Number Base Converter
Binary, octal, decimal, hex and beyond
Any base from 2 to 36, with grouped digits, two’s-complement view and a byte breakdown.
Number Base Converter
Runs in your browser · nothing uploaded| Unit | Symbol | Value |
|---|---|---|
| Binary | b2 | 1101 1110 1010 1101 1011 1110 1110 1111 |
| Octal | b8 | 33653337357 |
| Decimal | b10 | 3 735 928 559 |
| Hexadecimal | b16 | DEADBEEF |
| Base 32 | b32 | 3FARFNF |
| Base 36 | b36 | 1PS9WXB |
| Two's complement 32 | i32 | -559038737 |
| Bytes | hex | DE AD BE EF |
| Bit length | n | 32 |
01 — How to use Number Base Converter
02 — Getting good results
03 — Questions
No. Parsing and rendering are arithmetic in this browser tab, with nothing transmitted or stored.
Yes. Everything here uses arbitrary-precision integers, so a full 64-bit value keeps every digit. That matters because a standard JavaScript number holds only 53 bits exactly — parseInt silently loses the low digits of a large hex value, which is precisely the case this tool exists for.
Because it runs out of characters: ten digits plus twenty-six letters is thirty-six symbols. Going further needs a larger alphabet and an agreed ordering, which is what encodings like Base64 provide — a different problem with its own tool.
It is how essentially every computer represents signed integers. Its appeal is that addition and subtraction work identically on signed and unsigned values, so the hardware needs one adder rather than two — the sign falls out of the bit pattern rather than needing separate handling.
04 — More about Number Base Converter
Why hexadecimal, and why in pairs
Hexadecimal survives not because sixteen is a natural base for people but because of an exact structural correspondence: four binary digits hold sixteen values, so one hex digit maps to exactly four bits with nothing left over. That makes conversion between the two a per-digit lookup rather than arithmetic, and it is why a programmer can read a hex value as bits at a glance. Two hex digits make eight bits, which is one byte, which is why hex is conventionally written and grouped in pairs. Octal has the same property against three bits and was common when word sizes were multiples of three; it survives mainly in Unix file permissions, where three bits per permission group makes it genuinely the natural fit.
Two’s complement, and the asymmetry it creates
Two’s complement represents a negative number as the bit pattern that, added to the positive one, overflows to zero. The elegance is that the hardware needs no special case: the same adder handles signed and unsigned values, and subtraction is addition of a complement. It leaves one visible artefact, which is that the range is asymmetric. At eight bits there are 256 patterns, one of which is zero, leaving 255 to split between positive and negative — so the range runs from −128 to +127, and there is no positive 128. That is why the most negative integer at any width has no positive counterpart, and why negating it overflows back to itself: a genuine edge case that has caused real bugs in code that assumed negation was always safe.
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