About number base converter
A number base is how many different digits a counting system uses. People count in base 10, computers in base 2, and programmers often use base 16. The converter works with any base from 2 to 36.
A worked example
Convert 45 from decimal to base 5: 45 ÷ 5 = 9 remainder 0, 9 ÷ 5 = 1 remainder 4, 1 ÷ 5 = 0 remainder 1. Reading the remainders upward gives 140 in base 5. Check: 1 × 25 + 4 × 5 + 0 = 45. For bases above 10 the digits continue with the letters A to Z, so base 36 uses 0 to 9 and A to Z.
How place values work
Each digit position is worth a power of the base. In decimal the places are 1, 10, 100, 1000 and so on. In binary they are 1, 2, 4, 8, 16, and in hexadecimal 1, 16, 256, 4096.
Why number bases matters
- Computers store everything as binary; hexadecimal and octal are compact ways to write it.
- One hex digit equals exactly four binary digits, which is why programmers use it for colours, memory addresses and byte values.
- Octal groups three bits per digit and appears in Unix file permissions such as 755.
