Addition of Binary Numbers

Custom Search


A tutorial on how to add binary numbers, along with examples, exercises and answers is presented.

let us first add binary numbers with one digit
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10
1 + 1 + 1 = 11
The above simple additions are similar to those of decimal numbers except the last two: 1 + 1 = 10 since 10 is 2 in binary and 1 + 1 + 1 = 11 since 11 is 3 in binary.

We now add numbers with more than one digit: 1 1 1 1 + 1 1 0 1

1 1 1 1
+
1 1 0 1
____ ____ ____ ____ ____

1) We first add the digits in the "ones" column: 1 + 1 = 10. The 0 is put in the "ones" column and carry the 1 to the "twos" column.

1
1 1 1 1
+
1 1 0 1
____ ____ ____ ____ ____
0

2) We next add the digits in the "twos" column including the carry: 1 + 1 + 0 = 10. The 0 is put in the "twos" column and carry the 1 to the "fours" column.

1 1
1 1 1 1
+
1 1 0 1
____ ____ ____ ____ ____
0 0

3) We next add the digits in the "fours" column including the carry: 1 + 1 + 1 = 11. The 1 is put in the "fours" column and carry the 1 to the "eights" column.

1 1 1
1 1 1 1
+
1 1 0 1
____ ____ ____ ____ ____
1 0 0

4) We now add the digits in the "eights" column including the carry: 1 + 1 + 1 = 11. The 1 on the left is put in the "eights" column and the other 1 in the "sixteens" column.

1 1 1
1 1 1 1
+
1 1 0 1
____ ____ ____ ____ ____
1 1 1 0 0

You can check the above addition of binary numbers using their decimal representations. 1111 is 15 in decimal and 1101 is 13 in decimal. The answer is 11100 is 28 in decimal.

Exrecises

A) Add the binary numbers.
  1. 11 + 11
  2. 101 + 111
  3. 11111 + 11111
  4. 100111 + 1100011

Answers to Above Exercises

  1. 11 + 11 = 110
  2. 101 + 111 = 1100
  3. 11111 + 11111 = 111110
  4. 100111 + 1100011 = 10001010