GATE 2015 CS (CS2) – Question 55

Digital Logic · Boolean Algebra and Minimization · 2 marks · Numerical answer

How many minterms remain after minimizing $[D\prime+AB\prime+A\prime C+AC\prime D+A\prime C\prime D]\prime$?

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Correct answer: 1

Explanation

First D′ forces D=1 for the complemented expression to be one. Under D=1, the remaining inner terms are AB′+A′C+AC′+A′C′ = AB′+A′+AC′. Their complement requires A=1, B=1 and C=1. Together with D=1 this leaves only minterm ABCD, so the count is one.

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