ITPEC FE Morning April 2022 Question 21

The four-gate circuit that NORs each input with NOR(A, B) — its truth table gives 1 exactly when A and B are equal, which is Exclusive-NOR.

Label the gate outputs of circuit (d): P is the NOR of A and B; Q is the NOR of A and P; R is the NOR of P and B; Y is the NOR of Q and R. A NOR output is 1 only when both its inputs are 0.

Y is 1 for the inputs 00 and 11 and 0 when they differ, the truth table of XNOR.

Answer (d)

Why not others:

• •(a) — the gates with tied inputs give A and B, and their NOR is A · B; the last gate then outputs the negation of A · B + A · B, which is XOR, the complement of the wanted function.
• •(b) — the NOR of A and B is A · B by De Morgan's law, so the circuit is an AND gate.
• •(c) — a NOR with both inputs tied is an inverter, so it turns the NOR of A and B back into A + B: an OR gate.

Key rule: A NOR gate with its inputs tied together is a NOT gate, and NOR of two inverted inputs is AND; to identify a gate network, label every internal output and fill the four-row truth table.

Hardware · AI-written, may contain errors