The Four Main Number Systems
| System | Base | Digits Used | Use Case |
|---|---|---|---|
| Binary | 2 | 0, 1 | Computers, digital circuits |
| Octal | 8 | 0–7 | Unix file permissions, legacy systems |
| Decimal | 10 | 0–9 | Human everyday use |
| Hexadecimal | 16 | 0–9, A–F | Memory addresses, colours, Unicode |
Conversion Examples
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
| 1024 | 10000000000 | 2000 | 400 |
Why Programmers Use Hex
Hexadecimal is favoured by programmers because each hex digit exactly represents 4 binary bits (a nibble), making it compact and readable. A byte (8 bits) fits neatly in 2 hex digits: FF = 11111111. Memory addresses, CSS colours (#7c3aed), Unicode characters (U+0041 = 'A') and MAC addresses all use hexadecimal.
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