Database-Management-System
August 26, 2024DFD
August 26, 2024GATE 2010
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Question 9
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The Boolean expression for the output ‘f’ of the multiplexer shown below is
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P⊕Q⊕R
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P+Q+R
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Question 9 Explanation:
f = P’Q’ R + P’Q R’ + PQ’ R’ + PQR
= (P’Q’ + PQ)R + (P’Q+PQ’)R’
= (P⊕Q)’R + (P⊕Q)R’
= (P⊕Q⊕R)
= (P’Q’ + PQ)R + (P’Q+PQ’)R’
= (P⊕Q)’R + (P⊕Q)R’
= (P⊕Q⊕R)
Correct Answer: B
Question 9 Explanation:
f = P’Q’ R + P’Q R’ + PQ’ R’ + PQR
= (P’Q’ + PQ)R + (P’Q+PQ’)R’
= (P⊕Q)’R + (P⊕Q)R’
= (P⊕Q⊕R)
= (P’Q’ + PQ)R + (P’Q+PQ’)R’
= (P⊕Q)’R + (P⊕Q)R’
= (P⊕Q⊕R)