Computer Science Theory

The Binary number system

A base-2 number system using only 0 and 1 to represent data.

01011000 in decimal

Equal to 88 (64 + 16 + 8).

37 in binary

Equal to 00100101 (32 + 4 + 1).

Binary addition rules

0+0=0, 0+1=1, 1+0=1, 1+1=0 (carry 1), 1+1+1=1 (carry 1).

Binary addition method

Start from the right; if sum exceeds 1, carry 1 to the left.

Binary shifts

Left shift multiplies by 2; right shift divides by 2.

Overflow error

Occurs when a calculation result is too large for allocated bits.

Hexadecimal

A base-16 number system using digits 0-9 and letters A-F.

Why Hexadecimal is used

Shorter, easier for humans to read, and reduces transcription errors.

Binary to hexadecimal conversion

Split into 4-bit nibbles, convert to decimal, and use hex letters over 9.

Where Hexadecimal is used

HTML colour codes, MAC addresses, and memory addresses/error codes.

Logic gates

Electronic components taking inputs to produce a single output using simple rules.

AND Gate

Outputs 1 only if both inputs are 1.

OR Gate

Outputs 1 if either or both inputs are 1.

NOT Gate

Reverses a single input (1 becomes 0, 0 becomes 1).

Truth tables

Grids showing all possible inputs and their resulting outputs.

Compression

Making a file smaller to save storage and speed up network transfer.

Run Length Encoding (RLE)

Lossless compression replacing repeated data sequences with a value and count.

Huffman Coding

Lossless compression giving shorter binary codes to frequently appearing characters.

Lossy compression

Permanently removing less noticeable data so the original cannot be fully restored.

Lossless compression

Reducing file size without losing any original data.

Network

A number of connected devices that can communicate.

LAN (Local Area Network)

A network covering a single site, like a school.

WAN (Wide Area Network)

A network connecting different geographical locations, like a supermarket chain.

PAN (Personal Area Network)

A small short-range network connecting devices around a single person.

Stand alone

A single computer not connected to a network.

Advantages of networks

Sharing resources, easier maintenance, and hotdesking.

Wi-Fi

Connecting devices wirelessly to a network using radio waves.

Bluetooth

Wireless connection over short distances using radio waves for nearby devices.

Ethernet Cables

Copper wires connecting devices within a LAN.

Client

A device on a network requesting resources from a server.

Server

A device on a network providing a service, like a file server.

Switch

Sends data directly between devices within a network.

Router

Hardware responsible for transmitting data between different network types.

Network Interface Card (NIC)

Internal hardware allowing a device to connect to a network.

Wireless Access Point (WAP)

Transmits Wi-Fi signals allowing cable-free network connection.