Since binary number system has only two digits, the addition table for binary consists of only the following four entries:-
0+0=0 0+1=1 1+0=1 1+1=0 plus a carry of 1 to next higher column
Carry-overs are performed in the same manner as in decimal arithmetic. Since 1 is the largest digit in binary number system, any sum greater than 1 requires a digit to be carried over. For instance, 10 plus 10 binary requires addition of two 1s in the second position. Since 1+1=0 plus a carry-over of 1, the sum of 10+10 is 100 in binary.
By repeated use of the above rules, we can add any two binary numbers by adding two bits at a time.