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.
 11 + 11
 101 + 111
 11111 + 11111
 100111 + 1100011
Answers to Above Exercises
 11 + 11 = 110
 101 + 111 = 1100
 11111 + 11111 = 111110
 100111 + 1100011 = 10001010
