The Half Subtractor consists of four possible elementary operations, namely,
In all operations, each subtrahend bit is subtracted from the minuend bit. In case of second operation the minuend bit is smaller than the subtrahend bit, hence 1 is borrowed. Just as there are half and full-adders, there are half and full-subtractors.
A half subtractor is a combinational circuit that subtracts two bits and produces their difference. It also has an output to specify if a 1 has been borrowed. Let us designate minuend bit as A and the subtrahend bit as B. The result of operation A – B for all possible values of A and B is tabulated in Table 3.8.
As shown in the Table 3.8, half-subtractor has two input variables and two output variables. The Boolean expression for the outputs of half-subtractor can be determined as follows
K-map simplification for half-subtractor