Number Base Converter

When to use it

Every programmer meets the same three bases within a week of starting: binary for bit masks, hexadecimal for colour codes and memory addresses, octal in file permissions and a few legacy formats. This page converts a number between those three and decimal, and shows all four forms at once so you can check a value without switching tools.

It is equally useful in the other direction: a homework exercise asking for 255 in binary, or a colour code that needs to become three decimal channel values.

How the maths works

Place value: each digit is multiplied by the base raised to its position, counting from zero on the right. In base 16 the letters A to F stand for 10 to 15. The tool validates every character against the base you chose, so a 2 in binary or a G in hexadecimal is refused before any arithmetic happens.

Going the other way, the decimal value is divided repeatedly by the target base and the remainders are read bottom to top. That is how 255 becomes FF: 255 ÷ 16 = 15 remainder 15, and 15 is F in both positions.

A worked example

Convert 255 from decimal, the default on the page.

1. Binary: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, so 11111111.
2. Octal: 255 ÷ 8 = 31 remainder 7; 31 ÷ 8 = 3 remainder 7; 3 ÷ 8 = 0 remainder 3, so 377.
3. Hexadecimal: 255 = 15 × 16 + 15, so FF.
4. Check: 3 × 64 + 7 × 8 + 7 = 192 + 56 + 7 = 255.

Common values

The last row is the largest value that fits in twelve bits, which is why 4,095 keeps appearing in memory and graphics work.

Common mistakes

• Reading 10 in hex as ten. In base 16 it is sixteen: 1 × 16 + 0.
• Using digits the base does not have. Binary stops at 1 and octal at 7; a 9 in octal is an error, not a value.
• Forgetting that leading zeros do not change a value. 007 in octal is still seven, and 00FF is 255.
• Pasting very long strings. The page rejects results beyond the exact integer range instead of rounding them.

Keep exploring

• Data Storage Converter — decimal and binary units, the same confusion in another form.
• Number to Words — the decimal value spelled out in words.
• Roman Numeral Converter — a non-positional system for comparison.