Aspire Faculty ID #18482 · Topic: UGC NET Computer Science June 2023 (Paper II) · Just now
UGC NET Computer Science June 2023 (Paper II)

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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