Binary Addition

Binary addition can be carried out using the sum and carry method. As in base 10 the numbers are laid out in columns and each column added up. The units are placed in the answer and any extra (the carry) are placed in the next column. For example:

 

 

Step 1 is to add the units column. 9 + 4 is 13. So we write down three and carry the one. The tens column now has 6 + 3 + the 1 carried which is 10. We write down 0 and the tens column and carry the one. Finally the hundreds column is 1 + 5 + the 1 carried which is 7. This is placed in the hundreds column giving:

 

 

Binary addition is similar although there are only four rules.

1.    0 + 0 is 0
2.    0 + 1 is 1
3.    1 + 1 is 0 carry 1
4.    1 + 1 + 1 is 1 carry 1

Consider  the following example:

 

 

This is calculated  from the right as 0 + 1 is 1, 1 + 1 is 0 carry 1, 0 + 1 + 1 is 0 carry 1, 1 + 0 + 1 is 0 carry 1. The carry is then placed into the next column giving:

It is important to check your answer. We can do this by converting to decimal and performing the addition. 1010 is 10. 0111 is 7. 10 + 7 is 17 which is 10001.

Another example: Add 10010110 to 001100010.

 

 

The answer is 11111000. Check that this is correct by converting the answer to decimal.

Next: Hexadecimal Addition