Find the truth table for the function Y of A and B represented in the following figure.

Solution

Physics sir · 3 steps

Follow each wire: the top gate gives AB, the bottom gives B-bar, and the OR gate adds them.

1. Read the gates. The AND gate takes A and B, so its output is AB. The NOT gate takes only B, so its output is B̄. The OR gate combines these two outputs.

   Y = AB + B̄

2. Fill each row. Work out AB and B̄ for every input pair. Y is 1 whenever at least one of them is 1.

   A B	AB	B̄	Y = AB + B̄
   0 0	0	1	1
   0 1	0	0	0
   1 0	0	1	1
   1 1	1	0	1

3. So. The output column reads 1, 0, 1, 1. Y is 0 only when A = 0 and B = 1, which matches the truth table in option (b).

The idea to keep. For any gate circuit, write the Boolean expression at each gate output, then tabulate it row by row. Do not forget the bubble on a NOT gate: it flips the signal.

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