Identify the correct Logic Gate for the following output (Y) of two inputs A and B.

Solution

Physics sir · 3 steps

Read the waveforms slot by slot into a truth table, then see which circuit gives the same column of Y.

1. Read the slots. The dashed lines cut the graph into time slots, and in each slot you note A, B and Y. Over the slots you see AB = 11, 00, 01, 10, 11, 00, 01, 10 with Y = 0, 1, 1, 1, 0, 1, 1, 1.
2. Truth table. So Y = 1 for AB = 00, 01, 10 and Y = 0 only for AB = 11. The output goes low only when both inputs are high, and that is a NAND gate, Y = A · B̅.

   Source	Output expression	Y for AB = 00, 01, 10, 11	Matches?
   Graph	read off	1, 1, 1, 0	target
   (a) OR then NOT	A + B̅	1, 0, 0, 0	no
   (b) AND then NOT	A · B̅	1, 1, 1, 0	yes
   (c) OR with inverted A, then NOT	Ā + B̅ = AB̄	0, 0, 1, 0	no
   (d) NAND with inverted B	A · B̄̅ = Ā + B	1, 1, 0, 1	no

3. So. Only the AND gate followed by a NOT gate, which together make a NAND gate, reproduces the waveform. The answer is (b).

The idea to keep. For waveform questions, turn the graph into a truth table first. One output that differs from the rest, like a single 0 at AB = 11, names the gate straight away: here it is NAND.

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