Binary Addition

The rules of binary addition are given in following table

In the first three rows above, there is no carry, that is, carry = 0, whereas in the fourth row a carry is produced (since the largest digit possible is 1), that is, carry = 1, and similar to decimal addition it is added to next higher binary position.

Example 
1) Add 1011 and 1100

Solution


             1      0      1      1
  (+)      1      1      0      0
     1      0      1      1      1

Carry

Following figure shows Binary addition along with its equivalent decimal addition.

From the above example, we observe the following:

1. if the number of 1's to be added in a column is even then sum bit is 0, and if number of 1's to be added in a column is odd then the sum bit is 1.
2. Every pair of 1's in a column produces a carry (1) to be added to the next higher bit column.