Number Base Converter
Type a number in any row — the others update instantly.
Bit breakdown
Why computers use binary and hex
Digital circuits have two stable states, so all data is ultimately binary. Binary is unreadable at any length, and decimal does not line up with byte boundaries — but hexadecimal does: one hex digit is exactly four bits, and two hex digits are exactly one byte. That is why memory dumps, colour codes, MAC addresses and hashes are all written in hex.
Common bases
| Base | Digits | Where you meet it |
|---|---|---|
| 2 (binary) | 0–1 | Bit flags, permissions masks, low-level protocols |
| 8 (octal) | 0–7 | Unix file permissions — chmod 755 |
| 10 (decimal) | 0–9 | Everything humans count |
| 16 (hexadecimal) | 0–9, A–F | Colours, memory addresses, hashes, byte dumps |
| 36 | 0–9, A–Z | Short IDs and URL slugs — the densest base using only alphanumerics |
Converting by hand
To convert decimal to another base, divide repeatedly by the base and read the remainders from last to first. 255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15, so 255 is FF. Going the other way, multiply each digit by the base raised to its position: FF = 15×16 + 15 = 255.
Binary and hex prefixes in code
0b11111111 binary (JavaScript, Python, Rust, C++14)
0o377 octal (JavaScript, Python 3)
0377 octal (C, older JavaScript — a classic bug source)
0xFF hexadecimal (almost every language)
255 decimalTwo's complement
Signed integers store negative numbers as the two's complement: invert every bit and add one. In 8 bits, 11111111 is 255 unsigned but −1 signed. This is why a byte holds either 0–255 or −128–127 depending on how you interpret it, and why an unsigned subtraction that goes below zero wraps to a very large number.
Frequently asked questions
What is 255 in binary?
11111111 — eight ones, the largest value that fits in a single byte. In hex it is FF.
What is 0xFF in decimal?
255. Each hex digit is worth four bits, so FF is 15×16 + 15.
Why does chmod use octal?
Unix permissions come in groups of three bits — read, write, execute — for owner, group and others. One octal digit encodes exactly three bits, so 755 is 111 101 101.
What is the largest base supported?
Base 36, which uses 0–9 followed by A–Z. Beyond that there is no agreed alphabet, though Base58 and Base62 exist with their own custom character sets.
How large a number can it handle?
Arbitrarily large — conversion uses JavaScript BigInt, so integers well beyond 64 bits convert exactly with no precision loss.