Two's Complement Calculator
Convert any signed integer to its two's complement binary representation and back. Choose 8-bit, 16-bit, or 32-bit width, and see the binary, hexadecimal, unsigned equivalent, and step-by-step conversion.
Two's complement is the standard method computers use to represent signed integers (positive and negative whole numbers) in binary.
How Two's Complement Works:
- Positive numbers are stored the same as regular binary, with a leading 0 bit.
- Negative numbers are stored by inverting all the bits of the absolute value and adding 1.
Example (8-bit):
The number -42:
- Start with 42 in binary: 00101010
- Invert all bits: 11010101
- Add 1: 11010110
So -42 in 8-bit two's complement is 11010110.
Why Two's Complement?
- There is only one representation of zero (unlike sign-magnitude, which has +0 and -0).
- Addition and subtraction use the same hardware circuit.
- The most significant bit (MSB) acts as the sign bit: 0 for positive, 1 for negative.
Ranges:
- 8-bit: -128 to 127
- 16-bit: -32,768 to 32,767
- 32-bit: -2,147,483,648 to 2,147,483,647