A number base (or radix) tells you how many different digits are available. Everything stored in a computer is ultimately represented in binary, but humans also use decimal and hexadecimal when working with computers.
| Base | Name | Digits used | Used by |
|---|---|---|---|
| 2 | Binary | 0, 1 | Computer hardware |
| 10 | Decimal | 0–9 | Everyday human use |
| 16 | Hexadecimal | 0–9, A–F | Programmers / colour codes / memory addresses |
Binary uses only two digits: 0 and 1. Each digit is called a bit. Computers use binary because their circuits have exactly two stable states: on (1) and off (0).
The place values in an 8-bit (one byte) binary number are:
Example: 10110101₂ = 128 + 0 + 32 + 16 + 0 + 4 + 0 + 1 = 181₁₀
Hexadecimal uses 16 digits. When the digits run out (after 9), letters A–F are used:
Each hex digit represents exactly 4 bits (a nibble). So one byte = two hex digits.
Example: 2A₁₆ — place values are 16¹ and 16⁰ → (2 × 16) + (10 × 1) = 32 + 10 = 42₁₀
Example: the binary string 11111111 is written as FF in hex — much shorter!
| Decimal | Binary | Hex |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 5 | 0101 | 5 |
| 9 | 1001 | 9 |
| 10 | 1010 | A |
| 15 | 1111 | F |
| 16 | 0001 0000 | 10 |
| 255 | 1111 1111 | FF |
8 questions · 18 marks
| Term | Definition |
|---|
Timed exam conditions.