Identify the correct truth table of the given logical circuit.

Question

G1 Physics · Accepted Answer

From the circuit, the upper gate has both inputs connected to A. Therefore its output is simply A. The lower NAND gate has inputs A and B, so its output is overline(A·B). This signal is then inverted, giving A·B. The final gate is an AND gate whose inputs are A and overline(A·B). Hence, Y = A·overline(A·B). Using De Morgan's theorem, overline(A·B) = Ā+B̄. Therefore, Y = A(Ā+B̄) = AĀ+AB̄ = 0+AB̄ = AB̄. Now evaluate: A=0, B=0 → Y=0. A=0, B=1 → Y=0. A=1, B=0 → Y=1. A=1, B=1 → Y=0. Thus the corr…