Number Base Converter
A number base converter that shows binary, octal, decimal, hexadecimal and any custom base from 2 to 36 simultaneously — with the place-value expansion written out, fraction support and a bitwise playground.
How to use Number Base Converter
- Type a number into any base field — the others convert live as you type.
- Set the custom base slider to any radix from 2 to 36 for the fifth field.
- Read the place-value expansion underneath to see exactly how the digits produce the value.
- Check the two’s-complement panel for how the value is interpreted as a signed 8, 16 or 32-bit integer.
- Scroll to the bitwise playground to run AND, OR, XOR, NOT and shifts on two operands with a live bit grid.
About Number Base Converter
Base conversion is one of those tasks that is simple in principle and easy to get wrong at 2am. This converter keeps binary, octal, decimal, hexadecimal and one custom base of your choosing on screen at the same time, all bound to the same value: type into any field and the rest follow instantly. Input is validated per base, so a stray 9 in an octal field is flagged rather than silently misread, and letters in hex or base 36 are accepted in either case.
The “working” is the place-value expansion. For any input the tool writes out each digit multiplied by its power of the base and sums them, which is the entire content of what base conversion means and the fastest way to build real intuition for it. Fractional parts are supported for bases 2, 8 and 16 using negative powers, which also demonstrates why 0.1 in decimal cannot be represented exactly in binary — the origin of nearly every floating-point rounding question ever asked.
The bitwise playground turns the page into a proper programmer’s calculator. Two operands, live AND, OR, XOR, NOT, left shift and both right shifts, each displayed as an aligned bit grid so you can see individual bits flip rather than just reading a new number. Alongside it, the signed interpretation panel shows the same bit pattern read as an 8, 16 and 32-bit two’s-complement integer — the thing to check first when a value that should be small comes back as 4,294,967,295.
Frequently asked questions
How do I convert binary to decimal by hand?
Multiply each digit by its place value — a power of two — and add them up. 1011 is 1×8 + 0×4 + 1×2 + 1×1 = 11. The tool prints exactly this expansion for whatever you type, in whatever base.
Why is hexadecimal used in programming?
Because one hex digit maps to exactly four binary digits, so a byte is always two hex characters and conversion is mechanical rather than arithmetic. That makes hex a compact, lossless shorthand for binary — which is why colours, memory addresses and byte dumps all use it.
Can it convert fractions like 0.101 in binary?
Yes, for bases 2, 8 and 16 the fractional part is converted using negative powers of the base. Note that some fractions that terminate in one base repeat forever in another — 0.1 in decimal is an infinitely repeating binary fraction, which is the root cause of floating-point rounding surprises.
What is two’s complement?
The standard way computers represent signed integers: the top bit carries a negative weight, so in 8 bits 11111111 is −1 rather than 255. The tool shows how your value is interpreted as a signed 8, 16 and 32-bit integer alongside the unsigned reading.
What is the highest base supported?
Base 36, which uses the digits 0-9 followed by the letters A-Z. Anything higher would need characters with no agreed meaning. Letters are accepted in either case.
Does it work offline?
Yes. All conversion, including the bitwise operations, is computed in the page, so it keeps working with no connection.
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