Number Base Converter

Computers store numbers in binary, programmers read memory and colours in hexadecimal, and Unix file permissions use octal. This converter takes a whole number written in any base from 2 to 36 and shows it in binary, octal, decimal, hexadecimal and a base you choose, with digits grouped for reading. It uses arbitrary-precision integers, so a 64-bit ID or a 100-digit number converts exactly — ordinary JavaScript numbers lose accuracy above 9,007,199,254,740,991. It also shows how the value is stored in 8, 16, 32 or 64 bits using two’s complement, and what the same bits mean read as signed or unsigned — or as an IEEE 754 float. Type a decimal such as 0.1 or 3.14 and it shows exactly how a float32 and a float64 store it: the sign, exponent and mantissa bits, the hex, and the full decimal value actually held, which explains why 0.1 + 0.2 isn’t exactly 0.3.

1. Type the number. Spaces, underscores and a 0x, 0b or 0o prefix are fine.
2. Choose the base it’s written in, or set another base from 2 to 36.
3. Read it in every base and copy the one you need.
4. Choose a bit width to see the two’s-complement bit pattern and its signed and unsigned meanings; at 32 and 64 bits it also shows the same bits read as a float.
5. Type a decimal with a point or an exponent (0.1, 1e-7) to see its IEEE 754 float32 and float64 encodings.

• Fractions are shown as IEEE 754 floats, not converted to other bases: 0.1 has no finite binary expansion, so “0.1 in binary” is always an approximation.
• Numbers are limited to 4,096 digits.
• Bases above 10 use letters a–z for digits 10–35, case-insensitively.
• The two’s-complement view assumes a value that fits the chosen width; wider values are reported rather than silently wrapped.
• All conversion happens in your browser. Nothing is sent or saved.

Multiply each digit by 2 raised to its position, counting from 0 on the right, and add them up. 1011 is 1×8 + 0×4 + 1×2 + 1×1 = 11.

In 32-bit two’s complement, −1 is stored as 2³² − 1, which is every bit set: FFFFFFFF in hex. The same bits read as unsigned are 4,294,967,295.

Each octal digit is three permission bits: 7 is 111 (read, write, execute), 5 is 101 (read, execute). Choose octal as the input base and read the binary.

Most calculators use floating-point numbers, which round anything above 2⁵³. This tool uses exact integer arithmetic, so every digit is correct.