In the truth table of the above circuit the value of X and Y are :

Solution

Physics sir · 3 steps

Both AND outputs are 0 when A and B differ, and a NOR of two zeros gives 1.

1. Read the gates. The top AND gate gives AB. The bottom AND gate gets both inputs inverted, so it gives ĀB̄. Both feed a NOR gate, because the output has a bubble.

   E = AB + ĀB̄̅

   A, B	AB	ĀB̄	E (NOR)
   0, 0	0	1	0
   0, 1	0	0	1 (X)
   1, 0	0	0	1 (Y)
   1, 1	1	0	0

2. Check. The rows for 0, 0 and 1, 1 give 0, matching the given table. The circuit is an XOR gate, which outputs 1 only when the inputs differ.
3. So. X = 1 and Y = 1, which is option (a).

The idea to keep. Write the Boolean expression gate by gate, then fill a truth table. AB and ĀB̄ fed into a NOR makes an XOR gate, so the output is 1 only when the inputs differ.

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