Identify the correct truth table of the given logic circuit.

Solution

Physics sir · 3 steps

An AND gate with its inputs joined just passes the signal through, so this circuit is A AND (A NAND B).

1. Joined-input AND gates. Both inputs of the top AND gate come from the same wire A, so its output is A · A = A. In the same way, the AND gate after the NAND passes the NAND output through unchanged.
2. Lower branch. The NAND gate takes A and B and gives A̅B̅. This reaches the final AND gate unchanged.

   Y = A · A̅B̅ = A(Ā + B̄) = AĀ + AB̄ = AB̄

   A	B	A̅B̅	Y = A · A̅B̅
   0	0	1	0
   0	1	1	0
   1	0	1	1
   1	1	0	0

3. So. Y is 1 only when A = 1 and B = 0, giving the column 0, 0, 1, 0. That is option (a).

The idea to keep. Joining both inputs of an AND or OR gate makes it a plain wire, and joining both inputs of a NAND or NOR makes it a NOT gate. Simplify those first, then write the Boolean expression.

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