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