IGCSE Computer Science · ⁨מדעי המחשב IGCSE⁩

A computer can only work with two states: on and off. You write these as 1 and 0. A system that uses only two digits 数字 is called binary 二进制 (base 2).

Every kind of data 数据 — numbers, text, sound and images — must be changed into binary before a computer can use it. The computer processes this binary using logic gates 逻辑门, and stores it in registers 寄存器 (small, fast stores inside the processor 处理器).

A number system 数制 is a way of writing numbers using a fixed set of digits. You need three of them.

• denary 十进制 is the normal counting system (also called decimal).
• binary uses only 0 and 1.
• hexadecimal 十六进制 (hex) uses sixteen digits: 0–9, then A, B, C, D, E, F stand for 10, 11, 12, 13, 14, 15.

The base 基数 tells you how many different digits a system uses.

Place value

Each column in a number has a place value 位值. In binary the place values double from right to left. For an 8-bit number they are:

One bit 位 is a single 0 or 1. Eight bits make one byte 字节. Four bits (half a byte) is a nibble 半字节.

Converting between number systems

Denary → binary. Write the place values. Put a 1 under each value you need so they add up to your number; put 0 under the rest.

Example: change denary 150 to binary. $150 = 128 + 16 + 4 + 2$.

So $150$ = 10010110.

Binary → denary. Add the place values where there is a 1. 10010110 $= 128 + 16 + 4 + 2 = 150$.

Hexadecimal → binary. Change each hex digit into its own 4-bit group (a nibble).

Example: hex F08. $F = 1111$, $0 = 0000$, $8 = 1000$, so F08 = 1111 0000 1000.

Binary → hexadecimal. Group the bits into nibbles of 4, starting from the right. Change each nibble to one hex digit.

Denary → hexadecimal. The easy way is to change to binary first, then binary to hex.

This table helps with the hex letters:

Cambridge questions use binary numbers up to 16 bits long.

Worked example. Convert denary 100 to 8-bit binary, then to hexadecimal.

$100 = 64 + 32 + 4$, so the binary is 01100100. Splitting into nibbles, 0110 0100 $= 6$ and $4$, so the hexadecimal is 64.

Why hexadecimal is used

Hex is shorter than binary and easier for people to read and write. One hex digit replaces 4 binary digits, so you make fewer mistakes. The value does not change — hex is just a shorter way to show the same binary.

Computer scientists use hex for:

• MAC addresses and IPv6 addresses
• colour codes in HTML (for example #FF0000 is red)
• memory addresses 内存地址 and error codes
• showing the contents of memory (a "memory dump")

You can add two 8-bit binary numbers, column by column from the right, just like denary. The rules for one column are:

When a carry also comes in, $1 + 1 + 1 = 1$ with a carry of 1.

Example: add 01110110 (118) and 00110000 (48).

Overflow

An 8-bit register can hold denary values from 0 to 255 only. If an addition gives a result above 255, the answer needs a 9th bit. The register cannot hold this extra bit, so it is lost. This is called overflow 溢出 (an overflow error). It happens when a value goes outside the limit the register can store.

Example: 11001000 (200) $+$ 01001000 (72) $= 272$. In binary that is 1 00010000, which needs 9 bits. The leading 1 will not fit in 8 bits, so the stored answer is wrong.

A logical binary shift 逻辑二进制移位 moves all the bits left or right by a number of places.

• Bits that move off the end of the register are lost.
• Zeros are added at the empty end.

A left shift multiplies the number by 2 for each place moved. A right shift divides it by 2 for each place; the right-most bits (the least significant bit(s) 最低有效位) are lost.

Example: left shift 00110101 (53) by 2 places.

The result is 11010100 (212), which is $53 \times 4$. The two left-most bits were lost and two zeros came in on the right. If a 1 is pushed off the end, that information is gone for good.

So far the numbers were positive. Two's complement 补码 lets an 8-bit register hold negative numbers too.

In two's complement, the left-most bit (the most significant bit 最高有效位, or MSB) has a negative place value:

• If the MSB is 0, the number is positive.
• If the MSB is 1, the number is negative.

To make a positive number negative: write the positive binary, flip every bit (0↔1), then add 1.

Example: make $-40$.

• $+40$ = 00101000
• flip the bits = 11010111
• add 1 = 11011000

So $-40$ = 11011000. Check by adding the place values: $-128 + 64 + 16 + 8 = -40$.

To read a negative two's complement number, just add the place values (the MSB counts as $-128$). The range of an 8-bit two's complement number is $-128$ to $+127$.

Computers store text by giving every character a number, then storing that number in binary. The set of characters a computer can use, together with their numbers, is a character set 字符集.

• ASCII uses 7 bits per character, so it has 128 different characters. This is enough for English letters, digits and common symbols.
• Unicode uses more bits per character. It can represent far more characters — many languages, plus symbols and emoji 表情符号.

Because Unicode has more characters, it needs more bits per character than ASCII, so the same text takes more storage 存储.

A sound wave 声波 is smooth and always changing. To store it, the computer measures the height of the wave at regular moments. This is called sampling 采样, and each measurement is a sample.

• sample rate 采样率 is the number of samples taken each second (measured in Hz).
• sample resolution 采样分辨率 is the number of bits used for each sample. The height of the wave at a sample point is its amplitude 振幅.

A higher sample rate and a higher sample resolution give a more accurate recording, but a larger file.

A computer image is made of a grid of small dots called pixels 像素.

• resolution 分辨率 is the number of pixels in the image (for example $1920 \times 1080$).
• colour depth 颜色深度 is the number of bits used to store the colour of each pixel.

A higher resolution and a higher colour depth give a better-quality image, but a larger file.

Data storage is measured in the units below. A nibble is 4 bits and a byte is 8 bits; from the kibibyte upward, each unit is 1024 times the one before it (because $1024 = 2^{10}$, which fits binary).

Image file size (in bits) $=$ resolution $\times$ colour depth $=$ width $\times$ height $\times$ colour depth.

Example: an image is $1024 \times 1024$ pixels with a colour depth of 2 bytes ($= 16$ bits).

• bits $= 1024 \times 1024 \times 16 = 16\,777\,216$ bits
• bytes $= \div 8 = 2\,097\,152$ bytes
• KiB $= \div 1024 = 2048$ KiB
• MiB $= \div 1024 = 2$ MiB

Sound file size (in bits) $=$ sample rate $\times$ sample resolution $\times$ length in seconds.

Always divide by 1024 (not 1000) to change to KiB, MiB and so on. Give your answer in the unit the question asks for.

Worked example. A sound is recorded for 30 seconds at a sample rate of 8,000 Hz with a sample resolution of 16 bits. Find the file size in kibibytes (KiB).

• bits $= 8\,000 \times 16 \times 30 = 3\,840\,000$ bits
• bytes $= 3\,840\,000 \div 8 = 480\,000$ bytes
• KiB $= 480\,000 \div 1024 \approx 469$ KiB

Compression 压缩 makes a file smaller. A smaller file:

• uses less storage space,
• needs less bandwidth 带宽 (the amount of data a connection can carry),
• takes a shorter time to send (a shorter transmission 传输 time).

There are two types.

Lossless compression

Lossless 无损 compression makes the file smaller with no permanent loss of data. The original file can be rebuilt exactly.

One method is run-length encoding 行程编码 (RLE). It replaces a run of repeated values with one copy of the value and a count of how many times it repeats. For example WWWWWWWW (8 whites) is stored as "8 W". This works well when data has many repeats.

Lossy compression

Lossy 有损 compression makes the file much smaller by permanently removing some data. The removed data cannot be got back. For example:

• reducing the resolution or colour depth of an image,
• reducing the sample rate or sample resolution of a sound.

Use lossless when you must keep every detail (text and program files). Use lossy for photos, music and video, where a small loss of quality is worth a much smaller file.

• Convert denary → binary by subtracting the place values (128, 64, 32 …); binary → denary by adding the place values that hold a 1.
• To convert to hex, group the binary into nibbles of 4 bits from the right; each nibble is exactly one hex digit.
• Overflow happens when a result needs more bits than the register has (an 8-bit register only holds 0–255), so the extra bit is lost.
• File size in bits: for an image, width × height × colour depth; for sound, sample rate × resolution × seconds. Divide by 8 for bytes, then by 1024 for each larger unit.
• Lossless compression keeps every bit (text; run-length encoding); lossy permanently removes data (photos, music) for a much smaller file.

Data transmission 数据传输 means moving data from one place to another — for example from your computer to a website, or from a phone to a printer.

Data often travels along a cable. Two common ones are shown below.

Before it is sent, the data is broken down into small, equal-sized pieces called packets 数据包. Each packet travels separately and they are put back together at the other end.

Using packets has benefits:

• if one packet is lost or damaged, only that packet is sent again, not the whole file;
• packets can take different routes, so a busy or broken route can be avoided;
• many users can share the same connection at the same time.

Every packet has three parts.

The packet header holds:

• the sender's IP address 地址 (where the packet came from),
• the receiver's IP address (where it is going),
• the packet number (so the packets can be put back in the right order).

Packet switching 数据包交换 is the way packets are sent across a network.

• Special devices called routers 路由器 read each packet's header and choose the best route for it.
• Each packet may take its own path, so packets can travel different ways.
• Packets may arrive out of order.
• When the last packet has arrived, the packets are reordered using their packet numbers.

Serial and parallel

Serial sends one bit after another along a single wire. Parallel sends several bits at the same time along several wires, so it is faster over short distances.

Simplex, half-duplex and full-duplex

These describe the direction data can travel.

Choosing a method

The choice depends on the distance, the speed needed, the cost, and whether data must travel both ways at once.

The universal serial bus 通用串行总线 (USB) is a common interface 接口 (a connection point) for joining devices to a computer.

Benefits:

• the same connector is used by many devices (one standard);
• the device is detected automatically and the correct driver is loaded;
• it carries power, so it can charge or run a device;
• the connector only fits one way, so it is hard to plug in wrongly.

Drawbacks:

• the cable can only be a limited length (a few metres);
• older USB versions are slower than newer ones;
• transfer speeds can be lower than some other connection types.

While data travels, interference 干扰 can change it. Three things can go wrong:

• data loss — some bits do not arrive;
• data gain — extra bits are added;
• data change — some bits are flipped.

So the receiver checks whether the data arrived correctly.

Parity check

A parity check 奇偶校验 adds one extra bit, the parity bit 奇偶校验位, to each byte. There are two types:

• even parity — the total number of 1s in the byte (including the parity bit) must be even;
• odd parity — the total number of 1s must be odd.

Example (even parity): the data 1011001 has four 1s, which is already even, so the parity bit is 0:

To find an error: the receiver counts the 1s. If even parity was agreed but a byte arrives with an odd number of 1s, an error has happened during transmission.

A parity check cannot find every error. If two bits flip, the count may still look correct.

Worked example. A single parity bit tells you that an error happened, but not where. A parity block 奇偶校验块 can find the exact bit. Several bytes are sent together, each with a row parity bit, and one extra parity byte 奇偶校验字节 at the bottom holds a parity bit for each column. Even parity is used below, and one bit was flipped during transmission. Find it.

Row byte 3 breaks even parity, and column b3 breaks even parity. The flipped bit is where they cross: byte 3, bit b3. Changing it back from 1 to 0 repairs the data. A single parity bit only says an error happened; a parity block says exactly where, so the receiver can even fix it.

Checksum

A checksum 校验和 is a value worked out from all the data before sending. The receiver works out the checksum again from the data it received. If the two values do not match, an error has occurred and the data is resent.

Echo check

In an echo check 回送校验, the receiver sends the data back to the sender. The sender compares it with the original. If they differ, an error happened. (This needs the data to be sent twice, so it is slow.)

Automatic Repeat reQuest (ARQ)

Automatic Repeat reQuest 自动重传请求 (ARQ) uses messages called acknowledgements 确认.

• The receiver sends a positive acknowledgement if a packet arrived correctly, or a negative acknowledgement if it did not.
• The sender starts a timeout 超时 timer. If no positive acknowledgement comes back in time, the sender sends the packet again.

Check digit

A check digit 校验码 is an extra digit placed at the end of a number, worked out from the other digits. It is used to find mistakes when a number is typed in.

When the number is entered, the check digit is calculated again and compared. It can catch:

• an incorrect digit entered,
• a transposition error 换位错误 (two digits swapped, e.g. 21 typed as 12),
• a digit left out or an extra digit added,
• a phonetic error (a digit that sounds similar, e.g. 13 and 30).

Check digits are used in barcodes 条形码 and ISBNs (book numbers).

Why we need encryption

Encryption 加密 scrambles data so that it cannot be understood if it is intercepted 拦截 (caught) by the wrong person. The readable data is called plaintext 明文; after encryption it becomes ciphertext 密文.

Encryption does not stop data from being intercepted. It only stops the data from being understood.

Symmetric encryption

Symmetric encryption 对称加密 uses a single key 密钥 to both encrypt and decrypt the data. The sender and receiver must share this same secret key. The risk is that the key itself could be stolen while being shared.

Asymmetric encryption

Asymmetric encryption 非对称加密 uses two different keys:

• a public key 公钥 that anyone can have, used to encrypt;
• a private key 私钥 that is kept secret, used to decrypt.

Data encrypted with the public key can only be decrypted with the matching private key, so the key never has to be shared. This is safer than sharing one secret key.

• Data is sent in packets (a header with the addresses and packet number, a payload, and a trailer). Packets can take different routes and arrive out of order, then are reordered by their packet numbers.
• Match the transmission types: serial (one bit at a time, good over long distances) vs parallel (several bits at once, short distances); simplex / half-duplex / full-duplex describe the direction.
• A single parity bit only shows that an error happened; a parity block locates the exact wrong bit — the row and the column that both fail.
• Learn the error-detection methods and what each does: parity check, checksum, echo check, ARQ, and the check digit (for typed-in numbers).
• Symmetric encryption uses one shared key; asymmetric uses a public key to encrypt and a private key to decrypt, so no secret key is ever shared.

A computer system is made of two parts that work together.

• Hardware 硬件 is the physical 物理的 parts of the computer — the parts you can touch. Examples: the CPU, memory, keyboard, screen and hard disk.
• Software 软件 is the programs 程序 that control the computer and tell the hardware what to do.

Hardware cannot do anything useful on its own. Software needs hardware to run on. Both are needed.

Software is split into two types.

System software

System software 系统软件 controls the computer itself and gives a base for other programs to run on. Examples:

• operating system 操作系统 (see below);
• compiler 编译器 and linker 链接器 (tools that turn programs into a form the computer can run);
• device driver 设备驱动程序 — software that lets the operating system control a piece of hardware;
• utility software 实用程序 — small tools that look after the computer (for example anti-virus, backup, disk clean-up).

Below the operating system sits firmware 固件 – software stored permanently on ROM or flash that runs the moment the computer is switched on. The BIOS and the bootloader 引导程序 are firmware: they test the hardware and then load the operating system. So the layers stack up hardware → firmware → operating system → application software, each running on the layer below.

Application software

Application software 应用软件 lets the user do a useful task. Examples:

• word processing 文字处理 software (writing documents);
• spreadsheet 电子表格 software (working with numbers in a grid);
• database management system 数据库管理系统 (storing and searching data);
• web browser 网页浏览器 (viewing web pages).

An operating system (OS) is the main system software. It controls the whole computer and lets the hardware, the application software and the user work together. Without an OS the computer is very hard to use.

The OS has many roles:

• managing files — saving, opening, naming, moving and deleting files;
• handling interrupts (see below);
• providing a user interface 用户界面 so the user can control the computer;
• managing memory — deciding what is kept in RAM and where;
• managing peripherals 外围设备 and their drivers — controlling devices like printers;
• managing multitasking 多任务处理 — letting several programs run at once;
• providing a platform 平台 for running application software;
• managing security — user accounts, passwords and access rights.

An interrupt 中断 is a signal sent to the processor 处理器 to tell it that something needs attention now.

An interrupt can come from three sources:

• hardware — for example a key is pressed, or a printer runs out of paper;
• software — for example a program tries to divide by zero;
• the user — for example the user presses a "cancel" key.

When an interrupt arrives, the processor stops what it is doing, saves its place, and services (deals with) the interrupt. When that is done, it goes back to what it was doing before. This lets the computer react quickly to important events.

All computers process data using the central processing unit 中央处理器 (CPU). To make the CPU do work, people write programs in a programming language 编程语言. There are two kinds.

High-level languages

A high-level language 高级语言 is written in words that look a bit like English (for example Python). It is:

• easy for people to read, write and fix;
• independent of the computer — the same program can run on different types of computer.

Low-level languages

A low-level language 低级语言 is close to what the hardware actually uses. It includes:

• machine code 机器码 — instructions written in binary (0s and 1s), which the CPU runs directly;
• assembly language 汇编语言 — machine code written with short word codes (mnemonics) instead of binary.

A low-level language relates to the specific 特定的 type of CPU, so a program written for one CPU may not run on another. It is used when the programmer needs full control of the hardware or very fast, small code.

The CPU can only run machine code. A high-level program must first be changed into machine code. The software that does this is a translator 翻译程序. There are three types: a compiler and an interpreter (for high-level code), and an assembler (for low-level code).

Compiler

A compiler translates the whole program into machine code before it is run. After translating, the machine code can be run many times without translating again.

• translation happens once, in full;
• it reports all the errors together, at the end of translating;
• the finished program runs fast and does not need the compiler to run.

Interpreter

An interpreter 解释器 translates and runs the program one line at a time.

• it stops at the first error it finds, which helps when testing;
• the program runs more slowly, because it is translated each time it runs;
• the interpreter must be present every time the program runs.

Use a compiler when you want to share a fast, finished program. Use an interpreter when you are writing and testing a program and want to find errors easily.

Assembler

An assembler 汇编器 translates a low-level assembly-language program (written in mnemonics such as LDA, ADD) into machine code. Each mnemonic becomes one machine instruction – a direct one-to-one translation, unlike a compiler or interpreter, which work on high-level code.

Worked example. A team is writing a program. While developing it they want to find and fix errors quickly; when they ship it they want customers to run it fast without seeing the source code. Which translator suits each stage? While developing, use an interpreter: it translates and runs one line at a time and stops at the first error, so a mistake is easy to locate. To ship, use a compiler: it translates the whole program once into machine code, which then runs quickly with no translator present, and the customer receives only the executable rather than the source. The two are not rivals - name the stage and give the reason, because "a compiler is faster" on its own earns nothing.

An integrated development environment 集成开发环境 (IDE) is software that helps you write programs. It puts many useful tools in one place:

• a code editor 代码编辑器 — for typing in your program;
• a run time environment 运行时环境 — for running the program to test it;
• a translator — a compiler or interpreter to turn your code into machine code;
• error diagnostics 错误诊断 — messages that help you find and understand mistakes;
• auto-completion 自动补全 and auto-correction 自动纠错 — the IDE finishes or fixes code as you type;
• prettyprinting 美化打印 — laying out the code neatly with colour and indentation so it is easy to read.

• Hardware is the physical parts; software is the programs. System software runs the computer (OS, drivers, utilities); application software does a task for the user.
• A compiler translates the whole program at once (the finished program runs fast, and all errors are reported at the end); an interpreter translates line by line (it stops at the first error, runs slower, and is needed every time).
• High-level languages are close to English and run on any computer; low-level languages (assembly, machine code) are tied to one type of CPU.
• An interrupt is a signal that makes the CPU stop, save its place, service the event, then carry on where it left off.
• Learn the operating system's roles: managing files, memory, peripherals, multitasking, security and the user interface.

People often mix up these two terms, but they are not the same.

• The internet 互联网 is the infrastructure 基础设施 — the huge worldwide network of computers and the cables, routers and connections that join them.
• The world wide web 万维网 (WWW) is a collection of websites 网站 and web pages that you view using the internet.

So the internet is the network; the web is one of the things you use on that network.

A uniform resource locator 统一资源定位符 (URL) is a text-based address for a web page. You type it into a web browser 网页浏览器 to visit a page, for example https://www.example.com/index.html.

A web browser is the program you use to view web pages. Its role includes:

• rendering 渲染 the hypertext markup language 超文本标记语言 (HTML) — turning the page's code into what you see;
• displaying web pages on the screen;
• managing how a web page is presented — its layout, text and images.

When you type a URL and press enter, several steps happen:

1. The browser needs the website's IP address 网际协议地址, but a URL uses a name, not a number.
2. The browser asks a domain name service 域名服务 (DNS) — a system that stores the IP address for each web address.
3. The DNS finds the matching IP address and sends it back to the browser.
4. The browser uses the IP address to contact the web server 网页服务器 that stores the page.
5. The web server sends the page's HTML back to the browser.
6. The browser turns the HTML into the page and displays it.

If the DNS does not have the address, it asks another DNS server until the address is found.

Worked example. Break down the URL https://www.example.com/books/index.html. https is the protocol, the set of rules used to transfer the page (the s means the transfer is encrypted). www.example.com is the domain name, which identifies the web server and which a DNS server turns into an IP address. /books/index.html is the file path and file name of the resource stored on that server. Name each part together with its job: an answer that says "the first bit" and "the last bit" describes the URL without ever explaining it.

A cookie is a small text file that a website stores on your device. It lets the website remember things about you. There are two types.

Cookies are used to:

• save personal details so you do not type them again (such as login or address);
• track user preferences 用户偏好, such as your language or the things you like, so the site can suggest content.

A digital currency 数字货币 is money that exists only in electronic form 电子形式. There are no coins or notes. It is stored and moved between people using computers, and can be used to pay for things online.

A problem with digital money is trust: how do you stop someone spending the same money twice, or changing the records? Blockchain solves this.

A blockchain 区块链 is a digital ledger 数字账本 — a shared record of every transaction 交易. The record is copied across many computers, so no single person controls it and it is very hard to change.

The transactions are kept in blocks joined in a chain. Each block holds:

• the data of the transaction (who paid whom, and how much);
• a timestamp 时间戳 (the date and time);
• a hash value 哈希值 — a special code worked out from the block's contents.

Each block also stores the hash of the block before it. If someone changes an old block, its hash changes, so it no longer matches the next block. This breaks the chain and the change is spotted at once. This is how blockchain tracks transactions safely.

Cyber security 网络安全 means keeping computers, networks and data safe from attack. You must know these threats.

Types of malware

Malware is any software made to harm a computer. The main types are:

Impact of the threats

These attacks can steal personal data, delete or change files, stop a service from working, cost money, and make users lose trust in a company. For example, a DDoS attack can make an online shop unusable, so it loses sales.

You can protect data using these methods.

• access levels 访问权限 — each user can only see or change the data they need, nothing more.
• anti-malware 反恶意软件 software, including anti-virus 杀毒软件 and anti-spyware 反间谍软件 — scans for and removes harmful software.
• authentication 身份验证 — proving who you are before you get access. Methods include:
  • biometrics 生物识别 (fingerprint or face),
  • a password 密码,
  • two-step verification 两步验证 (a code sent to your phone as well as a password).
• automating software updates — updates fix weak points (bugs) in software automatically.
• checking the spelling and tone of messages — bad spelling or an odd, urgent tone can show a message is fake (phishing).
• checking the URL attached to a link — a wrong or strange web address warns you the link is unsafe.
• firewall 防火墙 — checks data going in and out of a network and blocks anything not allowed.
• privacy settings 隐私设置 — control who can see your information online.

• proxy server 代理服务器 — sits between the user and the internet, hiding the user's IP address and filtering out unsafe content.

• The internet is the worldwide network (the infrastructure); the world wide web is the pages you view on it — do not mix the two up.
• Learn how a page loads: the browser asks a DNS for the site's IP address, then requests the page from the web server, which returns the HTML.
• Match the malware types: virus (attaches to a file), worm (spreads by itself across a network), Trojan horse (pretends to be useful), spyware, ransomware.
• Match each threat to a defence: phishing/pharming → check the URL; brute force → strong passwords + two-step verification; interception → encryption; hacking/DDoS → a firewall.
• A session cookie is deleted when you close the browser; a persistent cookie is saved to remember you between visits.

The program development life cycle 程序开发生命周期 is the set of stages used to make a program. There are four stages.