255, 11111111, 377 and FF are the exact same number wearing four different outfits, and computing runs entirely on knowing how to swap between them.
Free math tool
Number Base Converter
Binary, octal, decimal, hexadecimal, or any custom base from 2 to 36, all shown at once.
Runs entirely in your browser. Nothing you enter is sent anywhere.
Positional notation, generalized
Decimal works in powers of 10: 255 means 2×100 + 5×10 + 5×1. Every other base uses the exact same idea with a different power, binary's 11111111 means seven 128's, 64's, 32's and so on down to 1, all added together, which happens to also equal 255. Changing base never changes the value, only how it's written.
Number base converter FAQ
Why does this reject a digit like "9" when converting from binary?
Binary only has two valid digits, 0 and 1. A "9" isn't a different binary value, it simply isn't a valid binary digit at all, the same way "G" isn't a valid decimal digit. This tool checks every character against what's actually legal in the base you selected instead of silently misreading it.
Why does hexadecimal use letters?
Hexadecimal (base 16) needs 16 distinct digits, and only having 0-9 available leaves it four short, so A, B, C, D, E and F stand in for 10 through 15. It's not arbitrary, it's the same logic that would apply to any base above 10, which is why bases up to 36 conventionally borrow the rest of the alphabet too.
Why is binary used in computing instead of decimal?
A transistor or a switch has two natural, reliably distinguishable states, on and off, which map directly onto binary's two digits. Building reliable hardware that distinguishes ten different voltage levels for base 10 is far harder than reliably distinguishing two, so binary won on practical engineering grounds, not mathematical superiority.
What is the highest base this converts?
Base 36, using every digit 0-9 and every letter A-Z. That's the practical ceiling for this style of positional notation using the Latin alphabet, going higher would need to invent new symbols.
Is my data private?
Yes. Every conversion runs in your browser. Nothing you enter is sent to a server.
Free number base converter by ANUPRESS
Same value, different costume
Every number system, decimal, binary, octal, hexadecimal, any base at all, uses positional notation: each digit’s position represents a power of the base, and the digit says how many of that power to count. 255 in decimal means 2 hundreds, 5 tens, 5 ones. 11111111 in binary means seven 128’s, 64’s, 32’s, 16’s, 8’s, 4’s, 2’s and 1’s, added together, which happens to total the exact same 255. Changing base is entirely a matter of notation, the underlying quantity never moves.
Why hexadecimal borrows letters
Base 16 needs sixteen distinct single-character digits, and the familiar 0 through 9 only supplies ten. Rather than invent new symbols, hexadecimal borrows A through F for ten through fifteen, so counting goes …8, 9, A, B, C, D, E, F, 10. That “10” isn’t ten, it’s sixteen, the same way “10” in binary is two, not ten, the value a digit represents always depends on which base you’re reading it in.
Why computers standardized on binary, and where hex fits in
A transistor reliably distinguishes two states, on and off, which maps directly onto binary’s two digits, building hardware that reliably distinguishes ten voltage levels for decimal is a much harder engineering problem. But raw binary is miserable for a human to read, eight digits just to write 255, so programmers lean on hexadecimal instead: each hex digit represents exactly four binary digits, so converting between them is quick mental math, while still being far more compact than staring at a wall of ones and zeros.