A logic circuit has three inputs A , B , and C . Inputs A and B are connected to a 2-input AND gate. The output of this AND gate and the input C are connected to an unknown 2-input logic gate G . The final output of the circuit is Y . The circuit satisfies the following conditions: (I) When A=1 and B=1 , the output Y is the exact logic complement of C . (II) When A=0 , B=1 , and C=0 , the output Y is 0 . The unknown

Step-by-step solution

Let X be the output of the AND gate. Then X = A B . The final output is Y = G(X, C) . From condition (I): When A=1 and B=1 , the output of the AND gate is X = 1 1 = 1 . We are given that Y = C . Therefore, G(1, C) = C . Let us check standard logic gates for this property: NAND gate: 1 C = C (Matches) NOR gate: 1 + C = 0 (Fails) XOR gate: 1 C = C (Matches) XNOR gate: 1 C = C (Fails) Thus, the gate G must be either a NAND gate or an XOR gate. From condition (II): When A=0 , B=1 , and C=0 , the output of the AND gate