Binary addition

  • We add binary values in columns just like we would with denary addition.
  • Each column is classified on the basis of place-value. In denary this is 10, in binary it is 2.
  • When we conduct a binary addition, we add the binary values as if they were normal integers but we represent the sums as binary.
    • For example: 1+1=2 for the calculation but the sum is 10

Examples

Example one

1010+0111=10001

10+7=17

In the first column: 1+0=1, so we simply put the binary value for 1:

1010
0111
____
   1

In the second column: 1+1=2. In binary this is represented as 10. So we put 0 beneath the bar and carry the 1:

 1
1010
0111
____
  01

In the third column, we repeat the previous process. We are presented with 1+0+1 which is 2. As 2 is 10 in binary, we put the zero beneath the line and carry the 1:

11
1010
0111
____
 001

In the final column, we again have 1+1 giving us 2 or 10 but at this point we cannot carry any more because we have reached the final column. So instead of carrying the 1 we just put both digits beneath the line 10.

 11
 1010
 0111
_____
10001

Example two

1001+0111=10000

9+7=16

 111
 1001
 0111
_____
10000