Cambridge IGCSE/A‑Level Computer Science – Full Syllabus Overview
This set of notes is designed to cover every core topic of the Cambridge Computer Science syllabus (0478). Each section highlights the key concepts, essential terminology, common exam verbs and a quick‑check example so you can revise efficiently for both IGCSE and A‑Level papers.
1. Data Representation – Binary Foundations
1.1 Why computers use binary
- Electronic circuits have two stable voltage levels: High (ON) ≈ 1 V and Low (OFF) ≈ 0 V.
- Binary (base‑2) maps directly onto these two states → simple, cheap, reliable hardware.
- All other data types (numbers, text, images, sound, video, etc.) are encoded as patterns of bits.
1.2 Basic binary terminology
| Term | Size | Typical use |
|---|
| Bit | 1 bit | Smallest unit (0 or 1) |
| Nibble | 4 bits | Convenient for hex conversion |
| Byte | 8 bits | Standard addressable unit |
| Word | CPU‑dependent (e.g., 32‑ or 64‑bit) | Number of bits processed at once |
1.3 Number systems used in computing
| System | Base | Digits |
|---|
| Binary | 2 | 0, 1 |
| Octal | 8 | 0 – 7 |
| Decimal | 10 | 0 – 9 |
| Hexadecimal | 16 | 0 – 9, A – F |
1.3.1 Binary ⇄ Decimal conversion
Binary → Decimal – add the value of each ‘1’ bit (2ⁿ).
Formula: N₁₀ = Σ bᵢ·2ⁱ
Example: 1011₂ = 1·2³ + 0·2² + 1·2¹ + 1·2⁰ = 11₁₀
Decimal → Binary – repeated division by 2, recording remainders.
| Step | Quotient | Remainder |
|---|
| 45 ÷ 2 | 22 | 1 |
| 22 ÷ 2 | 11 | 0 |
| 11 ÷ 2 | 5 | 1 |
| 5 ÷ 2 | 2 | 1 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Read remainders bottom‑up → 101101₂.
1.3.2 Binary ⇄ Hexadecimal conversion
- Group binary digits in fours (nibbles) from the right.
- Replace each nibble with its hex equivalent.
Example: 11010110₂ → 1101 | 0110 → D | 6 → D6₁₆
1.3.3 Binary ⇄ Octal conversion
- Group binary digits in threes from the right.
- Replace each group with the corresponding octal digit.
Example: 101110010₂ → 101 | 110 | 010 → 5 | 6 | 2 → 562₈
1.4 Binary arithmetic
1.4.1 Addition, carry and overflow
When the result needs more bits than the operand size, the extra bit is a carry. In unsigned arithmetic this indicates overflow.
| Operation (8‑bit) | Binary | Result | Overflow? |
|---|
| 200 + 100 | 11001000 + 01100100 | 00101100 | Yes |
| 50 + 25 | 00110010 + 00011001 | 01001011 | No |
1.4.2 Two’s‑complement (signed integers)
- Write the absolute value in binary (using the required bits).
- Invert all bits (one’s complement).
- Add 1 → two’s‑complement.
Example (8‑bit): –13
13₁₀ = 00001101₂ → invert → 11110010₂ → +1 → 11110011₂.
1.4.3 Logical shift operations (unsigned)
| Shift | Effect on bits | Mathematical effect |
|---|
Logical left (<<n) | Bits move left, 0s fill right‑most positions | Multiply by 2ⁿ |
Logical right (>>n) | Bits move right, 0s fill left‑most positions | Integer division by 2ⁿ (discard remainder) |
1.5 Character encoding
1.5.1 ASCII
- 7‑bit code (stored in an 8‑bit byte).
- 128 characters: control codes, digits, upper‑/lower‑case letters, punctuation.
| Char | Decimal | Binary (8‑bit) | Hex |
|---|
| A | 65 | 01000001 | 41 |
| a | 97 | 01100001 | 61 |
| 0 | 48 | 00110000 | 30 |
| Space | 32 | 00100000 | 20 |
1.5.2 Unicode (UTF‑8)
- Extends ASCII to > 140 000 characters.
- Variable‑length encoding:
- 0 – 127 → 1 byte (identical to ASCII).
- 128 – 2047 → 2 bytes (pattern
110xxxxx 10xxxxxx).
- 2048 – 65535 → 3 bytes.
- 65536 – 1 114 111 → 4 bytes.
1.6 Images – pixel representation
1.6.1 Pixel grid
An image = rectangular matrix of pixels. Each pixel stores colour data as binary.
1.6.2 Colour models & depth
- RGB – three channels (Red, Green, Blue). Common depths:
- 24‑bit colour = 8 bits per channel → 16 777 216 colours.
- 32‑bit colour = 24‑bit RGB + 8‑bit alpha (transparency).
- Indexed colour – palette of up to 256 colours; each pixel stores an 8‑bit index.
- Grayscale – single channel; 8‑bit → 256 shades.
1.6.3 Example – 24‑bit red pixel
R = 255 (11111111₂), G = 0 (00000000₂), B = 0 (00000000₂) → 11111111 00000000 00000000 → hex #FF0000.
1.6.4 Uncompressed image size
$$\text{Size (bits)} = \text{width} \times \text{height} \times \text{bits per pixel}$$
Example: 800 × 600 @ 24‑bit → 800 × 600 × 24 = 11 520 000 bits = 1 440 000 bytes ≈ 1.37 MiB.
1.6.5 Compression (exam‑style)
- Lossless – PNG, GIF – original data can be perfectly restored (RLE, Huffman).
- Lossy – JPEG, WebP – some data discarded; exploits limits of human vision.
1.7 Sound – digital audio
1.7.1 Sampling (temporal resolution)
- Sample rate = number of measurements per second (e.g., 44 kHz for CD).
- Nyquist theorem: sample rate must be ≥ 2 × highest audible frequency.
1.7.2 Bit depth (amplitude resolution)
- Number of bits per sample → number of possible amplitude levels (2ⁿ).
- Common depths: 8‑bit (256 levels), 16‑bit (65 536, CD quality), 24‑bit (16 777 216, professional).
1.7.3 Example – CD‑quality stereo audio
Sample rate = 44 100 Hz, Bit depth = 16 bits, Channels = 2
- Bits / s = 44 100 × 16 × 2 = 1 411 200 bits
- Bytes / s = 176 400 ≈ 172 KiB
- 1 min uncompressed ≈ 10.3 MiB.
1.7.4 General size formula
$$\text{Size (bytes)} = \frac{\text{sample rate} \times \text{bit depth} \times \text{channels} \times \text{duration (s)}}{8}$$
1.7.5 Audio compression
- Lossless – FLAC, ALAC.
- Lossy – MP3, AAC, OGG.
1.8 Binary storage prefixes
| Prefix | Symbol | Value (bytes) |
|---|
| Kibi | KiB | 2¹⁰ = 1 024 |
| Mebi | MiB | 2²⁰ = 1 048 576 |
| Gibi | GiB | 2³⁰ = 1 073 741 824 |
| Tebi | TiB | 2⁴⁰ = 1 099 511 627 776 |
1.9 Quick‑check checklist (exam verbs)
- Explain why binary is used in hardware.
- Convert between binary, decimal, octal and hexadecimal (both directions).
- Perform binary addition, identify overflow and give the two’s‑complement result.
- State the size of a bit, nibble, byte and word.
- Give the ASCII (binary/hex) code for a character and vice‑versa.
- Describe how an image is stored and calculate its uncompressed size.
- Explain sampling and bit depth for sound and calculate an uncompressed audio size.
- Distinguish lossless vs. lossy compression for images and audio.
- Use binary prefixes correctly in calculations.
2. Data Transmission – Moving Data Around
2.1 Basic concepts
- Digital signal – sequence of bits transmitted over a medium.
- Transmission can be serial (bits one after another) or parallel (multiple bits simultaneously).
- Directionality:
- Simplex – one‑way only (e.g., TV broadcast).
- Half‑duplex – two‑way but not simultaneously (e.g., walkie‑talkie).
- Full‑duplex – two‑way simultaneously (e.g., telephone).
2.2 Common transmission media
| Medium | Typical use | Key characteristics |
|---|
| Twisted‑pair copper (UTP/STP) | Ethernet LAN | Relatively cheap, limited distance, susceptible to EMI. |
| Coaxial cable | Broadband TV, older Ethernet | Better shielding, higher bandwidth than UTP. |
| Fiber‑optic | Backbone, ISP, data‑centre links | Very high bandwidth, immune to EMI, long distance. |
| Wireless (radio, infrared, Bluetooth, Wi‑Fi) | Mobile, LAN, IoT | Convenient, limited by interference & range. |
2.3 Error detection & correction
- Parity bit – adds a single bit to make the number of 1s even (even parity) or odd (odd parity). Detects single‑bit errors.
- Checksum – sum of data bytes; receiver recomputes and compares.
- CRC (Cyclic Redundancy Check) – polynomial division; widely used in Ethernet, storage.
- ARQ (Automatic Repeat Request) – if error detected, request retransmission (e.g., TCP).
2.4 Basic networking protocols (exam‑style)
- TCP/IP model – four layers: Application, Transport, Internet, Link.
- TCP – reliable, connection‑oriented.
- UDP – fast, connection‑less, no guarantee of delivery.
- HTTP / HTTPS – request/response protocol for web pages; HTTPS adds TLS encryption.
- DNS – translates domain names to IP addresses.
2.5 Simple encryption for transmission
- Symmetric encryption – same key for encrypt & decrypt (e.g., AES). Fast, but key distribution is an issue.
- Asymmetric encryption – public‑key/private‑key pair (e.g., RSA). Used for key exchange and digital signatures.
2.6 Quick‑check checklist (data transmission)
- Define serial vs. parallel transmission and give an example of each.
- State the three direction modes (simplex, half‑duplex, full‑duplex) and illustrate with a device.
- Identify a suitable medium for high‑speed long‑distance links and justify.
- Explain how a parity bit works and what type of error it can detect.
- Describe the role of TCP in reliable data transfer.
- Differentiate symmetric and asymmetric encryption in one sentence each.
3. Hardware – The Physical Computer
3.1 CPU architecture
- Von Neumann architecture – single memory for data and instructions; fetch‑decode‑execute cycle.
- FDE (Fetch‑Decode‑Execute) cycle – basic instruction processing steps.
- Key components:
- ALU (Arithmetic‑Logic Unit) – performs arithmetic and logical operations.
- Control Unit – generates control signals, orchestrates the FDE cycle.
- Registers – small, fast storage inside the CPU (e.g., accumulator, program counter).
- Performance factors: clock speed (Hz), number of cores, cache size, instruction set (CISC vs. RISC).
3.2 Memory hierarchy
| Level | Typical size | Speed (relative) | Purpose |
|---|
| Registers | KB | Fastest | CPU‑internal temporary data |
| Cache (L1/L2/L3) | KB‑MB | Very fast | Reduce main‑memory access latency |
| Primary memory (RAM) | GB | Fast | Active program & data storage |
| Secondary storage | GB‑TB | Slower | Permanent data (HDD, SSD, optical) |
| Cloud / network storage | Virtually unlimited | Variable | Remote backup & sharing |
3.3 Primary vs. secondary storage
- RAM (Random‑Access Memory) – volatile, fast, read/write.
- ROM (Read‑Only Memory) – non‑volatile, stores firmware (e.g., BIOS).
- Magnetic storage – HDD, floppy; large capacity, slower, mechanical parts.
- Solid‑State Drives (SSD) – flash memory, no moving parts, faster access.
- Optical media – CD, DVD, Blu‑ray; read‑only (or write‑once) using lasers.
3.4 Embedded systems
- Specialised computers built into devices (e.g., microwaves, automotive ECUs).
- Typically use microcontrollers (CPU + RAM + ROM on one chip) and run a single dedicated program.
3.5 Input & output devices
- Input: keyboard, mouse, touch screen, scanner, microphone, sensors (temperature, light, motion).
- Output: monitor, printer, speaker, actuator (motor, LED).
- Often mediated by I/O controllers and drivers.
3.6 Quick‑check checklist (hardware)
- Describe the three stages of the FDE cycle.
- Name two functions of the control unit.
- Explain why cache memory improves performance.
- Distinguish volatile from non‑volatile memory with an example.
- Give one advantage of SSDs over HDDs.
- Define an embedded system and provide a real‑world example.
4. Software – Programs & Operating Systems
4.1 System software vs. application software
- System software – manages hardware resources, provides a platform for applications (e.g., Operating System, device drivers, utility programs).
- Application software – performs specific user‑oriented tasks (e.g., word processor, web browser, games).
4.2 Operating system (OS) functions
- Process management – creates, schedules, terminates processes.
- Memory management – allocation, paging, virtual memory.
- File system – hierarchical storage, access control.
- Device management – drivers, I/O handling.
- Security – user authentication, permissions.
- User interface – CLI or GUI.
4.3 Firmware
Low‑level software stored in non‑volatile memory (e.g., BIOS, microcontroller bootloader). Provides basic control before the OS loads.
4.4 Programming languages – levels of abstraction
| Level | Examples | Typical use |
|---|
| Machine code | Binary instructions | CPU execution |
| Assembly | e.g., x86, ARM | Low‑level system programming |
| High‑level | Python, Java, C#, Scratch | Application development, teaching |
4.5 Translators
- Assembler – converts assembly to machine code.
- Compiler – translates high‑level source to machine code (or intermediate bytecode) in one step.
- Interpreter – executes high‑level code line‑by‑line without producing a separate executable.
4.6 Integrated Development Environments (IDEs)
- Combine editor, compiler/interpreter, debugger, and often a visual GUI builder.
- Examples: Eclipse, Visual Studio, PyCharm, BlueJ (useful for IGCSE).
4.7 Quick‑check checklist (software)
- State two main functions of an operating system.
- Differentiate firmware from an operating system.
- Explain the difference between a compiler and an interpreter.
- Give an example of a high‑level language used in the IGCSE syllabus.
- Describe what an IDE provides to a programmer.
5. The Internet & Its Uses
5.1 Internet vs. World Wide Web
- Internet – global network of interconnected computers using TCP/IP.
- WWW – collection of web pages accessed via HTTP/HTTPS; one of many services on the Internet.
5.2 URL structure
protocol://domain[:port]/path?query#fragment
- Protocol – e.g.,
http, https, ftp.
- Domain – human‑readable address (e.g.,
example.com).
- Port – optional numeric identifier (default 80 for HTTP, 443 for HTTPS).
- Path – location of the resource on the server.
- Query – parameters after
? (e.g., ?id=5).
- Fragment – anchor within a page after
#.
5.3 HTTP/HTTPS request‑response cycle
- Browser sends an HTTP request (method, URL, headers).
- Server processes request, retrieves resource.
- Server returns an HTTP response (status code, headers, body).
- Browser renders the body (HTML, CSS, JavaScript).
HTTPS adds TLS encryption, ensuring confidentiality and integrity.
5.4 DNS – translating domain names
- Client queries a DNS resolver.
- Resolver contacts authoritative name servers.
- IP address is returned and cached for future use.
5.5 Cookies
- Session cookie – stored temporarily, deleted when browser closes.
- Persistent cookie – stored on disk with an expiry date; used for login persistence, preferences.
- Privacy considerations – third‑party tracking, GDPR.
5.6 Digital currency (blockchain basics)
- Decentralised ledger where each block contains a list of transactions and a cryptographic hash of the previous block.
- Mining – participants solve a proof‑of‑work puzzle; the first to find a valid hash adds the block and receives a reward.
- Security relies on the immutability of the hash chain and the difficulty of altering past blocks.
5.7 Cyber‑security – protecting data & systems
- Threats:
- Malware (virus, worm, ransomware, spyware).
- Phishing & social engineering.
- Denial‑of‑service (DoS/DDoS) attacks.
- Brute‑force password attacks.
- Defences:
- Strong authentication (password policies, 2‑FA).
- Firewalls – filter inbound/outbound traffic.
- Encryption – TLS for data in transit, AES for data at rest.
- Anti‑malware software, regular updates, backups.
- Safe online habits – don’t click unknown links, verify HTTPS, use reputable sources.
5.8 Quick‑check checklist (Internet & security)
- Distinguish the Internet from the World Wide Web.
- Identify the four parts of a URL and give an example.
- Explain the purpose of DNS in one sentence.
- State the difference between a session and a persistent cookie.
- Summarise how a blockchain ensures transaction integrity.
- List two common cyber‑threats and one mitigation technique for each.
6. Automated & Emerging Technologies
6.1 Sensors, microprocessors & actuators
- Sensor – converts a physical quantity (temperature, light, motion) into an electrical signal.
- Microprocessor / microcontroller – processes sensor data and runs control algorithms.
- Actuator – converts an electrical command into physical action (motor, LED, speaker).
6.2 Example systems
- Smart home lighting – ambient light sensor → microcontroller decides dimming level → LED driver (actuator).
- Weather station – temperature & humidity sensors → microcontroller logs data → wireless module transmits to a server.
6.3 Robotics
- Combines sensors (feedback), a control program, and actuators to perform tasks.
- Advantages: repeatability, precision, ability to work in hazardous environments.
- Disadvantages: high cost, limited flexibility, reliance on power & programming.
6.4 Artificial Intelligence (AI) basics
- Expert system – rule‑based AI that mimics human decision‑making in a narrow domain.
- Machine learning – algorithms that improve performance from data (e.g., classification, regression).
- Typical workflow: data collection → training → testing → deployment.
6.5 Quick‑check checklist (automation)
- Define a sensor and give a real‑world example.
- Explain how