Which of the following circuits has the same output as that of the given circuit?

Solution

Physics sir · 3 steps

Both AND gates share A, so pull A out: B̄ + B is 1 and the whole circuit shrinks to NOT A.

1. Read each gate. The top AND gate gets A and B̄, so it gives AB̄. The bottom AND gate gets A and B, so it gives AB. Both feed a NOR gate.

   Y = AB̄ + AB̅ = A(B̄ + B)̅ = A · 1̅ = Ā

2. Output depends on A. Since B̄ + B = 1 always, B drops out completely. The circuit is just a NOT gate acting on A.

   Option	Circuit	Output	Same as Ā?
   (a)	NAND with both inputs tied to A	A · A̅ = Ā	Yes
   (b)	AND of A and B	AB	No
   (c)	NAND with both inputs tied to B	B̄	No
   (d)	AND followed by NOT	A̅B̅	No

3. So. A NAND gate with its inputs joined acts as a NOT gate on A, giving Ā. The answer is (a).

The idea to keep. Before drawing a full truth table, look for a common input and factor it out. Terms like B̄ + B = 1 often make a big circuit collapse to a single gate.

Answer from the NTA final answer key. Solution by PrepWiser.