Constructing a 2-input AND using only NOR gates: Evaluate the statement: “A minimum of three universal NOR gates is required to realize the logical operation of a 2-input AND gate.”

Introduction / Context:NOR is a universal gate, meaning any logic function can be implemented using only NOR gates. Determining the minimum number of NOR gates to realize other primitives is a common design skill, useful when standard cell availability is constrained or for theoretical proofs.

Given Data / Assumptions:

• Target function: 2-input AND, X = A * B.
• Available primitive: 2-input NOR gate.
• Standard positive-logic conventions.

Concept / Approach:Use De Morgan’s law: A * B = ~(~(A * B)) = ~(~A + ~B). Realize in two stages: first produce ~A and ~B using self-NOR (inversion), then NOR those results to obtain A * B. This construction uses three NOR gates total.

Step-by-Step Solution:

Verification / Alternative check:Truth table check confirms the final output matches AND. Known minimal implementations show three NORs are necessary and sufficient; two NORs cannot generate both required inversions and the final combination simultaneously.

Why Other Options Are Wrong:

Common Pitfalls:Forgetting that NOR-inverter uses both inputs tied together; attempting to reuse intermediate nodes incorrectly; mixing NAND and NOR equivalences.

Final Answer:Correct