Number Base Converter
Convert numbers between any base from 2 to 36 including binary, octal, decimal, and hex.
Returns the converted value with digit-by-digit working shown.
Number base conversion is the process of expressing a number in a different positional numeral system. Computers use binary (base 2) internally; programmers use hexadecimal (base 16) for readability; humans use decimal (base 10) by default; octal (base 8) is used in Unix file permissions.
Formula — Any base to decimal: Decimal Value = Σ(Digit × Base^Position) (Position counts from 0 starting at the rightmost digit)
Formula — Decimal to any base:
- Divide the decimal number by the target base
- Record the remainder
- Divide the quotient by the base again
- Repeat until quotient = 0
- Read remainders from bottom to top
Hex digit mapping: 10=A, 11=B, 12=C, 13=D, 14=E, 15=F
Worked example — Binary to Decimal: Binary: 1101₂ = (1×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 8 + 4 + 0 + 1 = 13₁₀
Worked example — Decimal to Hexadecimal: Decimal: 255 255 ÷ 16 = 15 remainder 15 (F) 15 ÷ 16 = 0 remainder 15 (F) Result (read bottom to top): FF₁₆
Quick reference — Common values:
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
Applications: Color codes (#FF6600 = RGB 255, 102, 0), IP addresses, memory addresses, Unix permissions (chmod 755 = binary 111 101 101).