Number System Converter
Convert between Binary, Octal, Decimal, and Hexadecimal
Decimal (base 10)
Base 10Binary (base 2)
Base 2Octal (base 8)
Base 8Hexadecimal (base 16)
Base 16What is number system conversion?
Number systems represent quantities in different bases. Decimal (base 10) is everyday use. Binary (base 2) is used by computers. Octal (base 8) and Hexadecimal (base 16) are used in programming, networking, and digital electronics.
Formula used
Decimal to Binary: divide by 2 repeatedly, read remainders bottom to top
13: 13÷2=6R1, 6÷2=3R0, 3÷2=1R1, 1÷2=0R1 → read up → 1101
Hex digits: 0-9 then A=10, B=11, C=12, D=13, E=14, F=15
255 decimal = FF hex (15×16 + 15 = 255)
How to use this calculator
- Type any value in any number system field (decimal, binary, octal, or hex)
- All other fields update instantly
- Hex values shown in uppercase
Example
Quick reference table:
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 255 | 11111111 | 377 | FF |
| 1024 | 10000000000 | 2000 | 400 |
Real-world use: Web colour #FF5733 = R:255, G:87, B:51. Max 8-bit value = 11111111₂ = 255₁₀ = FF₁₆.
Frequently asked questions
Electronic circuits have two states: on (1) and off (0). Binary maps perfectly to these. All data — text, images, video — is ultimately stored as 1s and 0s.
HTML/CSS colours (#RRGGBB), memory addresses, MAC addresses, IPv6 addresses, and byte-level debugging. Two hex digits represent exactly one byte (0–255).
11111111 binary = 255 decimal = FF hex. This is why 255 is the maximum for each RGB colour channel.