Two’s Complement Calculator

Calculate two’s complement values instantly. Enter a binary or decimal number, select the bit size, and get the signed binary representation with decimal and hexadecimal results.

Binary Result: -
Decimal Result: -
Hex Result: -

What is Two’s Complement?

Two’s complement is a binary representation method used by computers to store signed integers. It allows both positive and negative numbers to be represented using the same binary system.

To find the two’s complement of a binary number:

  1. Invert all bits (change 0 to 1 and 1 to 0).
  2. Add 1 to the inverted result.

Original:
  00001010

Invert bits:
  11110101

Add 1:
  11110110

Result:
  11110110

Two’s Complement Example

Convert decimal -10 into 8-bit two’s complement:


Positive 10:
00001010

Invert:
11110101

Add 1:
11110110

Therefore:
-10 = 11110110 (8-bit)

Why Computers Use Two’s Complement

  • Simplifies addition and subtraction operations.
  • Allows one binary system for positive and negative numbers.
  • Avoids separate negative zero representation.
  • Works efficiently with computer hardware.

Common Uses of Two’s Complement

  • CPU arithmetic operations.
  • Programming language integer storage.
  • Embedded systems and microcontrollers.
  • Digital electronics.
  • Binary calculations and computer architecture.

Frequently Asked Questions

Two’s complement is a binary method used to represent positive and negative numbers in computers.
Invert every binary bit and then add 1 to the result. The final binary value is the two’s complement representation.
It makes computer arithmetic easier because the same circuits can handle both positive and negative numbers.
Yes. An 8-bit, 16-bit, or 32-bit representation can produce different binary results because the number of available bits changes.
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