Number Base Reference
| Decimal | Binary | Hex | Octal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 8 | 1000 | 8 | 10 |
| 10 | 1010 | A | 12 |
| 15 | 1111 | F | 17 |
| 16 | 10000 | 10 | 20 |
| 255 | 11111111 | FF | 377 |
Binary Calculator
Convert between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8). Enter a value in any field and all others update automatically.
Number Base Converter
Frequently Asked Questions
Why do computers use binary?
Computers use binary because digital circuits have two stable states: on (1) and off (0), represented by high and low voltage. All data — text, images, video — is ultimately stored and processed as sequences of 1s and 0s.
What is hexadecimal used for?
Hexadecimal (hex) is a compact way to represent binary data. Each hex digit represents exactly 4 binary bits, making it much shorter to write. Common uses include: color codes (#FF5733), memory addresses (0x1A2B), error codes, and MAC addresses.
How binary place values work
Decimal uses powers of ten; binary uses powers of two. Each position doubles as you move left: 1, 2, 4, 8, 16, 32, 64, 128.
Reading 1011 from the right: 1 + 2 + 0 + 8 = 11.
Converting decimal to binary
Divide repeatedly by 2 and read the remainders bottom to top. For 13: 13÷2 = 6 r1, 6÷2 = 3 r0, 3÷2 = 1 r1, 1÷2 = 0 r1 → 1101.
Hexadecimal as shorthand
Hex is base 16, using 0–9 then A–F for 10–15. Its value is that one hex digit maps exactly to four binary digits, so long binary strings compress cleanly.
| Dec | Bin | Hex |
|---|---|---|
| 8 | 1000 | 8 |
| 10 | 1010 | A |
| 15 | 1111 | F |
| 255 | 11111111 | FF |
This is why colour codes look like #FF8800 — three pairs of hex digits, each a byte from 0 to 255 for red, green and blue.
Why computers use binary
A circuit reliably distinguishes two states — voltage present or absent — far more easily than ten. Everything above that is built on the same two symbols: text through character encodings, images through pixel values, instructions through opcodes.
It also explains why storage sizes cluster on powers of two. 256, 512, 1024 are round numbers in binary even though they look arbitrary in decimal.