Number Base Converter

How base conversion works

• To decimal: each place is worth a power of the base. Multiply each digit by its place value and add: FF in hex is 15 × 16 + 15 × 1 = 255.
• From decimal: divide by the new base again and again and keep the remainders. Read them from the bottom up: 255 ÷ 16 = 15 remainder 15, then 15 ÷ 16 = 0 remainder 15, so 255 = FF.
• Between binary, octal and hex: group the bits in threes (octal) or fours (hex). 11111111 = 1111 1111 = FF.
• Between any other two bases, go through decimal: first to decimal, then from decimal.

Hexadecimal

Hex (base 16) needs 16 digits, so after 0 to 9 it uses letters: A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15. One hex digit is exactly 4 bits, and two make a byte, from 00 to FF (255). That is why hex is everywhere in computing: web colors like #FF8800 are three bytes (red 255, green 136, blue 0), and memory addresses are written in hex.

Octal and other bases

Octal (base 8) uses the digits 0 to 7, and each octal digit is 3 bits. You may meet it in Unix file permissions: chmod 755 means 111 101 101, read, write and run for the owner (7) and read and run for everyone else (5). Bases above 16 carry on with letters up to Z = 35, so base 36 uses every digit and letter; it is used for short codes and IDs.

0 to 16 in four bases