Half-Subtractor

Half-subtractor is used to subtract one binary digit from another
to give DIFFERENCE output and a BORROW output. The truth table of a half-subtractor is shown in figure.  The Boolean expressions for half-subtractor are,
D = A’B+AB’ and Bo= A’B
Here, the DIFFERENCE  i.e. the D output is an EX-OR gate and the  BORROW i.e. Bo is  AND gate with complemented input A. Figure shows the logic implementation of a half-subtractor. Comparing a half-subtractor with a half-adder, it can be seen that,  the expressions for SUM and DIFFERENCE outputs are same. The expression for BORROW in the case of the half-subtractor is more or less same with CARRY of the half-adder. However, the case of BORROW output the  the minuend is complemented and then ANDing is done.

half_sub

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