Cambridge IGCSE Computer Science – Theory Syllabus Overview (Chapter 1-6)
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