What is the addition of binary numbers?

The addition of binary numbers is easy yet tedious at the same time. It is a fundamental feature of digital computers, and hence it is important to know how to add binary digits.

Almost all the operations of a computer depend on binary addition. Once we understand the addition of two binary digits, it is easier to understand subtraction, multiplication, and division of binary digits.

We can start by adding two binary bits. As you are aware a bit can be either 0 or 1. Therefore, we can have only four possible input combinations. The four possible input combinations and their output are as follows −

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

In the above four possibilities, we can observe that the fourth possibility results in a 2-bit output. The table shows the method of handling such output.

InputOutput
PQCarrySum (P + Q)
0000
0101
1001
1110

As shown in the table, the carry digit handles the possibility of overflow. Here, overflow refers to the extra digit that we obtain on adding 1 and 1. The overflow or carry digit is carried forward to the next most significant digit in the operation.

Example − Add 1011011 + 100111

1 0 1 1 0 1 1
+ 1 0 0 1 1 1
1 0 0 0 0 0 1 0
1 1 1 1 1 1           → Carry bits

In the example

1 + 1 = 0 (one carry)

1 + 1 (+ the carried digit 1) = 1 (one carry)

0 + 1 (+ the carried digit 1) = 0 (one carry)

1 + 0 (+ the carried digit 1) = 0 (one carry)

1 + 0 (+ the carried digit 1) = 0 (one carry)

0 + 1 (+ the carried digit 1) = 0 (one carry)

1 + 0 (+ the carried digit 1) = 0 (one carry)

The last digit that is carried is placed on the left-hand side of the result. Therefore, the output is 10000010.