Two's complement addition calculator

Two’s complement addition calculator 

This 2’s complement addition calculator adds two binary numbers in 2’s complement form and gives the result in seconds. 

What is 2’s complement?

Computers understand binary language which consists of 0s and 1s. The positive integers are represented easily in binary language. E.g 15 is represented as “1111” in binary.

But for a negative 15, we use 2’s complement. This way, the computer can understand that the given integer is negative. 

How to add binary numbers?

Here are the steps to add two’s complement.

1. Convert the decimal numbers into one’s complement. Add one and make it two’s complement. 

2. Add the two numbers.

3. If the overflow occurs, discard the carry.

Example:

Convert 15 and 18 into two’s complement and add them.

Solution: 

• Conversion: 

15 is represented in binary form as 0000 1111. Invert all the 1s and 0s to find one’s complement.

= 1111 0000

Add 1; =1111 0000 + 1 = 1111 0001

18 is represent in binary as 0001 0010. It’s two’s complement is

Inversion = 1110 1101

Adding 1 = 1110 1101 + 1 = 1110 1110

• Adding: 

1 1 1 1 0 0 0 1

1 1 1 0 1 1 1 0

_______________

1 1 1 0 1 1 1 1 1 

The “1” at the left-most is discarded.