eolas/Electronics_and_Hardware/Binary/Binary_addition.md

categories	tags
Mathematics Computer Architecture	binary binary-arithmetic

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