Developer Tools · 5 min read
Binary, Decimal & Hexadecimal — Number Systems Explained
Everything in a computer is ultimately 0s and 1s. Understanding binary, hex, and octal unlocks how computers think — and why your HTML color is #FF5733.
Number Systems at a Glance
| System | Base | Digits | Common Use |
|---|---|---|---|
| Binary | 2 | 0, 1 | Hardware, CPU instructions |
| Octal | 8 | 0–7 | File permissions (Unix: chmod 755) |
| Decimal | 10 | 0–9 | Everyday numbers |
| Hexadecimal | 16 | 0–9, A–F | Color codes, memory addresses |
The Same Number in 4 Bases
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Frequently Asked Questions
Binary maps to physical electrical states — 0 = off, 1 = on. Every transistor in a CPU is essentially a switch with two states.
Hex represents binary data compactly — 1 hex digit = 4 binary bits. Used for color codes, memory addresses, and debugging machine code.
Multiply each bit by 2 to the power of its position (right to left from 0): 1101 = 8+4+0+1 = 13.
Use PickConverter's free Number Base Converter. Convert binary, decimal, hex, and octal instantly.
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