Two's Complement Calculator (Signed / Unsigned Converter)

Computers store negative integers in two's complement: the same bits can mean −1 in a signed byte or 255 in an unsigned one. This converter shows both readings of a bit pattern at 8, 16, 32, 64, 128 or any custom width, with the binary, hex and octal forms, whether the value fits or wraps around, and the older one's complement and sign-magnitude encodings for comparison. All arithmetic uses exact big integers, so 64- and 128-bit values are never rounded.

How to use this tool

1. Type a number: a decimal like -42, or a hex/binary/octal bit pattern.
2. Say how it is written.
3. Choose the bit width — 8 for a byte, 32 for an int, 64 for a long, or a custom width.
4. Read the signed and unsigned values, the bit pattern and the overflow check.

Formula

pattern = x mod 2ⁿ · signed = pattern − 2ⁿ if pattern ≥ 2ⁿ⁻¹, else pattern

n is the bit width. A negative x becomes 2ⁿ − |x|, which is the same as inverting the bits of |x| and adding 1. Signed n-bit values run from −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1, unsigned from 0 to 2ⁿ − 1. A decimal outside both ranges keeps only its lowest n bits — the same wrap-around a C or Java cast performs.

Example

For −42 in 8 bits: 256 − 42 = 214, so the pattern is 1101 0110 = 0xD6, which an unsigned byte reads as 214. One's complement would be 1101 0101 and sign-magnitude 1010 1010. At 16 bits the same value is 0xFFD6, at 32 bits 0xFFFFFFD6.