Number Base Converter

Binary (base 2) is how hardware actually stores and moves data: each bit maps directly to one transistor's on/off state, so it's the only base a processor "speaks" natively. But raw binary is long and hard for humans to read or debug: a 32-bit value is 32 characters of 0s and 1s.

Hexadecimal (base 16) solves that readability problem because 16 = 2^4: every hex digit represents exactly 4 binary bits (a nibble), so a 32-bit value compresses to just 8 hex characters. That's why memory addresses, color codes (#FF5733), and byte dumps are almost always shown in hex rather than binary. It's binary's information density with far less visual noise. Octal (base 8, three bits per digit) shows up less often today, mostly in legacy Unix file permission notation (like chmod 755).

Select the base your number is currently written in (binary, octal, decimal, or hexadecimal), type the value, and the calculator instantly shows the equivalent in all four bases, along with a bit-pattern visualizer and the positional-notation and successive-division proofs. This tool converts whole numbers only. It doesn't currently handle bitwise operations (AND/OR/XOR/shifts), fractional values, or bases outside 2/8/10/16.

Starting from the calculator's default input, 255_(10):

255_(10) = 1111 1111_(2) (binary)

255_(10) = 377_(8) (octal)

255_(10) = FF_(16) (hexadecimal)

255 is a common byte-boundary value (2⁸ − 1), which is why it converts to a clean all-ones binary pattern and an all-F hex pattern, a useful sanity check when you're debugging byte-level data.

For general arithmetic, exponents, and logarithms in decimal, use the scientific calculator. To see integer division with remainders spelled out step by step (the same method this converter uses to go from decimal to another base), see the long division calculator.