A tutorial on how to add binary numbers, along with examples, exercises and answers is presented. Also a binary numbers calculator may be used to check results for more practice.
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.
A) Add the binary numbers.