The output of the given circuit diagram is -

Solution

Physics sir · 3 steps

Between the two OR gates you always feed in both A and Ā, so the NOR sees a 1 every time.

1. Two OR gates. The top OR gate gets A and B̄, so its output is A + B̄. The bottom OR gate gets B and Ā, so its output is Ā + B.
2. Final NOR gate. The NOR gate ORs these two outputs and then inverts the result. Inside the bracket you have A + Ā, which is always 1.

   Y = (A + B̄) + (Ā + B)̅ = (A + Ā) + (B + B̄)̅ = 1̅ = 0

   A, B	A + B̄	Ā + B	Y
   0, 0	1	1	0
   1, 0	1	0	0
   0, 1	0	1	0
   1, 1	1	1	0

3. So. At least one OR output is 1 for every input, so the NOR output is 0 in all four rows. That is the table in (d).

The idea to keep. Write the Boolean expression gate by gate, then look for a variable and its complement sitting together. A + Ā = 1 and A · Ā = 0 often collapse the whole circuit to a constant.

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