Identify the logic operation performed by the given circuit.

Solution

Physics sir · 3 steps

Two NOT gates feeding a NAND: apply De Morgan once and the bars cancel, leaving plain A + B.

1. Read the circuit. A and B each pass through a NOT gate first, so the NAND gate receives Ā and B̄. A NAND gives the complement of the AND of its inputs.

   Y = Ā·B̄̅ = Ā̄̄ + B̄̄̄ = A + B

2. De Morgan. The complement of a product is the sum of the complements. Each double bar cancels, so the output is A + B, which is the OR operation.

   A	B	Ā	B̄	Y = Ā·B̄̅
   0	0	1	1	0
   0	1	1	0	1
   1	0	0	1	1
   1	1	0	0	1

3. So. The output is 0 only when both inputs are 0 and 1 otherwise. That is the OR gate truth table, so the answer is (c).

The idea to keep. Inverting both inputs of a gate swaps AND with OR. NOT inputs into NAND gives OR, and NOT inputs into NOR gives AND. Check with the truth table if unsure.

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