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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $\oplus$ denote XOR operation. Let 1 and 0 denote the binary constants and F is the Boolean expression over two variables P and Q
$F(P,Q)=((1\oplus P)\oplus(P\oplus Q))+((P\oplus Q)\oplus(Q\oplus0))$
Which of the following is equivalent expression to F?
Solution
$((1\oplus P)\oplus(P\oplus Q))$
$=1\oplus P\oplus P\oplus Q$
$=1\oplus Q$
$=\overline{Q}$
Second part:
$((P\oplus Q)\oplus(Q\oplus0))$
$=P\oplus Q\oplus Q\oplus0$
$=P$
So,
$F=\overline{Q}+P$
$F=P+\overline{Q}$
This expression is not matching exactly with the given options. So, the correct simplified expression should be:
$P+\overline{Q}$
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