2s Complement Calculator - Binary Two's Complement Online

Binary 2's Complement Calculator

The Binary 2's Complement Calculator instantly computes the two's complement of any binary number. This free online tool is essential for computer science students, digital electronics engineers, assembly language programmers, and anyone working with signed binary number representations.

Two's complement is the standard method used by modern computers to represent signed (positive and negative) integers in binary. It simplifies arithmetic operations and eliminates the need for separate circuits to handle negative numbers.

4-bit: 1011 → 2's complement = 0101 (represents -5)
8-bit: 11110011 → 2's complement = 00001101 (represents -13)
4-bit: 0101 → 2's complement = 1011 (represents -5)

What is Two's Complement?

Two's complement is the most widely used method of representing signed integers in binary. In an N-bit two's complement system, positive numbers are represented identically to unsigned binary, while negative numbers are represented by inverting all bits (1's complement) and adding 1 to the result.

How to Calculate Two's Complement

1. Write the binary number.
2. Invert all bits (0 becomes 1, 1 becomes 0) — this gives the 1's complement.
3. Add 1 to the 1's complement result.
4. The result is the two's complement.

Two's Complement Formula

Two's Complement = 1's Complement + 1

OR equivalently:

Two's Complement = (2^N) - Value

where N is the number of bits

Example

Binary = 1011 (4-bit)

Step 1: Original  → 1011
Step 2: Invert    → 0100  (1's complement)
Step 3: Add 1     → 0101  (2's complement)

Value represented = -5

Two's Complement Conversion Table

Applications of Two's Complement

• Signed Integer Representation in CPUs
• Assembly Language and Machine Code
• ALU (Arithmetic Logic Unit) Design
• Computer Architecture and Processor Design
• Embedded Systems Programming
• Fixed-Point Arithmetic
• Digital Signal Processing (DSP)
• Computer Science and Programming Education

Programming Examples

Python

# Two's complement of 1011 in 4 bits
n = 0b1011
bits = 4
twos = (~n & (2**bits - 1)) + 1
bin(twos)

Output

'0b101'  (i.e., 0101)

C

// Signed int automatically uses 2's complement
int x = -5;
printf("%d", x);

Frequently Asked Questions