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IGCSE Computer Science Cheat Sheet

UNIT 1: DATA REPRESENTATION

Number Systems & Conversions

Base	Digits Used	Example
Binary (Base 2)	0,1	1010₂
Decimal (Base 10)	0-9	34₁₀
Hexadecimal (Base 16)	0-9, A-F	2F₁₆

Conversions

• Binary → Decimal: Multiply each bit by 2ⁿ (right to left).

Example: 1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 10₁₀

• Decimal → Binary: Divide by 2, record remainders.

• Hex → Binary: Convert each hex digit to 4-bit binary.

Example: A3₁₆ = 1010 0011₂

• Binary → Hex: Group in 4-bit chunks and convert.

Text Representation

• ASCII: 7-bit encoding (128 characters).

• Unicode: 16-bit or more (supports all languages).

Sound Representation

• Sample Rate: Number of samples per second (Hz).

• Bit Depth: Number of bits per sample (higher = better quality).

• Bit Rate = Sample Rate × Bit Depth × Channels.

• File Size Formula: Sample Rate × Bit Depth × Channels × Duration.

Image Representation

• Resolution: Number of pixels (width × height).

• Colour Depth: Number of bits per pixel (1-bit = 2 colours, 8-bit = 256 colours).

• File Size Formula: Resolution × Colour Depth (in bits).

Compression

Type	Description	Examples
Lossy	Removes unnecessary data, reduces quality	JPEG, MP3
Lossless	No data lost, larger file size	PNG, FLAC

UNIT 2: DATA TRANSMISSION

Types of Transmission

Type of Transmission	Definition	Example
Serial Transmission	Bits are sent one at a time, over a single wire, in a continuous stream. Suitable for long distances.	USB, Ethernet cables, Fiber-optic communication.
Parallel Transmission	Multiple bits are sent simultaneously using multiple wires. Faster but can cause signal interference over long distances.	Internal CPU data transfer, RAM connections.
Simplex Transmission	Data flows in one direction only. No return communication.	Television broadcast, Radio signals.
Half-Duplex Transmission	Data flows in both directions, but only one at a time.	Walkie-talkies, CB radios.
Full-Duplex Transmission	Data flows in both directions simultaneously. Allows real-time communication.	Telephone calls, Internet communication.

Error Detection

Method	Description
Parity Bit	Extra bit added to make sum even (even parity) or odd (odd parity).
Checksum	Sum of data values sent along with data. Receiver recalculates and compares.
ARQ (Automatic Repeat reQuest)	Requests retransmission if errors detected.
Echo Check	Data sent back to sender for verification.

Encryption

• Symmetric Encryption: Same key for encryption and decryption.

• Asymmetric Encryption: Uses a public key to encrypt and a private key to decrypt.

• Caesar Cipher: Shifts letters by a fixed number.

UNIT 3: COMPUTER ARCHITECTURE

Von Neumann Architecture Components

Component	Function
ALU (Arithmetic Logic Unit)	Performs calculations and logic operations.
Control Unit (CU)	Directs data flow, manages fetch-decode-execute cycle.
Registers	Small, fast memory inside CPU.
Program Counter (PC)	Stores address of next instruction.
Memory Address Register (MAR)	Stores address of data/instruction to be fetched.
Memory Data Register (MDR)	Stores data fetched from memory.
Current Instruction Register (CIR)	Stores the instruction being executed.
Accumulator	Stores intermediate results from ALU.

Buses in CPU

Bus	Function
Address Bus	Carries memory addresses.
Data Bus	Transfers actual data.
Control Bus	Sends control signals.

Fetch-Decode-Execute Cycle

1. Fetch:

• PC → MAR

• Address sent on address bus

• Instruction fetched to MDR

• PC incremented

2. Decode:

• CU decodes instruction from CIR

3. Execute:

• ALU processes data

• Results stored in accumulator

Factors Affecting CPU Performance

Factor	Effect
Clock Speed	Higher speed = more instructions per second.
Cache Size	More cache = faster access to frequently used data.
Number of Cores	More cores = more instructions processed in parallel.

Embedded Systems

• Definition: A dedicated system within a device (e.g., microwave, car engine control).

UNIT 10: BOOLEAN LOGIC

Logic Gate	Symbol	Truth Table
AND (A⋅B)	∧	1 only if both inputs are 1
OR (A+B)	∨	1 if at least one input is 1
NOT (¬A)	¬	Inverts input (0→1, 1→0)

Example Boolean Expression

Expression: (A ⋅ B) + ¬C

PRACTICE QUESTIONS

1. Data Representation

1. Convert 1101₂ to decimal.

2. Convert 58₁₀ to binary.

3. Convert A5₁₆ to binary.

2. Data Transmission

1. What is the difference between simplex, half-duplex, and full-duplex?

2. How does a checksum detect errors?

3. Why is encryption important?

3. Computer Architecture

1. What is the function of the accumulator?

2. Explain the fetch-decode-execute cycle.

3. Name two factors that affect CPU performance.

4. Boolean Logic

1. Complete the truth table for (A⋅B) + ¬C.

2. What does the OR gate do?

ANSWERS

1. Data Representation

1. 1101₂ = 13₁₀

2. 58₁₀ = 111010₂

3. A5₁₆ = 1010 0101₂

2. Data Transmission

1. Simplex: One way; Half-duplex: Both ways but one at a time; Full-duplex: Both ways simultaneously.

2. A checksum is recalculated at the receiver end and compared to detect errors.

3. Encryption prevents unauthorized access to data.

3. Computer Architecture

1. Stores intermediate results from ALU.

2. Fetches instruction → Decodes it → Executes it.

3. Clock speed, number of cores.

4. Boolean Logic

1. Truth table:

• A=1, B=0, C=1 → Output = 0

• A=1, B=1, C=0 → Output = 1