Two's Complement

Convert between signed decimal integers and their two's complement binary representation. Click individual bits to toggle them, or type decimal/binary values directly.

How It Works

Two's complement is the standard method computers use to represent signed integers in binary. The most significant bit (MSB) acts as the sign bit: 0 for positive, 1 for negative.

Positive numbers are stored the same way as unsigned binary. For example, +42 in 8-bit is simply 00101010.

Negative numbers are encoded in three steps:

1. Write the absolute value in binary
2. Invert all bits (bitwise NOT) — this gives the one's complement
3. Add 1 to the result — this gives the two's complement

For example, −42 in 8-bit: 00101010 → invert → 11010101 → +1 → 11010110.

Why two's complement? It allows addition and subtraction to use the same hardware circuit. There is exactly one representation of zero, and the range is asymmetric: an n-bit value can hold −2ⁿ⁻¹ to +2ⁿ⁻¹−1.

Range Reference