2.1 Half adder

The term “half adder” refers to fact that two half adders are required to form a full adder, which can be used to handle one bit position in binary adding.

A half adder has two inputs, and it has two outputs. Each of the two inputs corresponds to a value to be added. One of the output corresponds to the result of the adding, while the other corresponds to the carry of the addition.

The truth table of a half adder is presented as table 1. In this truth table, ‘X’ and ‘Y’ are the inputs, ‘R’ is the result, and ‘C’ is the carry.






XYRC




0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1





Table 1: Truth table of a half adder.

It is not difficult to see that the equation of ‘C’ is C = XY . The equation of ‘R’ is R = XY + XY . It helps to look at ‘R’ and ‘C’ as functions: R(X,Y ) = XY + XY and C(X,Y ) = XY .