2. Adding Binary Numbers

How, then, could we add two binary numbers?

For two input bits there are four possible combinations of inputs.

These four possibilities, and the resulting sums, are:

     0 + 0 =  0
     0 + 1 =  1
     1 + 0 =  1
     1 + 1 = 10

The last line indicates that we have a carry output.

Therefore, we can transform our results into a truth table, shown on the right.

Suddenly, this looks familiar:

• The carry output is a simple AND function.

• The sum is an XOR.