What is the Boolean expression for the output \(f\) of the combinational logic…
2010
What is the Boolean expression for the output \(f\) of the combinational logic circuit of NOR gates given below?
- A.
\(\overline{Q+R}\) - B.
\(\overline{P+Q}\) - C.
\(\overline{P+R}\) - D.
\(\overline{P+Q+R}\)
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Correct answer: A
Key idea: treat each NOR as an inverted OR and apply De Morgan to simplify.
Let A = not(P+Q), B = not(Q+R), C = not(P+R), D = not(Q+R).
The second-stage NOR outputs are E = not(A + B) and F = not(C + D). Using De Morgan, E = (P+Q)(Q+R) and F = (P+R)(Q+R).
Combine E and F: E + F = (Q+R)[(P+Q)+(P+R)] = (Q+R)(P+Q+R) = Q+R.
The final output is the NOR of E and F, so f = not(E + F) = not(Q+R).
Answer: f = not(Q+R).
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