Two's Complement Calculator

Enter Binary Number: Enter binary number (0 and 1 only)

Bit Length: Select the number of bits for representation

Two's Complement Result:

Original: 0101 = 5

Two's Complement: 1011 = -5

Step-by-Step Calculation:

Original binary number:

0101

Invert all bits (one's complement):

1010

Add 1 to the inverted number:

1010 + 1 = 1011

Understanding Two's Complement

What is Two's Complement?

Two's complement is a mathematical operation on binary numbers and the most common method of representing signed integers in computers. It solves the problem of negative number representation in binary systems.

Calculation Method

Invert Bits
Change all 0s to 1s and all 1s to 0s

Add 1
Add 1 to the inverted number using binary addition

Result
The final number is the two's complement

Number Range in Two's Complement

Bit Length	Minimum	Maximum	Range
4 bits	-8	7	16 numbers
8 bits	-128	127	256 numbers
16 bits	-32,768	32,767	65,536 numbers
32 bits	-2,147,483,648	2,147,483,647	4,294,967,296 numbers

Advantages of Two's Complement

➕

Single Zero Representation

Only one representation for zero (000...0)

🔢

Simple Arithmetic

Same circuit for addition and subtraction

⚡

Efficient Hardware

No special cases for negative numbers

Common Examples

4-bit: 0101 (+5)

0101 → 1010 → 1011

+5 → -5

8-bit: 00000101 (+5)

00000101 → 11111010 → 11111011

+5 → -5

4-bit: 1000 (-8)

1000 → 0111 → 1000

-8 → +8 → -8 (same)