Two's Complement Calculator

Convert between binary and decimal using two's complement representation. Find the two's complement of binary numbers and perform signed binary operations.

Operation Type

Bit Length

Decimal Number

Range: -2^(n-1) to 2^(n-1)-1 (for selected bit length)

Binary Number (Two's Complement)

Enter binary digits (0 and 1 only) matching the selected bit length

Binary Number

Enter binary number to find its two's complement

First Binary Number

Second Binary Number

Enter binary numbers of the same bit length

Result

Range Information

Step-by-Step Solution

Select an operation and enter values, then click "Calculate" to see the step-by-step solution.

What is Two's Complement?

Two's complement is a mathematical operation used to represent signed integers in binary. It's the most common method for representing negative numbers in computer systems.

Formula: Two's complement = One's complement + 1

Key Features

Single representation for zero
Arithmetic operations work without special handling
Range: -2^(n-1) to 2^(n-1)-1
Most significant bit (MSB) indicates sign
1 = negative, 0 = positive

Common Bit Length Ranges

4-bit: -8 to 7
8-bit: -128 to 127
16-bit: -32,768 to 32,767
32-bit: -2,147,483,648 to 2,147,483,647