Four NOR gates are connected as shown in figure. The truth table for the given figure is :

Solution

Physics sir · 4 steps

Call the first gate's output C, then push each input pair through gate by gate.

1. Label the gates. The left gate gives C = A + B̅. The top gate takes A and C and gives P = A + C̅. The bottom gate takes C and B and gives Q = C + B̅. The last gate gives Y = P + Q̅.
2. NOR rule. A NOR gate outputs 1 only when both its inputs are 0. Any input at 1 makes the output 0.

   A, B	C	P	Q	Y
   0, 0	1	0	0	1
   0, 1	0	1	0	0
   1, 0	0	0	1	0
   1, 1	0	0	0	1

3. Check by algebra. P = A̅·(A + B) = A̅B and Q = AB̅. Then Y = A̅B + AB̅̅, which is XNOR: 1 when the inputs are equal.
4. So. The output column is 1, 0, 0, 1, which matches option (d).

The idea to keep. For any gate network, name every intermediate output and tabulate all four input pairs. Remember that four NOR gates in this layout make XNOR, while the same layout with NAND gates makes XOR.

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