasible to find two inputs with the same digest, and a tiny change in input changes the digest completely. Hashing is one-way — you cannot get the input back. It is used for storing password checks, integrity checks, and digital signatures.

    A cryptographic hash maps the input hello to one digest and the input hellp, with one letter changed, to a completely different digest; hashing cannot be reversed
    A cryptographic hash gives a fixed digest; a tiny input change changes it completely, and it cannot be reversed

    Quantum cryptography

    Quantum cryptography uses the physics of light to distribute keys: the bits of a key are sent as photons whose quantum states encode the values. "Describe its purpose": to transmit an encryption key securely, in such a way that any attempt to intercept it can be detected, because measuring a photon changes its state; an eavesdropper 窃听者 therefore leaves evidence, and the corrupted key is thrown away and a new one sent. Benefits: interception is always detectable; the key cannot be copied without being altered; it is secure against future advances in computing power (a mathematical key can eventually be cracked, a quantum one cannot be read without disturbing it). Drawbacks: it needs specialised, expensive equipment; it works only over limited distances on dedicated optical fibre (or line of sight), not across the existing internet; it distributes the key only, so ordinary encryption still protects the message; and it is a new technology with few suppliers and little experience.

    Explore

    Hashing and the avalanche effect

    A hash is one-way: easy to compute, practically impossible to reverse. A tiny change in the input flips a large, unpredictable part of the output — the avalanche effect that makes hashes good for passwords.

    Explore

    The Caesar cipher

    Shift each letter to encrypt the message. A simple cipher shows the idea of a key — and why a small key is easy to break.

    Vocabulary Train
    English Chinese Pinyin
    encryption 加密 jiā mì
    plaintext 明文 míng wén
    ciphertext 密文 mì wén
    decryption 解密 jiě mì
    quantum cryptography 量子密码学 liàng zǐ mì mǎ xué
    eavesdropper 窃听者 qiè tīng zhě
    symmetric encryption 对称加密 duì chèn jiā mì
    key distribution 密钥分发 mì yào fēn fā
    asymmetric encryption 非对称加密 fēi duì chèn jiā mì
    integrity 完整性 wán zhěng xìng
    public key 公钥 gōng yào
    private key 私钥 sī yào
    hardware security key 硬件安全密钥 yìng jiàn ān quán mì yào
    session key 会话密钥 huì huà mì yào
    cryptographic hash 密码散列 mì mǎ sàn liè
    digest 摘要 zhāi yào
    Exercise sheet
    17.1

    SSL / TLS

    TLS 传输层安全 (Transport Layer Security, the successor to the Secure Socket Layer, SSL) is a protocol that gives encryption and authentication for data sent over a network. It encrypts the data in transit, authenticates the server with a certificate, and provides integrity (detecting tampering).

    Outline of a TLS handshake:

    1. the client connects and proposes cipher options.
    2. the server picks one and sends its digital certificate (with its public key) — issuing and validating these certificates is digital certification.
    3. the client checks the certificate.
    4. the two ends exchange a fresh session key using asymmetric crypto.
    5. all later traffic uses fast symmetric encryption with the session key.

    The result is an encrypted, authenticated, integrity-checked tunnel for higher-level protocols (HTTP, SMTP). It is appropriate wherever sensitive information is sent: HTTPS web browsing, online banking and payments, secure email, and VPNs.

    "Describe the purpose of SSL/TLS" and "state two functions." The purpose is to provide secure communication between a client and a server over a network. Its functions: it encrypts the data sent, so that it cannot be read if intercepted; it authenticates 认证 the server (and optionally the client) by means of a digital certificate, so the client knows it is talking to the genuine site; and it checks the integrity of the data, so that changes in transit are detected. Two examples of where it is appropriate: online banking and online shopping (card payments); also logins, private email, file transfer, VoIP and instant messaging: any transaction in which private data crosses the internet.

    The two protocols that make up TLS. The handshake 握手 protocol sets up the session: it agrees the encryption algorithms (cipher suite), authenticates the server with its certificate, and exchanges the session key. The record protocol then carries the data: it encrypts each message with the session key, adds an integrity check, and passes it to the transport layer.

    A sequence diagram between a client and a server: the client asks for a secure connection, the server replies with its digital certificate and public key, the client checks the certificate, creates a session key and sends it encrypted with the server's public key, the server decrypts it with its private key, and both sides then communicate with symmetric encryption
    How a secure session starts: the certificate proves who the server is, the server's public key protects the session key on its way over, and the session key protects everything after that

    "Explain how SSL/TLS is used when client–server communication is initiated" (six marks). (1) The client (browser) sends a request to the server for a secure connection, saying which encryption methods it supports. (2) The server sends back its digital certificate, which contains its public key. (3) The client checks the certificate is valid (issued by a trusted Certificate Authority, not expired, for the right domain). (4) The client generates a session key, encrypts it with the server's public key and sends it. (5) The server decrypts the session key with its private key. (6) Both sides now hold the session key and all further data is sent using symmetric encryption with it. Give the steps in this order; the marks are for the certificate, the public key, the session key and the switch to symmetric encryption.

    Explore

    The TLS handshake

    Step through what happens before a padlock appears. The slow public-key crypto is used only to agree a shared key; the actual page then travels under fast symmetric encryption.

    Vocabulary Train
    English Chinese Pinyin
    TLS 传输层安全 chuán shū céng ān quán
    authenticates 认证 rèn zhèng
    handshake 握手 wò shǒu
    17.1

    Digital certificates

    A digital certificate 数字证书 binds an identity (a domain, an organisation) to a public key, and is signed by a trusted Certificate Authority 证书颁发机构 (CA). It contains the subject (who it identifies), the subject's public key, the issuer (the CA), a validity period, and the CA's signature over all of it.

    A user sends a request with their identity and public key to a Certificate Authority, which verifies the identity and issues a signed digital certificate containing the public key, CA identification, user id, digital signature and other information
    A Certificate Authority issues a digital certificate binding an identity to a public key

    To verify one, the client (which holds a list of trusted root CAs):

    1. checks the expiry dates.
    2. checks the subject name matches the URL.
    3. checks it is signed by a trusted CA, using the CA's public key to verify the signature.
    4. follows the certificate chain up to a trusted root.

    If anything fails, the browser shows the "Your connection is not private" warning. When it verifies cleanly, the client knows the identity was vetted by a trusted CA, the public key really belongs to that identity, and the certificate is current.

    "Describe what is meant by a digital certificate" (two marks). An electronic document, issued by a Certificate Authority, that verifies the identity of its owner (a person, organisation or website) and contains the owner's public key. Items found in one: the serial number; the name of the owner (subject) and, for a website, its domain; the owner's public key; the name of the issuing CA; the validity period (dates); the signature algorithm used; and the CA's digital signature of the whole certificate.

    "Explain how an organisation acquires a digital certificate" (four marks). (1) The organisation generates its own key pair, a public key and a private key. (2) It sends a request containing its public key and its identity details to a Certificate Authority. (3) The CA verifies the identity (checks that the applicant really is the organisation or owns the domain). (4) The CA creates the certificate containing the public key and the identity, signs it with the CA's own private key, and returns it. (5) The organisation installs the certificate on its server so that it can be sent to clients. The private key never leaves the organisation.

    "Explain why a digital certificate is required to validate a digital signature." To check a signature the receiver needs the sender's public key, and needs to be sure that the key really belongs to the claimed sender; the certificate supplies the public key together with the identity, and because the certificate is signed by a trusted CA the receiver can trust that binding. Without it an impostor could publish a public key in someone else's name and sign messages as them. The same reasoning answers "what should be included with a program downloaded from the internet to prove it is genuine": a digital signature, checked against the publisher's certificate.

    Vocabulary Train
    English Chinese Pinyin
    digital certificate 数字证书 shù zì zhèng shū
    Certificate Authority 证书颁发机构 zhèng shū bān fā jī gòu
    17.1

    Digital signatures

    A digital signature 数字签名 proves who signed a message and that it was not changed. To sign:

    1. compute a cryptographic hash of the message.
    2. encrypt the hash with the sender's private key — that is the signature.
    3. send the message and the signature.

    To verify: compute the hash of the received message; decrypt the signature with the sender's public key to get the sender's hash; compare. If they match, the message was signed by the holder of the private key (authentication 身份验证) and was not changed (integrity). A signature does not hide the message — for confidentiality as well, encrypt and sign.

    The sender hashes the message to a digest and encrypts it with their private key to form the signature; the receiver re-hashes the message and decrypts the signature with the sender's public key, then compares the two digests
    Signing hashes the message and encrypts the digest with the private key; the receiver checks it with the public key

    "Explain the role of a digital certificate in creating a digital signature" (three marks). The sender's certificate was issued by a CA and contains the sender's public key together with the sender's identity; the sender produces the signature by hashing the message and encrypting the hash with their private key, the partner of the key in the certificate; the receiver uses the public key from the certificate to decrypt the hash and, because the certificate binds that key to the sender, the signature proves who signed.

    "Explain how a digital signature is used to verify a message" (four marks). (1) The receiver decrypts the signature with the sender's public key (taken from the sender's certificate), which yields the hash that the sender computed. (2) The receiver hashes the received message with the same hash algorithm. (3) The two hashes are compared. (4) If they match, the message came from the holder of the private key (authentic) and has not been altered since it was signed (integrity); if they differ, the message is rejected. A banker receiving confidential data with a signature does exactly this before trusting it; the data itself may separately be encrypted with the banker's public key for confidentiality.

    Putting it together

    A secure request to https://www.bank.com: the server sends its certificate; the client verifies it against trusted CAs; the client uses the server's public key to exchange a session key; then data flows encrypted with that key. Encryption stops eavesdroppers, the certificate proves the server's identity, and integrity checks stop a man-in-the-middle 中间人攻击 altering the data.

    Worked example. Alice sends Bob a contract. She wants Bob to be certain it came from her and was not altered, and she wants nobody else to be able to read it. Which keys does she use, and in which direction? These are two different jobs needing two different key pairs. For the signature (authentication and integrity): Alice hashes the contract and encrypts that hash with her own private key; Bob decrypts it with Alice's public key and compares it against his own hash of the message. Only Alice holds her private key, so only she could have produced it. For confidentiality: Alice encrypts the contract itself with Bob's public key, so only Bob's private key can open it. One rule keeps all four straight: you sign with your own private key and encrypt with the recipient's public key. A signature on its own does not hide the message.

    Vocabulary Train
    English Chinese Pinyin
    digital signature 数字签名 shù zì qiān míng
    authentication 身份验证 shēn fèn yàn zhèng
    man-in-the-middle 中间人攻击 zhōng jiān rén gōng jī
    17.1

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    encryption converting plaintext into ciphertext using an algorithm and a key so that it cannot be understood if intercepted
    plaintext / ciphertext the original readable data / the encrypted, unreadable form of it
    symmetric key cryptography the same secret key is used to encrypt and to decrypt, so it must be shared securely by both parties
    asymmetric key cryptography a pair of related keys is used: the public key encrypts and only the matching private key decrypts
    public key a key made available to anyone, used to encrypt messages to its owner and to verify the owner's signatures
    private key a key known only to its owner, used to decrypt messages encrypted with the public key and to sign
    SSL/TLS protocols that provide secure (encrypted, authenticated, integrity-checked) communication between a client and a server
    digital certificate an electronic document issued by a Certificate Authority that verifies the owner's identity and contains their public key
    digital signature a hash of a message encrypted with the sender's private key, proving who sent it and that it is unaltered
    Certificate Authority a trusted organisation that verifies identities and issues and signs digital certificates
    quantum cryptography the use of quantum states of photons to distribute keys so that any interception is detected
    17.1

    Exam tips

    • Symmetric: one shared secret key, fast, key exchange is the weakness. Asymmetric: public key to encrypt, private key to decrypt, slow, no exchange problem. Two differences, two drawbacks, two reasons: the exam asks for them in pairs.
    • Confidentiality uses the receiver's keys (public to lock, private to unlock); a signature uses the sender's keys (private to sign, public to check). Say whose key every time.
    • The TLS start-up is six steps: request, certificate with public key, check, session key encrypted with the public key, decrypted with the private key, symmetric encryption from then on.
    • A certificate is identity plus public key, signed by a CA; acquisition is key pair, request, verification, signing, installation. It is needed to validate a signature because it proves whose public key it is.
    • A signature is a hash encrypted with the private key; verification is decrypt, re-hash, compare. Integrity and authenticity are the two things it proves.
    • Quantum cryptography distributes keys and detects eavesdropping; its limits are cost, distance and novelty.

    Common mistakes

    • Saying a message is encrypted with the sender's public key; the receiver's public key encrypts, the receiver's private key decrypts.
    • Describing a signature as "encrypting the message with the private key" instead of encrypting its hash.
    • Claiming a certificate contains the private key; it holds the public key and the identity, signed by the CA.
    • Listing "the server sends its private key" in the TLS handshake; only the public key travels, inside the certificate.
    • Giving "SSL/TLS makes the connection faster" as a function; its functions are encryption, authentication and integrity.
    • Confusing hashing with encryption: a hash cannot be reversed and has no key; encryption is reversible with the key.
    • Answering "why is a certificate needed for a signature" with "to encrypt it"; it is needed to trust the public key.
  • 18

    Artificial Intelligence (AI)

    18.1

    What AI is

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of how graphs can be used to aid Artificial Intelligence (AI) Purpose and structure of a graph Use A algorithm* and Dijkstra’s algorithm to perform searches on a graph Candidates will not be required to write algorithms to set up, access, or perform searches on graphs
    Show understanding of how artificial neural networks have helped with machine learning
    Show understanding of Deep Learning, Machine Learning and Reinforcement Learning and the reasons for using these methods. Understand machine learning categories, including supervised learning, unsupervised learning
    Show understanding of back propagation of errors and regression methods in machine learning

    Source: Cambridge International syllabus

    Artificial intelligence 人工智能 (AI) builds systems that do tasks normally needing human intelligence — recognising speech and images, translating, playing games, driving, generating text. Most modern AI uses machine learning 机器学习 — algorithms that learn patterns from data instead of being programmed step by step. Within it, deep learning 深度学习, using neural networks 神经网络 with many layers, has been dominant since the 2010s.

    A humanoid robot 人形机器人 puts many of these abilities into one body: it uses AI to see faces, understand speech and move its face and arms in a lifelike way.

    A grey humanoid robot with a lifelike face looking upward, its mechanical neck, chest and arms exposed, on a white background
    A humanoid robot uses AI to see, listen and respond like a person
    Three nested rounded boxes: Artificial Intelligence contains Machine Learning, which contains Deep Learning, each with a short note
    Deep learning is part of machine learning, which is part of AI
    Explore

    AI learning type lab

    Classify AI examples by the type of learning or concern involved.

    Vocabulary Train
    English Chinese Pinyin
    artificial intelligence 人工智能 rén gōng zhì néng
    machine learning 机器学习 jī qì xué xí
    deep learning 深度学习 shēn dù xué xí
    neural networks 神经网络 shén jīng wǎng luò
    humanoid robot 人形机器人 rén xíng jī qì rén
    Exercise sheet
    18.1

    Graphs in AI

    Many AI problems sit on a graphnodes 节点 (states, places) joined by edges (moves, relationships).

    • pathfinding: roads form a graph; the shortest route is a graph search (Dijkstra's algorithm, the A* algorithm).
    • game playing: each board position is a node, each move an edge; minimax 极小化极大 with alpha-beta pruning searches the game tree.
    • state-space search: a planning problem is moving between states by applying operators to reach a goal.
    • knowledge representation: a semantic network 语义网络 has concepts as nodes and relationships as edges ("dog IS-A animal"); a knowledge graph 知识图谱 stores facts about the world for search engines and assistants.
    A weighted graph of nodes A to G; the shortest path from A to G via B and E is highlighted in orange
    AI problems often sit on a graph; here the shortest path is highlighted

    Standard tools for navigating graphs include breadth-first search 广度优先搜索 and depth-first search 深度优先搜索.

    "Describe the purpose and structure of a graph in an AI system." Purpose: to represent a problem as a set of states (or places) and the possible moves between them, so that an algorithm can search it for a solution, such as the shortest or cheapest route, or the best next move. Structure: a set of nodes (vertices), each representing a state, location or item, joined by edges representing the connections between them; each edge may carry a weight (a cost, distance or time), and edges may be directed (one-way) or undirected. "Explain the use of graphs to aid AI": the graph is the model on which the AI's search algorithms run: A* and Dijkstra's algorithm find optimal paths through it (navigation, routing), game positions form a tree searched for the best move, and knowledge stored as a graph lets a system reason about how facts are related.

    A weighted graph of six nodes from H to G with distances on the edges and a heuristic estimate to the goal written in red at each node, used for the Dijkstra and A-star worked examples The graph used below: the edge numbers are real distances; the red numbers are each node's heuristic 启发式 estimate of how far the goal still is, which only A uses*

    Dijkstra's algorithm. It finds the shortest distance from the start to every node. Keep a table of the best distance found so far to each node (start 0, all others infinity). Repeatedly take the unvisited node with the smallest distance, mark it visited, and for each neighbour check whether going through this node gives a shorter distance; if so, update it and record where it came from. Stop when every node is visited (or the target is).

    Worked example. Find the shortest distances from H to every other node in the graph above.

    step visit H A B C D G
    start 0
    1 H (0) 0 4 (H) 3 (H)
    2 B (3) 0 4 (H) 3 9 (B)
    3 A (4) 0 4 3 9 (A) 8 (A)
    4 D (8) 0 4 3 9 (A) 8 10 (D)
    5 C (9) 0 4 3 9 8 10 (D)
    6 G (10)

    Shortest distances: A 4, B 3, D 8, C 9, G 10, and the path to G is H–A–D–G (read the "came from" labels backwards). At step 3, A offers D a distance of $4 + 4 = 8$, better than the 9 found through B, so D is updated; at step 5, C could reach G at $9 + 3 = 12$, worse than 10, so nothing changes. Showing these comparisons is the "working" the question asks for.

    The A* algorithm. Dijkstra explores in every direction. A* adds a heuristic $h$, an estimate of the distance still to go, and always expands the node with the smallest $f = g + h$, where $g$ is the distance travelled so far. With a sensible heuristic (never over-estimating), it finds the same shortest path while looking at far fewer nodes, which is why satnavs and games use it. The exam gives $h$ for each node and a table to fill in.

    Worked example. Find a path from H to G with A*, showing the working.

    node expanded $g$ so far $h$ $f = g + h$ neighbours added (node: $g$, $h$, $f$)
    H 0 7 7 A: 4, 5, 9; B: 3, 6, 9
    B (tie with A; either) 3 6 9 D via B: 9, 2, 11
    A 4 5 9 C: 9, 3, 12; D via A: 8, 2, 10 (better than 11, keep)
    D 8 2 10 G: 10, 0, 10; C via D: 9 (no better)
    G 10 0 10 goal reached

    Path H–A–D–G, length 10, the same as Dijkstra's, but C was never expanded. Each time a node is reached by a second route, keep the smaller $g$; the search ends when the goal is the node with the smallest $f$. State the $g$, $h$ and $f$ values in every row: those are the marks.

    Vocabulary Train
    English Chinese Pinyin
    graph
    nodes 节点 jié diǎn
    edges biān
    minimax 极小化极大 jí xiǎo huà jí dà
    semantic network 语义网络 yǔ yì wǎng luò
    knowledge graph 知识图谱 zhī shí tú pǔ
    breadth-first search 广度优先搜索 guǎng dù yōu xiān sōu suǒ
    depth-first search 深度优先搜索 shēn dù yōu xiān sōu suǒ
    heuristic 启发式 qǐ fā shì
    18.1

    Artificial neural networks (ANNs)

    An ANN is inspired by the brain's neurons. An artificial neuron 人工神经元:

    • takes several input values, multiplies each by a weight 权重, and adds them up with a bias term 偏置项.
    • applies an activation function 激活函数 (a non-linear function such as ReLU) to the sum.
    • outputs the result, which feeds neurons further on.
    A single artificial neuron: three inputs each multiplied by a weight, summed with a bias, passed through an activation function, giving one output value
    A single neuron: each input times its weight, summed with a bias, then an activation function

    Neurons sit in layers: an input layer, one or more hidden layers 隐藏层 (where useful internal patterns are learned), and an output layer. With many hidden layers it is a deep neural network 深度神经网络, and training it is deep learning.

    Circles in four columns: an input layer of three nodes, two hidden layers of five nodes each, and one output node, all connected
    A neural network with an input layer, two hidden layers and an output layer

    ANNs let models learn complex patterns straight from raw data (pixels, audio, text) without hand-designed features — driving breakthroughs in image recognition 图像识别, speech recognition 语音识别, machine translation 机器翻译, and game playing. They do well with large amounts of data, noisy or very complex input, and patterns too hard to capture with explicit rules.

    "Explain what is meant by an artificial neural network." A model of the brain's network of neurons, made of layers of connected nodes: an input layer, one or more hidden layers and an output layer. Each connection has a weight; each node sums its weighted inputs and passes the result through an activation function to the next layer. "Explain how ANNs enable machine learning" (three marks): the network is trained on many examples; for each example the output is compared with the expected result and the error is used to adjust the weights (back propagation) so that the error falls; after enough examples the weights encode the patterns in the data, and the network can then classify or predict for new data it has never seen. "State the reason for multiple hidden layers": each additional layer combines the features found by the layer before it into more complex, more abstract features, so the network can learn more complex relationships (edges, then shapes, then objects); that is what makes a network deep.

    Explore

    Tap the parts of a neural network

    Explore the layers. Data flows left to right: the input layer takes the features, the hidden layers learn patterns, and the output layer gives the answer — with every connection carrying a weight that training adjusts.

    Vocabulary Train
    English Chinese Pinyin
    weight 权重 quán zhòng
    artificial neuron 人工神经元 rén gōng shén jīng yuán
    bias term 偏置项 piān zhì xiàng
    activation function 激活函数 jī huó hán shù
    hidden layers 隐藏层 yǐn cáng céng
    deep neural network 深度神经网络 shēn dù shén jīng wǎng luò
    image recognition 图像识别 tú xiàng shí bié
    speech recognition 语音识别 yǔ yīn shí bié
    machine translation 机器翻译 jī qì fān yì
    18.1

    Machine learning, deep learning, reinforcement learning

    Machine learning

    The umbrella term — any algorithm that learns from data. Three paradigms:

    • supervised learning 监督学习 — the data has labels 标签 (images tagged "cat"/"dog"); the algorithm learns input → label. Used for classification 分类 (a category) and regression.
    • unsupervised learning 无监督学习 — no labels; the algorithm finds structure, e.g. a cluster 聚类 of similar customers.
    • reinforcement learning (below).

    Use ML when explicit rules would be impractical (spam filters, recommendations, fraud detection).

    Two scatter plots: in supervised learning every training point is labelled cat or dog and the model learns a boundary between them; in unsupervised learning the points are unlabelled and the model finds two clusters by itself
    The same data seen two ways: with labels, the task is to learn what separates the classes; without labels, the task is to discover that there are groups at all

    "Describe supervised learning and unsupervised learning" (the marked wordings). Supervised learning: the algorithm is trained on labelled training data 训练数据, each example paired with the correct output (the target); it learns the relationship between inputs and outputs and uses it to classify or predict for new inputs; the answers are known while training, so the error can be measured. Unsupervised learning: the data is unlabelled, with no correct answers given; the algorithm looks for patterns, structure or groupings in the data by itself (clustering similar items, finding associations); the output is a set of categories or relationships that were not defined in advance. How they differ: labelled against unlabelled data; known outputs against discovered structure; supervised is used to predict (classification, regression), unsupervised to explore (clustering, anomaly detection). Both are categories of machine learning; the third is reinforcement learning.

    A pipeline: labelled training data trains a model, the trained model classifies new unlabelled data, and outputs how many of each type were found
    Supervised learning: a model is trained on labelled data, then recognises new data

    Deep learning

    A subset of ML using deep neural networks. Lower layers learn simple patterns (edges, phonemes), higher layers combine them into abstract concepts. It needs lots of data and lots of compute (GPUs); for small datasets, simpler ML methods often do better.

    "Explain what is meant by deep learning" (three marks). Machine learning that uses artificial neural networks with many hidden layers (deep networks); the network is trained on very large amounts of data, and each layer extracts features from the output of the layer below, so that the network learns the features it needs by itself rather than having them specified by the programmer. Reasons for using it: it can solve problems too complex for hand-written rules or shallow models (recognising faces, understanding speech, translating text); it improves as more data becomes available; it removes the need for human feature engineering; and it can handle unstructured data such as images, sound and text. How it is made more effective: more (and better-labelled) training data; more layers or nodes, within the limits of overfitting; more processing power (GPUs) and training time; tuning the learning rate and other parameters. Examples: speech recognition in voice assistants, image recognition in medical scans and self-driving cars, machine translation, recommendation systems.

    Reinforcement learning

    In reinforcement learning 强化学习, an agent 智能体 acts in an environment; each action changes the state and returns a reward 奖励. The agent learns a policy 策略 (a strategy) that maximises the total reward over time, by trial and error with no labels up front. Used for sequential-decision problems — games, robot control, autonomous driving.

    "Explain what is meant by reinforcement learning" (three marks). An agent learns by interacting with its environment: it takes an action, the environment moves to a new state and returns a reward (or penalty), and the agent adjusts its behaviour so as to maximise the total reward over time. There is no labelled data: the agent learns by trial and error, discovering which actions are good from the rewards it collects, and gradually forms a policy that says what to do in each state. Used where the right answer is not known in advance but the result of an action can be scored: game playing (chess, Go), robot control, traffic-light timing, resource allocation. A computer playing a board game against a user learns in this way, or searches the game tree with minimax to choose the move whose worst outcome is best.

    A loop between two boxes: the agent sends an action to the environment, which returns a new state and a reward back to the agent
    Reinforcement learning: the agent acts, the environment returns a new state and a reward, and the agent learns from it

    A self-driving car 自动驾驶汽车 is a real example. Lidar 激光雷达 and camera sensors (the spinning unit on the roof) build a live picture of the road, and a learned policy decides how to steer, speed up and brake safely.

    A white Waymo self-driving car on a city street, with a spinning lidar sensor unit on its roof and extra cameras at the front corners
    A self-driving car uses cameras and lidar sensors to see the road around it
    Several orange industrial robot arms welding a car body as it moves along a factory production line
    Industrial robot arms on a production line: reinforcement learning can teach a robot to control its movements
    Vocabulary Train
    English Chinese Pinyin
    labels 标签 biāo qiān
    reinforcement learning 强化学习 qiáng huà xué xí
    supervised learning 监督学习 jiān dū xué xí
    classification 分类 fēn lèi
    unsupervised learning 无监督学习 wú jiān dū xué xí
    cluster 聚类 jù lèi
    training data 训练数据 xùn liàn shù jù
    self-driving car 自动驾驶汽车 zì dòng jià shǐ qì chē
    agent 智能体 zhì néng tǐ
    reward 奖励 jiǎng lì
    policy 策略 cè lüè
    lidar 激光雷达 jī guāng léi dá
    18.1

    Training an ANN: backpropagation

    Training adjusts the weights so outputs match the targets. The standard method is backpropagation 反向传播 (back propagation of errors) with gradient descent 梯度下降. For each training example:

    1. forward pass — feed the input through to the output.
    2. compute the error with a loss function 损失函数 (a single number for how wrong the output is).
    3. backward pass — propagate the error backwards, finding each weight's gradient (how much it contributed to the error) using the chain rule.
    4. update the weights by a small step (set by the learning rate 学习率) that reduces the error.

    Repeat over many examples and many passes (epochs 训练轮次) until the error stops shrinking. The name "back" comes from step 3: the error flows from the output back towards the input, so every weight's gradient is found in one sweep. After training, a new input needs only one forward pass to get a prediction.

    "Describe the back propagation of errors method" (four marks). (1) An input is fed forward through the network and its output is compared with the expected (target) output; (2) the difference is the error; (3) the error is passed backwards through the network, layer by layer from the output to the input, and each weight's share of the error is calculated; (4) the weights are adjusted in proportion to their contribution, in the direction that reduces the error; (5) the process is repeated with many examples until the error is as small as required. The point of the method is that a network with hidden layers has no direct way of knowing which internal weight caused an output error; back propagation apportions the blame.

    A U-shaped curve of squared error against weight, with steps moving downhill towards the minimum error
    Training adjusts the weights to reach the minimum error
    Vocabulary Train
    English Chinese Pinyin
    learning rate 学习率 xué xí lǜ
    backpropagation 反向传播 fǎn xiàng chuán bō
    gradient descent 梯度下降 tī dù xià jiàng
    loss function 损失函数 sǔn shī hán shù
    epochs 训练轮次 xùn liàn lún cì
    18.1

    Regression

    Some tasks predict a number (a house price, tomorrow's temperature) — regression 回归, as opposed to classification (a category).

    Linear regression 线性回归 fits a straight line (or hyperplane):

    $$y = m_{1} x_{1} + m_{2} x_{2} + \ldots + m_{n} x_{n} + c.$$

    Choose the coefficients to minimise the sum of squared errors against the training data. Use it when the relationship looks roughly linear and you want an interpretable model. For curved data, use polynomial, decision-tree, or neural-network regression methods — same idea: define a model, define a loss, and adjust the parameters to minimise it. Regression and classification are both supervised; the choice depends on whether the answer is a number or a category.

    "Describe regression methods in machine learning" (two marks). Statistical methods that find the relationship between input variables and a continuous output, by fitting a function (a line or curve) to the training data with the smallest total error; the fitted function is then used to predict the output for new inputs. Linear regression fits a straight line; other methods fit curves. Regression predicts a value (a price, a temperature, a time); classification predicts a category, which is the distinction the exam asks for.

    A scatter of points with a straight best-fit line through them; dashed vertical lines show the error between each point and the line
    Linear regression fits the line that makes the total squared error (the dashed gaps) as small as possible
    Explore

    Fitting a regression line

    Drag the controls. Linear regression draws the straight line that makes the squared distances to the data points as small as possible — then it predicts a number for any new input.

    Vocabulary Train
    English Chinese Pinyin
    regression 回归 huí guī
    linear regression 线性回归 xiàn xìng huí guī
    18.1

    How AI is used in a real scenario

    Many exam scenarios use the same pattern — a deep-learning model trained on labelled data, often several combined into a pipeline:

    • customer identification at an automated shop: the system is trained on labelled face images; a camera captures a face; image recognition extracts a representation; it is matched against registered customers; the closest match identifies the person.
    • reading text from images: image recognition finds text regions; optical character recognition 光学字符识别 extracts the characters; machine translation converts them; text-to-speech 文本转语音 reads them aloud.
    • checkout item-detection: object-detection AI, trained on labelled product images, sees which items go into a basket and charges the account.

    By the time a user interacts with the system, the model is fast — it only does forward-pass inference; the intelligence is in the patterns learned during training.

    Model answers for the scenario questions. A car-park camera reads registration numbers: the camera captures an image; an AI trained on many labelled images of number plates locates the plate in the image; character recognition (a deep-learning classifier, again trained on labelled characters) converts the plate into text; the text is stored with the time and matched when the car leaves. A CCTV system detects and tracks a person: image-recognition software trained on labelled images of people identifies a person in each frame; the system compares successive frames to follow their movement; unusual movement can trigger an alert. Speech turned into commands: speech recognition trained on many recorded voices converts the sound into text; the system matches the text to a set of known commands; it improves as it is corrected. A camera that focuses on faces: a face-detection model trained on labelled faces finds the face region, and the lens is adjusted to bring that region into focus. A bank's face-recognition login: the app captures the face, a deep network extracts its features, and they are compared with the stored features for that customer. In every case the pattern is: trained on labelled examples, extracts features, matches or classifies new input.

    Worked example. For each task, say whether it needs regression or classification, and what the output layer of an ANN would look like: (a) predict tomorrow's temperature; (b) decide whether an email is spam. Ask what kind of thing is being predicted. (a) A temperature is a number on a continuous scale, so this is regression, and the output layer is a single neuron holding that value. (b) Spam or not-spam is a category, so this is classification, and the output gives a probability per class. Both are supervised learning: each needs labelled examples to train on, and training adjusts the weights by backpropagation to reduce the error. The deciding question is simply number-or-category - not how difficult the task feels.

    Vocabulary Train
    English Chinese Pinyin
    optical character recognition 光学字符识别 guāng xué zì fú shí bié
    text-to-speech 文本转语音 wén běn zhuǎn yǔ yīn
    18.1

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    graph (in AI) a set of nodes representing states or places, joined by edges representing connections, often weighted, that a search algorithm can explore
    Dijkstra's algorithm finds the shortest distance from a start node to every other node by always visiting the unvisited node with the smallest distance so far
    A* algorithm a shortest-path search that expands the node with the smallest total of distance so far plus a heuristic estimate of the distance to the goal
    artificial neural network a model of the brain's neurons: layers of nodes joined by weighted connections, trained by adjusting the weights
    machine learning algorithms that learn from data and improve with experience rather than following fixed rules
    supervised learning learning from labelled training data in which the correct output for each input is known
    unsupervised learning learning from unlabelled data by finding patterns, groupings or structure in it
    reinforcement learning an agent learns by trial and error, choosing actions in an environment to maximise the rewards it receives
    deep learning machine learning using neural networks with many hidden layers, trained on large amounts of data, each layer extracting features from the one below
    back propagation of errors comparing the network's output with the target, passing the error back through the layers and adjusting each weight to reduce it
    regression fitting a function to training data in order to predict a continuous output value from inputs
    18.1

    Exam tips

    • Graph answers name nodes, edges and weights, and what they represent; then the algorithm. Dijkstra: table of distances, visit the smallest, update neighbours. A*: $g$, $h$ and $f = g + h$ in every row, expand the smallest $f$.
    • ANN answers name the layers, the weighted connections and training; deep learning adds many hidden layers, large data and automatic feature extraction, with a reason and an example.
    • The three categories in one line each: labelled data and known outputs; unlabelled data and discovered structure; agent, environment, actions and rewards.
    • Back propagation: compare with the target, error backwards through the layers, adjust weights to reduce it, repeat. Regression predicts a value; classification predicts a category.
    • Scenario questions want the pipeline: trained on labelled examples, extracts features, recognises or classifies new input; name the type of AI (image recognition, speech recognition, deep learning).

    Common mistakes

    • Describing a graph as "a chart"; in AI it is nodes and edges.
    • Running Dijkstra by picking the nearest neighbour of the current node rather than the smallest overall distance not yet visited; or forgetting to update a node when a shorter route appears.
    • Adding $h$ into $g$ for the next step in A*; $g$ is only the real distance, $h$ is recomputed from the table.
    • Saying deep learning is "learning a lot"; it is the many hidden layers.
    • Confusing unsupervised learning with reinforcement learning; the first finds structure in data, the second learns from rewards.
    • Describing back propagation without the comparison with the expected output or without saying the weights are adjusted.
    • Calling a prediction of a price "classification"; a continuous value is regression.
  • 19

    Computational thinking and Problem-solving

    19.1

    Searching algorithms

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of linear search and binary search methods Write an algorithm to implement a linear search Write an algorithm to implement a binary search The conditions necessary for the use of a binary search How the performance of a binary search varies according to the number of data items
    Show understanding of insertion sort and bubble sort methods Write an algorithm to implement an insertion sort Write an algorithm to implement a bubble sort Performance of a sorting routine may depend on the initial order of the data and the number of data items
    Show understanding of and use Abstract Data Types (ADT) Write algorithms to find an item in each of the following: linked list, binary tree Write algorithms to insert an item into each of the following: stack, queue, linked list, binary tree Write algorithms to delete an item from each of the following: stack, queue, linked list Show understanding that a graph is an example of an ADT. Describe the key features of a graph and justify its use for a given situation. Candidates will not be required to write code for a graph structure
    Show how it is possible for ADTs to be implemented from another ADT Describe the following ADTs and demonstrate how they can be implemented from appropriate built-in types or other ADTs: stack, queue, linked list, dictionary, binary tree
    Show understanding that different algorithms which perform the same task can be compared by using criteria (e.g. time taken to complete the task and memory used) Including use of Big O notation to specify time and space complexity

    Source: Cambridge International syllabus

    Big O: how algorithms scale
    Insertion sort: slide each card into place
    Bubble sort, pass by pass
    Binary search: halve and conquer

    A search finds a target value in a collection (often an array 数组) and returns its position, or "not found".

    An open telephone directory
    Searching a sorted list, like a phone book, is far faster than checking every entry one by one

    Linear search

    A linear search 线性查找 walks from start to end, comparing each element with the target:

    FOR i ← 1 TO n
        IF A[i] = target THEN RETURN i
    NEXT i
    RETURN -1   // not found
    

    No preparation is needed, so it works on any list. Worst case O($n$) (target at the end or absent); best case 1 comparison. Use it on unsorted data or small lists. (The returned -1 is a sentinel value — an impossible position that means "not found"; the caller tests IF result = -1.)

    The exam's version. Paper 3 asks you to complete a linear search written with a flag and a WHILE loop, and Paper 4 to write a function that returns the index or a count. Both look like this:

    FUNCTION LinearSearch(Data : ARRAY OF INTEGER, Target : INTEGER) RETURNS INTEGER
        DECLARE Index, Count : INTEGER
        Count ← 0
        FOR Index ← 1 TO 100
            IF Data[Index] = Target THEN
                Count ← Count + 1
            ENDIF
        NEXT Index
        RETURN Count          // how many times Target occurs; 0 means not found
    ENDFUNCTION
    

    To stop at the first match instead, use a WHILE Index <= 100 AND NOT Found loop that sets Found ← TRUE and remembers the index. The marks are for the loop over every element, the comparison, and what is returned when the value is absent.

    A row of alphabet cells A to Z; cells A to V are shaded as checked and W is highlighted as the match, with a pointer below W
    Linear search checks every letter in turn — 23 comparisons to find W

    Binary search

    A binary search 二分查找 needs the data sorted. Look at the middle element; if it is the target, done; if the target is smaller, search the left half, else the right half — halving the range each time:

    low ← 1
    high ← n
    WHILE low <= high DO
        mid ← (low + high) DIV 2
        IF A[mid] = target THEN RETURN mid
        IF A[mid] < target THEN
            low ← mid + 1
        ELSE
            high ← mid - 1
        ENDIF
    ENDWHILE
    RETURN -1
    

    Worst case O($\log_{2} n$) — for a million items, about 20 comparisons. Much faster than linear search on large sorted arrays, but you must sort first (a one-off O($n \log n$) cost), worth it if you search many times.

    "State the condition necessary for a binary search." The data must be in order (sorted, ascending or descending, on the key being searched). "Describe how to perform a binary search" (three marks): (1) find the middle item of the list (or of the current range) and compare it with the target; (2) if it matches, the search ends; if the target is smaller, repeat on the lower half, if larger, on the upper half; (3) keep halving the range until the item is found or the range is empty, which means it is not present.

    The exam's version, with the bounds and a flag, is the one to reproduce when asked to complete the algorithm:

    DECLARE Lower, Upper, Mid : INTEGER
    DECLARE Found : BOOLEAN
    Lower ← 0
    Upper ← 99
    Found ← FALSE
    WHILE Lower <= Upper AND NOT Found
        Mid ← (Lower + Upper) DIV 2
        IF Names[Mid] = Target THEN
            Found ← TRUE
        ELSE
            IF Names[Mid] < Target THEN
                Lower ← Mid + 1
            ELSE
                Upper ← Mid - 1
            ENDIF
        ENDIF
    ENDWHILE
    IF Found THEN OUTPUT Mid ELSE OUTPUT "Not found" ENDIF
    

    "Explain how the performance varies with the number of items." Each comparison halves the number of items left, so the maximum number of comparisons is about $\log_{2} n$: doubling the size of the list adds only one more comparison. This is O($\log n$). "Compare linear and binary search": a linear search needs up to $n$ comparisons (O($n$)) and, on average, half that, but works on unsorted data; a binary search needs at most $\log_{2} n$ (O($\log n$)) and is far faster for large lists, but the data must first be sorted and it must allow direct access to the middle item (an array, not a linked list). For $1000$ items: $1000$ against $10$ comparisons.

    Three rows showing binary search on the sorted alphabet; the active low-to-high range halves each step as the middle letter M, then T, then W is compared with W
    Binary search halves the range each step (low / mid / high) — just 3 comparisons to find W
    A library card catalogue: a wall of small wooden drawers, one pulled open to show the cards filed in order
    A card catalogue: sorted records are what make a binary search possible — halve, look, halve again
    Explore

    Linear vs binary search

    Search for a value. Binary search halves the list each step (only on sorted data); linear search checks one by one.

    Vocabulary Train
    English Chinese Pinyin
    binary search 二分查找 èr fēn chá zhǎo
    array 数组 shù zǔ
    linear search 线性查找 xiàn xìng chá zhǎo
    Exercise sheet
    19.1

    Sorting algorithms

    Bubble sort

    A bubble sort 冒泡排序 repeatedly walks the array, swapping adjacent pairs that are out of order, so the largest "bubbles" to the end each pass:

    FOR pass ← 1 TO n - 1
        swapped ← FALSE
        FOR i ← 1 TO n - pass
            IF A[i] > A[i + 1] THEN
                temp ← A[i]
                A[i] ← A[i + 1]
                A[i + 1] ← temp
                swapped ← TRUE
            ENDIF
        NEXT i
        IF swapped = FALSE THEN EXIT FOR   // already sorted
    NEXT pass
    

    Best case O($n$) (already sorted, with the early exit); average/worst O($n^{2}$). Simple but slow for large $n$.

    Insertion sort

    An insertion sort 插入排序 builds a sorted prefix from the left, inserting each new element into place by shifting larger ones right:

    FOR i ← 2 TO n
        key ← A[i]
        j ← i - 1
        WHILE j >= 1 AND A[j] > key DO
            A[j + 1] ← A[j]
            j ← j - 1
        ENDWHILE
        A[j + 1] ← key
    NEXT i
    

    Best case O($n$) (already sorted); worst O($n^{2}$). Good for small or nearly-sorted arrays. It sorts in place 原地 and is stable 稳定 (keeps the order of equal elements).

    Tracing a sort

    A common task is to show the array after each outer pass. For [D, T, H, R] with insertion sort: pass 1 (key T) no change; pass 2 (key H) → [D, H, T, R]; pass 3 (key R) → [D, H, R, T].

    Writing a sort from scratch. "Write pseudocode to sort DataArray[1:1000] into ascending order" is answered by a complete bubble sort with the early-exit flag, or an insertion sort, declared and indented; either scores full marks if it works for every input:

    DECLARE Pass, Index, Temp : INTEGER
    DECLARE Swapped : BOOLEAN
    Pass ← 1
    REPEAT
        Swapped ← FALSE
        FOR Index ← 1 TO 1000 - Pass
            IF DataArray[Index] > DataArray[Index + 1] THEN
                Temp ← DataArray[Index]
                DataArray[Index] ← DataArray[Index + 1]
                DataArray[Index + 1] ← Temp
                Swapped ← TRUE
            ENDIF
        NEXT Index
        Pass ← Pass + 1
    UNTIL Swapped = FALSE OR Pass = 1000
    

    For descending order change > to <; to sort records or a 2D array by one field, compare that field but swap the whole record (or every column). Asked to write an insertion sort "that performs the same task" as a given bubble sort, keep the same array name and direction and reproduce the insertion sort above with the comparison reversed if the order is descending.

    "Describe two ways the performance of a sort is affected by the data" (two marks). (1) The number of items: an $O(n^{2})$ sort takes four times as long for twice as many items. (2) How far the data is already in order: a bubble sort with a flag, or an insertion sort, finishes in one pass over already-sorted data ($O(n)$) and does the most work on data in reverse order; the number of swaps depends on how many pairs are out of order. (Also accepted: the range or number of duplicate values, and whether the items are large records that are expensive to move.) Bubble and insertion sort are both O($n^{2}$) in the worst and average cases and O($n$) at best; quicksort and merge sort are O($n \log n$), which is why they are used for large data.

    Rows tracing an insertion sort of D, T, H, R across three passes; the sorted prefix is shaded and arrows show each larger element shifting right to let the key drop in
    An insertion sort of [D, T, H, R], shifting each key into its place pass by pass
    Explore

    Watch a sort run

    Step through a sort and watch the bars settle into order — how a sorting algorithm works pass by pass.

    Vocabulary Train
    English Chinese Pinyin
    insertion sort 插入排序 chā rù pái xù
    bubble sort 冒泡排序 mào pào pái xù
    in place 原地 yuán dì
    stable 稳定 wěn dìng
    19.1

    ADTs in algorithms

    The Abstract Data Types (ADTs) from Topic 10 appear inside many algorithms: a stack drives depth-first traversal and undo; a queue 队列 drives breadth-first traversal and print ordering; a linked list 链表 lets data grow and shrink.

    ADTs can be built from other ADTs, not just from arrays: a queue from two stacks; a stack from a linked list (push = prepend a head node 节点); a queue from a linked list with head and tail pointers 指针; a binary tree 二叉树 from nodes with two child pointers; a dictionary 字典 stores key→value pairs (often on a hash table). Layering this way separates concerns — the algorithm using the ADT need not know how it is built.

    The ADTs the exam asks you to describe and implement

    Stack (last in, first out): items are added (pushed) and removed (popped) at the same end, the top; a pointer TopOfStack holds the index of the top item. Implemented with an array and that one pointer: push checks the stack is not full, increments the pointer and stores the item; pop checks it is not empty, returns the top item and decrements the pointer.

    FUNCTION Push(Item : INTEGER) RETURNS BOOLEAN
        IF TopOfStack = 9 THEN RETURN FALSE ENDIF      // full (array 0 to 9)
        TopOfStack ← TopOfStack + 1
        StackData[TopOfStack] ← Item
        RETURN TRUE
    ENDFUNCTION
    FUNCTION Pop() RETURNS INTEGER
        IF TopOfStack = -1 THEN RETURN -1 ENDIF        // empty
        TopOfStack ← TopOfStack - 1
        RETURN StackData[TopOfStack + 1]
    ENDFUNCTION
    

    Queue (first in, first out): items join at the rear (enqueue) and leave from the front (dequeue); two pointers and a count. In a linear queue the front pointer creeps along the array until the space at the start is wasted; a circular queue 循环队列 wraps both pointers round with MOD, so every cell is reused.

    A circular queue of six array cells holding three items in cells 3 to 5, with the front pointer at 3 and the rear at 5, and a dashed arrow showing that the next item wraps round into cell 0
    A circular queue: the rear and front pointers step forward with MOD, so the array's first cells are reused once their items have left
    FUNCTION Enqueue(Item : STRING) RETURNS BOOLEAN
        IF Count = 6 THEN RETURN FALSE ENDIF            // full
        Rear ← (Rear + 1) MOD 6
        QueueArray[Rear] ← Item
        Count ← Count + 1
        RETURN TRUE
    ENDFUNCTION
    FUNCTION Dequeue() RETURNS STRING
        IF Count = 0 THEN RETURN "" ENDIF               // empty
        DECLARE Item : STRING
        Item ← QueueArray[Front]
        Front ← (Front + 1) MOD 6
        Count ← Count - 1
        RETURN Item
    ENDFUNCTION
    

    Linked list: a sequence of nodes, each holding a data item and a pointer to the next node; a start pointer gives the first node and a null pointer (0 or $-1$) ends the list. In an array implementation two parallel arrays hold the data and the pointers, and unused cells are chained into a free list 空闲列表 so that an insertion knows where to put the new node.

    Two parallel arrays Data and Pointer implementing a linked list of the names Ann, Ben and Dan: the start pointer is 1, the pointers chain 1 to 3 to 2 to 0, and the unused cells 4, 5 and 6 form the free list
    A linked list in two arrays: the order of the list is in the pointers, not in the positions; inserting a name means taking a cell from the free list and re-linking two pointers
    FUNCTION FindInList(Target : STRING) RETURNS INTEGER   // index, or 0 if absent
        DECLARE Current : INTEGER
        Current ← Start
        WHILE Current <> 0
            IF Data[Current] = Target THEN RETURN Current ENDIF
            Current ← Pointer[Current]
        ENDWHILE
        RETURN 0
    ENDFUNCTION
    

    To insert into an ordered list: take the first free cell (NewNode ← FreeList, FreeList ← Pointer[FreeList]), store the item, then walk the list with a Previous and Current pointer until Data[Current] > Item or the end; set Pointer[NewNode] ← Current and Pointer[Previous] ← NewNode (or Start ← NewNode if it goes first). To delete, re-link the previous node past the deleted one and return the cell to the free list.

    Binary tree: a root node, each node holding data, a left pointer to a subtree of smaller values and a right pointer to a subtree of larger values. Implemented as a 2D array (or three 1D arrays) Tree[Index, 0..2] for left pointer, data, right pointer, with a root pointer and a next-free pointer.

    FUNCTION FindInTree(Target : INTEGER) RETURNS INTEGER   // index, or -1
        DECLARE Current : INTEGER
        Current ← Root
        WHILE Current <> -1
            IF Tree[Current, 1] = Target THEN RETURN Current ENDIF
            IF Target < Tree[Current, 1] THEN
                Current ← Tree[Current, 0]      // go left
            ELSE
                Current ← Tree[Current, 2]      // go right
            ENDIF
        ENDWHILE
        RETURN -1
    ENDFUNCTION
    

    To insert: store the item in the next free node with both pointers $-1$; if the tree is empty make it the root; otherwise walk down from the root, going left or right by comparison, until the pointer you would follow is $-1$, and set that pointer to the new node. An ADT from another ADT: a stack is a linked list where push and pop both work at the start; a queue is a linked list with a start and an end pointer; a queue can be made from two stacks (push onto one, pop from the other, moving everything across when the second is empty); a binary tree's nodes are records or objects linked by pointers, so it is built from a linked structure of nodes. Say which operations of the new ADT map onto which operations of the old one.

    A binary tree with root 27, a left subtree of 19, 16, 21 and 17, and a right subtree of 36, 42, 89 and 55, with the root, the left and right pointers, and a leaf node labelled
    A binary tree: each node has up to two child nodes
    A binary search tree with root 4 (left subtree 2 over 1 and 3, right subtree 6 over 5 and 7); pre-order visits 4 2 1 3 6 5 7, in-order 1 2 3 4 5 6 7 (sorted), post-order 1 3 2 5 7 6 4
    Three depth-first traversals of a binary tree: pre-order, in-order (sorted order) and post-order
    Vocabulary Train
    English Chinese Pinyin
    linked list 链表 liàn biǎo
    stack zhàn
    queue 队列 duì liè
    node 节点 jié diǎn
    pointers 指针 zhǐ zhēn
    binary tree 二叉树 èr chā shù
    dictionary 字典 zì diǎn
    circular queue 循环队列 xún huán duì liè
    free list 空闲列表 kòng xián liè biǎo
    19.1

    Comparing algorithms

    Time complexity

    Time complexity 时间复杂度 is how the running time grows with input size $n$, written in Big-O notationO表示法 (the dominant term): O(1) constant, O($\log n$) binary search, O($n$) linear search, O($n \log n$) good sorts, O($n^{2}$) bubble/insertion sort. A smaller order is better at scale, even if another algorithm is faster for small $n$.

    To make that concrete: to sort a million items, an $O(n \log n)$ sort finishes in a fraction of a second, while an $O(n^{2})$ sort can take minutes.

    Worked example. A sorted list holds $1000$ items. How many comparisons does each search need in the worst case?

    A linear search checks items one at a time, so it may need up to $1000$ comparisons — this is $O(n)$. A binary search halves the list each step, so it needs at most $\lceil \log_2 1000 \rceil = 10$ comparisons — this is $O(\log n)$. Doubling the list to $2000$ items adds only one comparison to the binary search, but up to another $1000$ to the linear search — which is why the order of growth, not raw speed, decides the winner at scale.

    Describing an order. O(1): the time is constant, independent of the number of items (pushing onto a stack, reading an array element). O($\log n$): the time grows with the logarithm of the number of items, so doubling the data adds only a fixed extra step (binary search). O($n$): the time grows in proportion to the number of items (linear search, one pass through a list). O($n \log n$): a little worse than linear (efficient sorts). O($n^{2}$): the time grows with the square of the number of items, so doubling the data quadruples the time (bubble and insertion sort). "State the Big O of a binary search of Names[0:99]" is answered $O(\log n)$, and "describe its meaning" as above; Big O measures how the time or memory scales, not the actual time.

    A graph of running time against input size n for the common orders: O(1) and O(log n) stay almost flat, O(n) rises gently, O(n log n) more steeply, and O(n squared) climbs away fastest
    How the common orders of growth compare: a smaller order wins at scale
    A line graph of running time against the number of elements n: bubble sort and insertion sort rise steeply as O(n squared), while quick sort stays low as O(n log n)
    How sorting time grows with the number of elements $n$: $O(n^2)$ sorts climb away from an $O(n\log n)$ sort

    Space complexity

    Space complexity 空间复杂度 is the extra memory needed. Bubble and insertion sort use O(1) extra (in place); merge sort uses O($n$); recursion uses stack memory proportional to its depth. There is often a time–memory trade-off.

    Other criteria

    Simplicity (easier to code and maintain), stability, and adaptiveness (faster on nearly-sorted data). The right algorithm depends on the data and the constraints.

    Explore

    How running time grows with n

    Slide n upward and compare the curves: O(1) and O(log n) stay almost flat, O(n) rises steadily, O(n²) explodes. This is why Big-O — not a stopwatch — is how we compare algorithms on large inputs.

    Explore

    Big-O growth

    Change the input size n and compare how fast each algorithm's work grows — the idea behind time complexity.

    Vocabulary Train
    English Chinese Pinyin
    time complexity 时间复杂度 shí jiān fù zá dù
    Big-O notation 大O表示法 dà O biǎo shì fǎ
    space complexity 空间复杂度 kōng jiān fù zá dù
    19.2

    Recursion

    Syllabus
    Candidates should be able to: Notes and guidance
    Show understanding of recursion Essential features of recursion How recursion is expressed in a programming language Write and trace recursive algorithms When the use of recursion is beneficial
    Show awareness of what a compiler has to do to translate recursive programming code Use of stacks and unwinding

    Source: Cambridge International syllabus

    Recursion: the call stack winds up and unwinds

    Recursive algorithms use recursion 递归: the routine calls itself with a smaller version of the same problem, until a base case 基本情形 ends the chain. It has two parts: the base case (small enough to solve directly — without it the recursion never stops) and the recursive case 递归情形 (reduce the input and call itself).

    Factorial 阶乘:

    FUNCTION Factorial(n : INTEGER) RETURNS INTEGER
        IF n = 0 OR n = 1 THEN
            RETURN 1
        ELSE
            RETURN n * Factorial(n - 1)
        ENDIF
    ENDFUNCTION
    

    Recursion is natural for self-similar problems: trees, divide-and-conquer 分治 (binary search, merge sort), and nested data. When it is a poor fit, a loop is usually cleaner.

    "Describe what is meant by recursion" (two marks). A function or procedure that is defined in terms of itself: it calls itself from within its own body, with a smaller version of the problem each time, until a base case is reached. "State three essential features of recursion": (1) a base case (stopping condition) that returns a value without a further call; (2) a general case 一般情形 in which the routine calls itself; (3) each call moves the problem closer to the base case (the parameter is reduced), so that the recursion terminates. Some schemes add: values are returned as the calls unwind.

    "Describe when the use of recursion is beneficial, and give an example." When the problem is naturally defined in terms of smaller versions of itself, so that the recursive solution is shorter, clearer and closer to the mathematical definition than a loop would be: a factorial or Fibonacci number, a binary search, traversing a binary tree, merge sort or quicksort, and processing nested structures such as folders within folders. It is a poor choice when the depth is large (the stack may overflow) or when the same sub-problem is computed many times (naive Fibonacci).

    Tracing a recursive call

    For Factorial(4): the calls go down to Factorial(1)=1, then unwinding multiplies back up: 2*1=2, 3*2=6, 4*6=24. Final result 24. Track each pending call on a stack.

    Worked example. The function below is given without an explanation. Trace Unknown(3, 5) and state its output and return value.

    FUNCTION Unknown(BYVAL X, BYVAL Y : INTEGER) RETURNS INTEGER
        IF X < Y THEN
            OUTPUT X + Y
            RETURN Unknown(X + 1, Y - 1) + 1
        ELSE
            RETURN 0
        ENDIF
    ENDFUNCTION
    

    Call 1: $X = 3, Y = 5$: $3 < 5$, output 8, call Unknown(4, 4). Call 2: $4 < 4$ is false, return 0. Unwinding: call 1 returns $0 + 1 = 1$. Output 8, return value 1. Write the trace as a table with a row per call (parameters, condition, output, what it returns), and do the returns from the deepest call upwards: that is the unwinding the mark scheme looks for.

    Worked example (Fibonacci). Fib(n) returns n when n < 2, otherwise Fib(n - 1) + Fib(n - 2). Find Fib(5).

    Fib(5) = Fib(4) + Fib(3); Fib(4) = Fib(3) + Fib(2); Fib(3) = Fib(2) + Fib(1); Fib(2) = Fib(1) + Fib(0) = 1 + 0 = 1. So Fib(3) = 1 + 1 = 2, Fib(4) = 2 + 1 = 3, Fib(5) = 3 + 2 = 5. The base case is reached many times (Fib(2) is computed three times), which is why this version is slow: it makes 15 calls for $n = 5$ and roughly doubles the calls for every increase in $n$.

    Converting recursion to iteration. Every recursive routine can be rewritten with a loop, which uses less memory and is faster: keep a running result and loop from the base case upwards. Factorial as a loop:

    FUNCTION Factorial(N : INTEGER) RETURNS INTEGER
        DECLARE Result, Count : INTEGER
        Result ← 1
        FOR Count ← 2 TO N
            Result ← Result * Count
        NEXT Count
        RETURN Result
    ENDFUNCTION
    

    Asked to change a recursive insertion sort or search into an iterative one, replace the self-call with a loop over the index that the recursion was stepping through, and turn the base case into the loop's exit condition.

    The call stack for Factorial(4): each call pushes a frame down to the base case Factorial(1)=1, then the stack unwinds, returning 2 = 2 times 1, 6 = 3 times 2 and 24 = 4 times 6
    Recursion uses the call stack: calls push frames down to the base case, then returns unwind back up

    Risks

    • infinite recursion if the base case is missed — crashes with a stack overflow 栈溢出.
    • high memory use for deep recursion.
    • slow if it repeats work (naive Fibonacci is exponential — use a loop or memoisation 记忆化).
    Explore

    Recursion unwinds from the leaves up

    Step through fib(4) in the order the calls actually finish: the leaves (base cases) resolve first, then each parent combines its children. Notice fib(2) is computed twice — that repeated work is why naive recursion is slow.

    Vocabulary Train
    English Chinese Pinyin
    recursion 递归 dì guī
    base case 基本情形 jī běn qíng xíng
    recursive case 递归情形 dì guī qíng xíng
    factorial 阶乘 jiē chéng
    divide-and-conquer 分治 fēn zhì
    general case 一般情形 yì bān qíng xíng
    stack overflow 栈溢出 zhàn yì chū
    memoisation 记忆化 jì yì huà
    Exercise sheet
    19.2

    What the compiler does for recursive code

    Recursion needs each call to have its own copy of its parameters 参数 and local variables 局部变量. The compiler keeps these on the call stack 调用栈. For each call it pushes a stack frame 栈帧 holding the parameters, the local variables, and the return address 返回地址 (where to resume in the caller). When the function returns, the return value is handed back, the frame is popped, and control resumes at the return address.

    Because each call has its own frame, recursive calls don't trample each other's variables. The stack can grow large for deep recursion, which is why very deep recursion may overflow it. This is the same call-and-return mechanism used for ordinary (non-recursive) calls — there is no special "recursion mechanism".

    "Explain why a stack is suitable for implementing recursion" (three marks). Each recursive call must save its return address, its parameters and its local variables, and the calls are completed in the reverse order to that in which they were made (the last call made is the first to finish), which is exactly the last in, first out behaviour of a stack: each new call pushes a frame, and each return pops the most recent frame, restoring the caller's state and telling it where to continue. This is the compiler's job when it translates recursive code: it generates the push of a stack frame on every call and the pop on every return, and the frames are unwound as the results come back.

    Vocabulary Train
    English Chinese Pinyin
    call stack 调用栈 diào yòng zhàn
    parameters 参数 cān shù
    local variables 局部变量 jú bù biàn liàng
    stack frame 栈帧 zhàn zhēn
    return address 返回地址 fǎn huí dì zhǐ
    19.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    linear search checking each item in turn from the start until the target is found or the end is reached
    binary search repeatedly comparing the target with the middle item of a sorted list and discarding the half that cannot contain it
    bubble sort repeatedly passing through the list, swapping adjacent items that are in the wrong order, until a pass makes no swaps
    insertion sort taking each item in turn and inserting it into its correct place among the items already sorted
    abstract data type a collection of data and the operations that can be performed on it, defined independently of how it is stored
    stack a last-in-first-out structure with push and pop at the top
    queue a first-in-first-out structure with items added at the rear and removed from the front
    linked list a sequence of nodes, each holding data and a pointer to the next node, with a start pointer
    binary tree nodes each holding data and pointers to a left subtree of smaller values and a right subtree of larger values
    Big O notation a way of classifying the time (or memory) an algorithm needs by how it grows with the size of the input
    recursion a routine that calls itself with a smaller version of the problem until a base case stops the calls
    base case the condition under which a recursive routine returns without calling itself
    unwinding the returns of a chain of recursive calls, from the deepest call back to the first, as the stack frames are popped
    19.2

    Exam tips

    • Searches: linear needs no order and O($n$); binary needs a sorted array, halves each time and is O($\log n$). Know both algorithms by heart, including the bounds and the flag.
    • Sorts: bubble with a swapped flag, insertion with a key that shifts larger items right; both O($n^{2}$) worst, O($n$) on sorted data. Performance depends on the number of items and how ordered they are.
    • ADT implementations are pointer bookkeeping: a top pointer; front, rear and count with MOD; start, pointers and a free list; root with left and right pointers. Always check for full and empty.
    • Big O is about scaling: constant, logarithmic, linear, square. Say "doubling the data adds one comparison" for a binary search.
    • Recursion: base case, general case, progress towards the base case; beneficial when the problem is defined in terms of itself; a stack holds the return addresses and variables because calls return in reverse order. Trace with a table and unwind from the deepest call.

    Common mistakes

    • Using a binary search on unsorted data, or on a linked list; and setting Lower ← Mid instead of Mid + 1, which loops for ever.
    • A bubble sort inner loop that runs to the end of the array every pass, or a swap without a temporary variable.
    • A push or enqueue that does not test for full, or a pop or dequeue that does not test for empty.
    • Moving the queue's front pointer without MOD in a circular queue, or treating front = rear as always meaning empty.
    • Inserting into a linked list by shifting the array contents; only the pointers change.
    • A recursive function with no base case, or one whose recursive call does not make the problem smaller.
    • Tracing a recursive call but forgetting to add the pending work on the way back up.
    • Answering "why a stack" with "because it is fast"; the reason is the last-in-first-out order of the returns.
  • 20

    Further Programming

    20.1

    Programming paradigms

    Syllabus
    Candidates should be able to: Notes and guidance
    Understanding what is meant by a programming paradigm
    Show understanding of the characteristics of a number of programming paradigms:
    Low-level Low-level Programming: • understanding of and ability to write low-level code that uses various addressing modes: immediate, direct, indirect, indexed and relative
    Imperative (Procedural) Imperative (Procedural) programming: • Assumed knowledge and understanding of Structural Programming (see details in AS content section 11.3) • understanding of and ability to write imperative (procedural) programming code that uses variables, constructs, procedures and functions. See details in AS content
    Object Oriented Object-Oriented Programming (OOP): • understanding of the terminology associated with OOP (including objects, properties/attributes, methods, classes, inheritance, polymorphism, containment (aggregation), encapsulation, getters, setters, instances) • understanding of how to solve a problem by designing appropriate classes • understanding of and ability to write code that demonstrates the use of OOP
    Declarative Declarative programming: • understanding of and ability to solve a problem by writing appropriate facts and rules based on supplied information • understanding of and ability to write code that can satisfy a goal using facts and rules

    Source: Cambridge International syllabus

    A programming paradigm 编程范式 is a style of programming — a way of structuring programs, with its own ideas and language features. Four programming paradigms are in this syllabus.

    "Describe what is meant by an imperative (procedural) language" (two marks). A language in which the program is a sequence of instructions that are executed in order and that change the program's state; the programmer says how the task is done, using procedures, sequence, selection and iteration. "Describe what is meant by a declarative language": the program states facts and rules (what is known and what is wanted) and the language's inference engine works out how to find the answer; the programmer does not give the sequence of steps.

    Identify the paradigm from a code sample (a regular Paper 3 question): LDD 200, ADD #5, STO 201 is low-level (mnemonics, registers, memory addresses); FOR Count ← 1 TO 10 … NEXT Count with procedures and assignments is imperative; CLASS Dog … PRIVATE Name : STRING … PUBLIC PROCEDURE NEW(…) is object-oriented; type(lion, wild). and dangerous(X) IF type(X, wild) is declarative (logic). In the matching question: low-level pairs with "mnemonics that correspond directly to machine instructions", imperative with "a sequence of statements that change the state", OOP with "objects that combine attributes and methods", declarative with "facts and rules, with no order of execution given".

    Four paradigms: low-level, imperative, object-oriented and declarative
    Four paradigms: low-level, imperative, object-oriented and declarative

    Low-level programming

    Programming close to the hardware in machine code 机器码 or assembly language 汇编语言, where each instruction maps to what the CPU runs. It gives direct access to registers 寄存器 and memory addresses 内存地址, using different addressing modes 寻址方式 (immediate, direct, indirect, indexed and relative). It is very fast and compact, but architecture-specific, tedious, and hard to maintain. This is low-level 低级 programming, used for device drivers, firmware and bootloaders.

    The five addressing modes. The syllabus asks for low-level code that uses each addressing mode (the instruction set is in Topic 4). The operand of a load instruction can be read five ways, and the exam gives you the memory contents and asks what the accumulator holds:

    A memory table with addresses 105, 106, 107, 27 and 145 and their contents, beside five rows showing what the accumulator receives from LDM #105, LDD 105, LDI 105, LDX 105 with IX = 2, and a relative jump
    The same operand, 105, read five ways: as a value, as an address, as the address of an address, as an address plus the index register, and as an offset from the current instruction
    • immediate (LDM #105): the operand is the value; ACC becomes 105.
    • direct (LDD 105): the operand is the address of the value; ACC becomes the contents of 105, here 27.
    • indirect (LDI 105): the operand is the address of an address; ACC becomes the contents of 27, here 91. Used for pointers and for data whose position is decided at run time.
    • indexed (LDX 105): the address is the operand plus the index register IX; with IX = 2, ACC becomes the contents of 107. Used to step through an array by incrementing IX.
    • relative (JMR +65): the target is an offset from the address of the current instruction, which makes the code relocatable.

    Worked example. Memory: 105 holds 27, 106 holds 64, 200 holds 0. Write code to add the contents of 105 and 106, store the result in 200 and output it. LDD 105 (ACC = 27), ADD 106 (ACC = 91), STO 200, OUT. To double the value in 105 instead: LDD 105, ADD 105, STO 105. State the register contents after each line when asked to trace.

    Imperative (procedural) programming

    In imperative programming 命令式编程 the programmer writes a sequence of commands that change the program's state — assignments, conditionals, loops, function calls. Variables 变量 hold state; statements change it; code is organised into procedures and functions (also called structured or structural programming). This is the style of Topics 9 and 11 (Python, C). Strong when the algorithm has clear sequential steps.

    Object-oriented programming (OOP)

    In object-oriented programming 面向对象编程 programs are built from objects 对象 — units combining data (attributes 属性) and operations (methods 方法). Objects are instances 实例 of classes. The four pillars:

    • encapsulation 封装 — an object's data is hidden behind its methods; outside code uses the public methods only, not the data directly. This protects the object and lets its internals change without breaking callers. For example, a BankAccount hides its balance; you change it only through deposit() and withdraw(), which can enforce a rule like "never go below zero".
    • inheritance 继承 — a subclass 子类 specialises a superclass 父类, inheriting its attributes and methods and adding or overriding 重写 them. Models "is-a" ("a Manager is an Employee").
    • polymorphism 多态 — different objects respond to the same method call differently; the caller need not know the exact type. Every Shape has Area(), and a Circle and a Rectangle each implement it their own way.
    • abstraction 抽象 — show a simple interface and hide the implementation.

    Other terms:

    • a constructor 构造函数 is a special method run when an object is created, to set up its attributes.
    • getters and setters read and write an object's attributes (its properties) through methods.
    • aggregation 聚合 and containment 包含 build an object from other objects (a "has-a" relationship).

    OOP is used for large systems, GUIs, simulations and games.

    The same call shape.Area() runs different code for each object: a Circle computes pi r squared, a Rectangle computes width times height
    Polymorphism: the same method call runs each object's own code
    A UML class diagram for Shape: a three-part box with the class name, private attributes (Name, Area, Perimeter, marked with minus) and public methods (SetShape, calculateArea, calculatePerimeter, marked with plus)
    A class diagram for a Shape: private attributes and public methods
    A UML inheritance diagram: the employee superclass at the top, with partTime and fullTime subclasses below, each joined to the superclass by a hollow-triangle generalisation arrow and adding its own attributes and methods
    Inheritance: partTime and fullTime are subclasses of employee
    A BankAccount object with a private balance reached only through the public methods deposit() and withdraw(); outside code cannot touch the data directly
    Encapsulation: an object's data is private, reached only through its public methods

    OOP as the examiner marks it

    Definitions. Class: a template (blueprint) that defines the attributes and methods of the objects of that type. Object: an instance of a class, created from it, with its own values for the attributes ("an occurrence of an object" is the exam's phrase for an instance). Attribute (property): a data item belonging to a class. Method: a procedure or function belonging to a class that acts on its attributes. Encapsulation: combining the attributes and methods in one class and restricting external access to the data: the attributes are private and can only be read or changed through public methods. Inheritance: a subclass acquires the attributes and methods of its parent (super) class and can add its own or override them. Polymorphism: methods with the same name that behave differently in different classes; typically a subclass redefines a method of its parent, and the right version runs for each object. Containment: a class has an object of another class as an attribute (a car has an engine). "Identify the feature that restricts external access to the data" is encapsulation; "the term for an occurrence of an object" is instance.

    "Outline the structure of a class" (three marks): attributes (properties) that hold the object's data, usually declared private; methods (procedures and functions) that act on those attributes, usually public; and a constructor, a method that runs when an object is created to initialise the attributes. "Give three benefits of OOP": code is reused through inheritance; data is protected by encapsulation, so it can only be changed by the class's own methods; a large program is split into classes that are written and tested independently, so it is easier to maintain and extend; classes model real-world entities, so the design is easier to understand; polymorphism lets the same call work for different objects.

    The class in pseudocode, as Paper 3 sets it:

    CLASS Car
        PRIVATE Registration : STRING
        PRIVATE Year : INTEGER
        PRIVATE Mileage : INTEGER
        PUBLIC PROCEDURE NEW(NewReg : STRING, NewYear : INTEGER)
            Registration ← NewReg
            Year ← NewYear
            Mileage ← 0
        ENDPROCEDURE
        PUBLIC FUNCTION GetMileage() RETURNS INTEGER
            RETURN Mileage
        ENDFUNCTION
        PUBLIC PROCEDURE AddMileage(Extra : INTEGER)
            Mileage ← Mileage + Extra
        ENDPROCEDURE
    ENDCLASS
    

    An object is created with MyCar ← NEW Car("AB12 CDE", 2020) and used with MyCar.AddMileage(150) and OUTPUT MyCar.GetMileage(). A subclass reuses the parent's constructor through SUPER:

    CLASS ElectricCar INHERITS Car
        PRIVATE BatteryCapacity : REAL
        PUBLIC PROCEDURE NEW(NewReg : STRING, NewYear : INTEGER, NewCapacity : REAL)
            SUPER.NEW(NewReg, NewYear)
            BatteryCapacity ← NewCapacity
        ENDPROCEDURE
    ENDCLASS
    

    The same class in Python, as Paper 4 expects it: attributes are made private with a double underscore, the constructor is __init__, and a subclass names its parent in brackets and calls super().__init__(…):

    class Car:
        def __init__(self, reg, year):
            self.__registration = reg
            self.__year = year
            self.__mileage = 0
        def get_mileage(self):
            return self.__mileage
        def add_mileage(self, extra):
            self.__mileage = self.__mileage + extra
    
    class ElectricCar(Car):
        def __init__(self, reg, year, capacity):
            super().__init__(reg, year)
            self.__capacity = capacity
    
    cars = []
    cars.append(Car("AB12 CDE", 2020))
    cars.append(ElectricCar("EV21 XYZ", 2023, 75.0))
    cars[1].add_mileage(150)
    print(cars[1].get_mileage())
    

    In Java the same ideas are private/public fields, a constructor with the class's name, extends and super(…); in VB.NET Private/Public, Sub New, Inherits and MyBase.New. A polymorphic method is written in the parent and overridden in the child with the same name; a call through a parent-type variable runs the child's version.

    Data structures as objects. Paper 4 builds a stack, linked list or binary tree from a Node class whose attributes are the data and one or two references to other nodes; a Tree (or LinkedList) class holds the root (or start) and the methods.

    A binary tree of Node objects: the Tree object's Root points to the node 15, whose Left and Right references point to the nodes 8 and 19, and so on, with None for empty references
    A binary tree built from objects: each Node holds Data plus Left and Right references, and the Tree holds the Root; inserting walks down the references
    CLASS Node
        PUBLIC Data : INTEGER
        PUBLIC Left : Node          // NULL when there is no child
        PUBLIC Right : Node
        PUBLIC PROCEDURE NEW(NewData : INTEGER)
            Data ← NewData
            Left ← NULL
            Right ← NULL
        ENDPROCEDURE
    ENDCLASS
    
    CLASS Tree
        PRIVATE Root : Node
        PUBLIC PROCEDURE Insert(NewData : INTEGER)
            DECLARE NewNode, Current : Node
            DECLARE Placed : BOOLEAN
            NewNode ← NEW Node(NewData)
            IF Root = NULL THEN
                Root ← NewNode
            ELSE
                Current ← Root
                Placed ← FALSE
                WHILE NOT Placed
                    IF NewData < Current.Data THEN
                        IF Current.Left = NULL THEN
                            Current.Left ← NewNode
                            Placed ← TRUE
                        ELSE
                            Current ← Current.Left
                        ENDIF
                    ELSE
                        IF Current.Right = NULL THEN
                            Current.Right ← NewNode
                            Placed ← TRUE
                        ELSE
                            Current ← Current.Right
                        ENDIF
                    ENDIF
                ENDWHILE
            ENDIF
        ENDPROCEDURE
    ENDCLASS
    

    A find method walks the same path and returns TRUE when Current.Data = Target, FALSE when it reaches NULL; an in-order output method is recursive: output the left subtree, the node, then the right subtree. For a linked list the node has one reference, Next, and the list class holds Start; for a stack built from a list, push and pop both work at Start.

    Worked example. A game has characters. Each has a name, health (starting at 100) and a position given by X and Y. Write a class Character with a constructor and a method Move(DX, DY); then a subclass Wizard that adds Mana (starting at 50) and a method CastSpell() that takes 10 mana and returns TRUE if there was enough.

    CLASS Character
        PRIVATE Name : STRING
        PRIVATE Health : INTEGER
        PRIVATE X : INTEGER
        PRIVATE Y : INTEGER
        PUBLIC PROCEDURE NEW(NewName : STRING, StartX : INTEGER, StartY : INTEGER)
            Name ← NewName
            Health ← 100
            X ← StartX
            Y ← StartY
        ENDPROCEDURE
        PUBLIC PROCEDURE Move(DX : INTEGER, DY : INTEGER)
            X ← X + DX
            Y ← Y + DY
        ENDPROCEDURE
    ENDCLASS
    
    CLASS Wizard INHERITS Character
        PRIVATE Mana : INTEGER
        PUBLIC PROCEDURE NEW(NewName : STRING, StartX : INTEGER, StartY : INTEGER)
            SUPER.NEW(NewName, StartX, StartY)
            Mana ← 50
        ENDPROCEDURE
        PUBLIC FUNCTION CastSpell() RETURNS BOOLEAN
            IF Mana >= 10 THEN
                Mana ← Mana - 10
                RETURN TRUE
            ELSE
                RETURN FALSE
            ENDIF
        ENDFUNCTION
    ENDCLASS
    

    The marks are for private attributes, a constructor that sets every attribute, the inheritance line, the call to the parent's constructor, and a method that uses and changes the object's own data. When the question asks for a class diagram, draw a box in three parts (name; attributes with - for private; methods with + for public) and join a subclass to its parent with an arrow pointing at the parent.

    Declarative programming

    In declarative programming 声明式编程 you say what to compute, not how — the runtime works out the steps. Two kinds:

    • functional programming 函数式编程 — built from pure functions 纯函数 (no side effects 副作用; same input always gives the same output) composed together. Examples: Haskell, Lisp.
    • logic programming 逻辑编程 — state facts and rules; the engine answers a goal (query) by inference. Example: Prolog.

    A familiar declarative example is SQL 结构化查询语言: SELECT * FROM Customer WHERE Country = 'UK' says what you want, not how to walk the records.

    Facts, rules and goals are what the exam tests in the declarative paradigm. Given these facts 事实 (statements that are true) and a rule 规则 (a conclusion that holds when its conditions hold):

    01 type(leopard, wild).
    02 type(lion, wild).
    03 type(tabby, domestic).
    04 size(leopard, large).
    05 size(lion, large).
    06 size(tabby, small).
    07 dangerous(X) IF type(X, wild) AND size(X, large).
    

    "Write the result of the goal type(X, wild)": X = leopard, X = lion. The engine matches the goal against each fact in turn; every match is a solution, and a capital letter is a variable that the match fills in. "Write a fact to show that a cheetah is wild": type(cheetah, wild). "Explain what line 07 does": it defines a rule with the conclusion dangerous(X), which is true for any X that is both wild and large, so dangerous(A) returns A = leopard, A = lion. "Write a rule: a feature F may be available for a body style B if F is a feature and B is a body style and F is not unavailable for B": may_be_available(F, B) IF feature(F) AND body_style(B) AND NOT unavailable(F, B). Copy the exact predicate names and argument order used in the question's facts; a new fact ends with a full stop, and a rule's conditions are joined with AND.

    Comparing paradigms

    Paradigm Strength Typical languages
    Low-level maximum control, speed assembly
    Imperative direct, intuitive C, Python
    Object-oriented modular, models entities Java, C#, Python
    Functional clear, no side effects Haskell, F#
    Logic inference, rules Prolog
    Database data queries SQL

    Modern languages often mix paradigms — Python supports all of procedural, OOP and functional. The right one depends on the problem.

    Explore

    Programming concept lab

    Connect examples to the programming idea they show.

    Vocabulary Train
    English Chinese Pinyin
    programming paradigm 编程范式 biān chéng fàn shì
    facts 事实 shì shí
    rule 规则 guī zé
    low-level 低级 dī jí
    registers 寄存器 jì cún qì
    memory addresses 内存地址 nèi cún dì zhǐ
    objects 对象 duì xiàng
    attributes 属性 shǔ xìng
    methods 方法 fāng fǎ
    machine code 机器码 jī qì mǎ
    assembly language 汇编语言 huì biān yǔ yán
    addressing modes 寻址方式 xún zhǐ fāng shì
    imperative programming 命令式编程 mìng lìng shì biān chéng
    Variables 变量 biàn liàng
    object-oriented programming 面向对象编程 miàn xiàng duì xiàng biān chéng
    instances 实例 shí lì
    classes lèi
    encapsulation 封装 fēng zhuāng
    inheritance 继承 jì chéng
    subclass 子类 zi lèi
    superclass 父类 fù lèi
    overriding 重写 chóng xiě
    polymorphism 多态 duō tài
    abstraction 抽象 chōu xiàng
    constructor 构造函数 gòu zào hán shù
    aggregation 聚合 jù hé
    containment 包含 bāo hán
    declarative programming 声明式编程 shēng míng shì biān chéng
    functional programming 函数式编程 hán shù shì biān chéng
    pure functions 纯函数 chún hán shù
    side effects 副作用 fù zuò yòng
    logic programming 逻辑编程 luó jí biān chéng
    SQL 结构化查询语言 jié gòu huà chá xún yǔ yán
    Exercise sheet
    20.2

    File processing

    Syllabus
    Candidates should be able to: Notes and guidance
    Write code to perform file-processing operations Open (in read, write, append mode) and close a file Read a record from a file and write a record to a file Perform file-processing operations on serial, sequential, random files
    Show understanding of an exception and the importance of exception handling Know when it is appropriate to use exception handling Write program code to use exception handling

    Source: Cambridge International syllabus

    This extends the file 文件 handling from Topic 10, processing serial, sequential and random (direct-access) files. Pseudocode operations: OPENFILE name FOR READ | WRITE | APPEND (READ opens an existing file, WRITE creates/overwrites, APPEND adds to the end); READFILE name, line; WRITEFILE name, value; CLOSEFILE name; and EOF(name) which is TRUE at the end.

    Read a whole file:

    OPENFILE "names.txt" FOR READ
    WHILE NOT EOF("names.txt") DO
        READFILE "names.txt", thisName
        OUTPUT thisName
    ENDWHILE
    CLOSEFILE "names.txt"
    

    Search a file (stop when found):

    found ← FALSE
    OPENFILE "people.txt" FOR READ
    WHILE NOT EOF("people.txt") AND NOT found DO
        READFILE "people.txt", line
        IF line = target THEN found ← TRUE
    ENDWHILE
    CLOSEFILE "people.txt"
    

    Updating a file in place

    Most languages can't edit a text file in place. Instead: open the original for READ and a temporary file for WRITE; for each line, write the new version if it should change, else the original; close both; then replace the original with the temp file. The same pattern handles deleting lines (skip them) and inserting lines.

    Updating a file in place: read the original file, write the changed lines to a temp file, then replace the original with the temp file
    Updating a file in place: read the original, write changes to a temp file, then replace the original

    Records and random-access files

    Opening modes. READ: the file must exist and reading starts at the beginning. WRITE: a new file is created, and an existing file of that name is overwritten. APPEND: writing adds to the end of an existing file. Every file that is opened is closed with CLOSEFILE, and EOF(name) is TRUE when the last item has been read.

    Three file organisations. In a serial file the records are in the order they were added; in a sequential file they are in key order; both are read from the start. A random file 随机文件 (direct-access file) stores each record at an address calculated from its key by a hashing 哈希 function, so one record is found without reading the others. Records are declared as a user-defined type:

    TYPE AccountRecord
        DECLARE AccNo : INTEGER
        DECLARE Name : STRING
        DECLARE Balance : REAL
        DECLARE Active : BOOLEAN
    ENDTYPE
    
    A key 2317 hashed with MOD 1000 to the address 317, then SEEK and GETRECORD on the file Acc.dat, shown as a row of equal-size record slots with slot 317 highlighted
    Finding one record in a random file: the key is hashed to an address, the file pointer seeks straight to that slot and the record is read; no other record is touched

    The random-file operations in pseudocode are OPENFILE "Acc.dat" FOR RANDOM, SEEK "Acc.dat", Address (move the file pointer to that record), GETRECORD "Acc.dat", Rec (read the record there) and PUTRECORD "Acc.dat", Rec (write the record there). Finding a customer by account number, as Paper 3 sets it:

    DECLARE Rec : AccountRecord
    DECLARE Target, Address : INTEGER
    INPUT Target
    Address ← Target MOD 1000              // the hashing function
    OPENFILE "Acc.dat" FOR RANDOM
    SEEK "Acc.dat", Address
    GETRECORD "Acc.dat", Rec
    WHILE Rec.AccNo <> Target AND Rec.AccNo <> 0    // 0 marks an empty slot
        Address ← Address + 1               // a collision: try the next slot
        SEEK "Acc.dat", Address
        GETRECORD "Acc.dat", Rec
    ENDWHILE
    IF Rec.AccNo = Target THEN
        OUTPUT Rec.Name, Rec.Balance
    ELSE
        OUTPUT "No such account"
    ENDIF
    CLOSEFILE "Acc.dat"
    

    To store a record, hash its key, SEEK to the address and PUTRECORD, stepping on past any slot already occupied. Marks go to the hash, the SEEK before the GET or PUT, the comparison with the target, the handling of a collision, and closing the file.

    Worked example. ActiveFile.dat holds AccountRecord records. Write pseudocode that copies every record whose Active field is FALSE to the end of ArchiveFile.dat.

    DECLARE Rec : AccountRecord
    OPENFILE "ActiveFile.dat" FOR READ
    OPENFILE "ArchiveFile.dat" FOR APPEND
    WHILE NOT EOF("ActiveFile.dat")
        READFILE "ActiveFile.dat", Rec
        IF Rec.Active = FALSE THEN
            WRITEFILE "ArchiveFile.dat", Rec
        ENDIF
    ENDWHILE
    CLOSEFILE "ActiveFile.dat"
    CLOSEFILE "ArchiveFile.dat"
    

    Text files in Python (Paper 4): file = open("HighScore.txt", "r"), then for line in file: with line.strip() and line.split(",") to separate the fields, int(…) to convert a score, and file.close(); to write, open(name, "w") (or "a" to append) and file.write(str(score) + "\n"). A high-score table is read into a list of records, the new score inserted at its place, and the whole list written back. The examiner marks the open with the correct mode, a loop that reads every line, the conversion of text to numbers, and the close.

    Pitfalls

    Forgetting to close a file (data may be lost); opening for WRITE when you meant APPEND (overwrites everything); reading past EOF; hard-coded paths — a path like /Users/Admin/data.txt breaks on another machine, so use a relative constant such as DataFile = "./data/scores.txt".

    Explore

    File access route

    Follow a file from storage to program and back safely.

    Vocabulary Train
    English Chinese Pinyin
    file 文件 wén jiàn
    random file 随机文件 suí jī wén jiàn
    hashing 哈希 hā xī
    Watch lesson Exercise sheet
    20.2

    Exception handling

    An exception 异常 is an error or unexpected condition during execution — divide by zero, file not found, network failure, an array 数组 index out of range. Exception handling 异常处理 lets a program detect it and respond gracefully instead of crashing.

    It matters because real programs face errors that cannot be prevented up front (files moved, networks down, bad input); without it, every operation needs its own IF check; and it separates the normal flow from the error handling, so the main path reads cleanly. For example, a file may be deleted by another user between your program checking it exists and actually opening it — you cannot prevent that, only handle the failure when it happens.

    "Describe, with an example, what is meant by an exception" (two marks). An unexpected event or error that occurs during the execution of a program (at run time) and interrupts its normal flow; for example dividing by zero, opening a file that does not exist, converting non-numeric input to an integer, an array index out of range, or running out of memory. "Identify two possible causes of exceptions" is answered from that list, plus "a device or network is not available" and "invalid data type entered".

    "State the reasons for including exception handling" (three marks). To stop the program crashing (terminating unexpectedly); to output a meaningful message to the user rather than a system error; to allow the program to recover and continue, for example by asking for the input again, or to close files safely before it ends; and because some errors cannot be predicted when the program is written. "Describe how program termination due to an exception can be avoided": put the statements that might raise the exception inside a TRY block; write an EXCEPT (catch) block for that exception that handles it, for example by outputting a message, so that execution continues after the block instead of stopping. "Explain what is meant by exception handling": detecting an exception when it occurs and running code (the handler) that deals with it so that the program continues.

    Pattern

    TRY
        OPENFILE "data.txt" FOR READ
        READFILE "data.txt", line
        OUTPUT line
        CLOSEFILE "data.txt"
    EXCEPT FileNotFound
        OUTPUT "Sorry, the file does not exist."
    EXCEPT ReadError
        OUTPUT "Sorry, error reading the file."
    ENDTRY
    

    The TRY block holds the code that might fail; the first matching EXCEPT block runs. Real languages also have a catch-all EXCEPT and a FINALLY block that runs whether or not an exception happened — useful for cleanup (closing files).

    Exception flow: if the TRY block raises an exception, control jumps to the matching EXCEPT; with no exception it is skipped. Either way the FINALLY block runs, then the program continues
    Exception flow: an exception jumps to the matching EXCEPT; FINALLY always runs before the program continues

    Raising an exception

    A subroutine that detects an error can raise 抛出 an exception so the caller handles it:

    PROCEDURE Divide(a : INTEGER, b : INTEGER) RETURNS INTEGER
        IF b = 0 THEN
            RAISE DivideByZero
        ENDIF
        RETURN a DIV b
    ENDPROCEDURE
    

    Where to handle exceptions

    Handle them close to the error if the response is simple (a message, a retry), or higher up the call stack 调用栈 if only the outer code knows what to do (a top-level GUI loop logs the error and shows a friendly dialog). Don't swallow exceptions silently — at least log them, or debugging becomes impossible.

    Common exceptions: FileNotFound, IOError, DivisionByZero, IndexOutOfRange, InvalidArgument, NullReference, OutOfMemory. Wrapping each failing operation in a TRY with the right EXCEPT handlers gives a program that degrades gracefully instead of crashing.

    Worked example (Paper 4). Write a function that reads whole numbers, one per line, from a file whose name is passed as a parameter and returns them in a list. It must not crash if the file does not exist or a line is not a whole number.

    def read_scores(filename):
        scores = []
        try:
            file = open(filename, "r")
            for line in file:
                scores.append(int(line))
            file.close()
        except FileNotFoundError:
            print("The file", filename, "does not exist")
        except ValueError:
            print("A line in the file was not a whole number")
        return scores
    

    The try block holds the code that can fail (the open and the conversion); each except names one exception and does something useful; the function still returns a list, so the caller continues. In Java the same shape is try { … } catch (FileNotFoundException e) { … } catch (NumberFormatException e) { … }; in VB.NET Try … Catch ex As FileNotFoundException … End Try. Marks: the risky statements inside the try, the correct exception names, a message for each, and the program continuing afterwards; a catch-all except: gets the crash mark but not the "appropriate exception" mark.

    Worked example. A text file of members needs one member's phone number changed. Why can the program not simply overwrite that line, and what is the pattern? A text file's lines are different lengths, and the file has no gaps to absorb a difference: a longer replacement would run into the next record, and a shorter one would leave part of the old line behind. So the pattern is to open the original for READ and a temporary file for WRITE, read every line in turn, writing the new version for the line that changes and the original line for all the others, close both, then replace the original with the temporary file. The same shape handles deleting (skip the line) and inserting (write the extra line). Note that every line gets written, not only the changed one - writing just the new record and losing the rest of the file is the classic slip.

    Explore

    How exception handling flows

    Step through what happens when code fails. The exception jumps out of the normal flow to a handler, FINALLY cleans up either way, and the program carries on instead of crashing.

    Vocabulary Train
    English Chinese Pinyin
    array 数组 shù zǔ
    exception 异常 yì cháng
    exception handling 异常处理 yì cháng chǔ lǐ
    raise 抛出 pāo chū
    call stack 调用栈 diào yòng zhàn
    20.2

    Definitions the examiner accepts

    A definition question is marked against fixed wording. Learn these exactly, and give one answer only.

    Term Definition
    programming paradigm a style or way of programming, with its own way of structuring a program
    imperative language the program is a sequence of statements that change the program's state; the programmer says how the task is done
    declarative language the program states facts and rules and the inference engine works out how to find the answer
    class a template defining the attributes and methods of the objects of that type
    object (instance) an occurrence of a class, with its own values for the attributes
    attribute a data item that belongs to a class
    method a procedure or function that belongs to a class and acts on its attributes
    encapsulation keeping the attributes and methods together in a class and restricting external access to the data, so that it is changed only through public methods
    inheritance a subclass acquires the attributes and methods of its parent class and can add or override them
    polymorphism methods with the same name that behave differently for different classes
    constructor a method that runs when an object is created and initialises its attributes
    containment a class has an object of another class as one of its attributes
    fact a statement in a declarative program that is true
    rule a conclusion that holds when its conditions are true
    serial, sequential, random file records in the order added; records in key order; each record at an address calculated from its key
    exception an unexpected error or event during execution that interrupts the normal flow
    exception handling detecting an exception when it occurs and running code that deals with it so that the program continues
    20.2

    Exam tips

    • Paradigms: know the one-line description of each and be ready to name the paradigm from a code sample; low-level questions want the five addressing modes and what the accumulator receives.
    • OOP definitions come up every session: class, object, attribute, method, encapsulation, inheritance, polymorphism, constructor. Write a class in pseudocode with PRIVATE attributes, a PUBLIC NEW and getters; a subclass with INHERITS and SUPER.NEW.
    • Declarative: a goal with a variable returns every matching fact; a rule is a conclusion IF conditions joined with AND; copy the question's predicate names exactly.
    • Files: the three modes and what each does to an existing file; READFILE in a WHILE NOT EOF loop; random files use a hash, SEEK, GETRECORD and PUTRECORD, with a step-on for collisions.
    • Exceptions: definition with an example, three reasons for handling them, and TRY with a named EXCEPT that lets the program continue.

    Common mistakes

    • Describing a declarative program as "a sequence of steps that gives the answer"; it states what is true and what is wanted, not how.
    • Confusing an object with a class, or an instance with an attribute; the question "an occurrence of an object" wants instance.
    • Declaring the attributes PUBLIC, or reaching them from outside the class instead of through a getter, which loses the encapsulation marks.
    • A subclass constructor that sets the parent's attributes directly instead of calling SUPER.NEW.
    • Explaining polymorphism as "many objects"; it is the same method name behaving differently for different classes.
    • Opening a file FOR WRITE to add a record, which destroys the existing contents; use APPEND.
    • Reading a random file from the start; SEEK to the hashed address first.
    • Putting the exception handler around code that cannot fail, or catching everything with no message, or describing exception handling as "checking the input with IF".

Log in or create account

IGCSE, A-Level & AP