A-Level Computer Science · ⁨Khoa học máy tính A-Level⁩

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 位.
• 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.

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 1110 → 2 2 E → 22E.

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.

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):

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.

Binary addition

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

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.

The same byte read as unsigned and as signed: only the agreed interpretation tells them apart 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.

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.

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

• memory addresses 内存地址 in low-level programming — 0x7FFE.
• colour values in HTML/CSS — #FF8800.
• MAC addresses — AC:DE:48:00:11:22.

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

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.

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.

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").

File size

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 $\approx 17.2\ \text{MiB}$.

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 帧. 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.

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.

Bitmap vs vector

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.

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.

File size

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.)

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 熵.

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.

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

• 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.

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.

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.

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.

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.

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).

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.

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).

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.

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.

• 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

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.

• 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 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.

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.

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.

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).

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.

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.

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.

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.

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

• 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.

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.

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".

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

• 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).

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

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".

The same memory split matters in a wearable device: its fixed program must remain available after power off, while its live readings change during use.

• 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.

"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.

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.

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

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.

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).

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).

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.

NOT (inverter)

AND — output 1 only if all inputs are 1

OR — output 1 if at least one input is 1

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

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

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

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.

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.

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:

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.

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

• 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.