Number Bases

Computers store and process all data using binary (base 2), using only the digits 0 and 1. However, Cambridge 9618 requires fluency in three number systems:

Binary (Base 2)

Each binary digit is called a bit. Groups of 8 bits form a byte. Larger units include kilobyte (KB = 2¹⁰ bytes), megabyte (MB = 2²⁰ bytes), gigabyte (GB = 2³⁰ bytes).

Place Values in Binary

Each position in a binary number has a place value that is a power of 2, increasing from right to left:

Example: Convert binary 10110101 to denary:
128+0+32+16+0+4+0+1 = 181

Denary to Binary Conversion

Method: repeatedly divide by 2, recording remainders from bottom to top.

Example: Convert 181 to binary:
181÷2=90 r1, 90÷2=45 r0, 45÷2=22 r1, 22÷2=11 r0, 11÷2=5 r1, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1
Reading remainders bottom to top: 10110101

Hexadecimal (Base 16)

Hexadecimal uses 16 symbols. Letters A–F represent values 10–15:

Hex to Binary Conversion

Each hex digit maps directly to exactly 4 binary digits (a nibble):

3F → 3 = 0011, F = 1111 → 00111111

A7 → A = 1010, 7 = 0111 → 10100111

Binary to Hex Conversion

Split binary into groups of 4 from the right, then convert each group:

11010110 → 1101 0110 → D 6 → D6

Hex to Denary

Multiply each digit by its positional value (16⁰, 16¹, 16², …):
2B = (2 × 16) + (11 × 1) = 32 + 11 = 43

Why Use Hexadecimal?

• Much shorter than binary — 2 hex digits = 8 binary digits
• Easier to read and remember than long binary strings
• Used in memory addresses, colour codes (e.g. #FF5733), MAC addresses, error codes
• Each hex digit corresponds to exactly 4 bits — easy conversion

Units of Storage

Note: Cambridge 9618 uses the IEC binary definition (1 KB = 1024 bytes), not the SI decimal definition (1 KB = 1000 bytes).