Number Base Converter

What is a number base?

A number base (or radix) is how many distinct digits a counting system uses. We normally use base 10 (decimal) with digits 0 to 9. Computers use base 2 (binary) with only 0 and 1, and programmers often use base 16 (hexadecimal) with digits 0 to 9 plus A to F. This converter translates a value between binary, octal (base 8), decimal, hexadecimal, and any base from 2 to 36.

How conversion works

Every base represents the same underlying quantity; only the notation changes. To convert decimal to binary, you repeatedly divide by 2 and read the remainders from bottom to top. To convert binary back to decimal, you multiply each digit by its place value (a power of 2) and add them up. The tool shows this step-by-step breakdown and uses arbitrary-precision integers, so very large numbers keep their exact value.

Why hexadecimal is everywhere in computing

Hexadecimal is popular because it maps cleanly onto binary: one hex digit equals exactly four bits, so a byte (8 bits) is just two hex digits. That makes hex a compact, human-readable shorthand for binary data. You will see it in color codes (#FF8800), memory addresses, MAC addresses, hashes, and byte dumps. Octal (base 8) plays a similar role in a few places, most notably Unix file permissions.

Quick reference

• Decimal 10 = binary 1010 = octal 12 = hex A
• Decimal 255 = binary 11111111 = hex FF (one byte's maximum)
• 1 hex digit = 4 bits; 2 hex digits = 1 byte