Logical equivalence of gates: Which implementation produces the same Boolean function as a NOR gate?

Introduction / Context:Universal gate design often relies on recognizing when combinations of simple gates emulate others. Understanding these equivalences allows flexible implementation with limited gate libraries and aids schematic interpretation.

Given Data / Assumptions:

• NOR is defined as Y = (A + B)'.
• INVERTER provides logical complementation of its input.
• We compare cascaded gates to a single NOR gate.

Concept / Approach:By definition, a NOR gate outputs the inversion of an OR function. Therefore, an OR gate whose output is fed into an inverter produces exactly the same truth table as a NOR gate. This follows directly from the composition Y = NOT(OR(A, B)).

Step-by-Step Solution:Start with OR output: Z = A + B.Invert Z: Y = Z' = (A + B)'.Recognize equality: Y equals the NOR of A and B.Hence, OR followed by INVERTER is functionally identical to NOR.

Verification / Alternative check:Truth table enumeration shows identical outputs for all four input combinations. Logic simulators will show gate-level equivalence after optimization.

Why Other Options Are Wrong:NAND then INVERTER: equals AND (since NOT(NAND) = AND), not NOR.AND then INVERTER: equals NAND, not NOR.NOR then INVERTER: equals OR, the opposite of NOR.

Common Pitfalls:Confusing the order of gates or assuming inverter placement does not matter; inversion placement is critical for function.

Final Answer:OR gate immediately followed by an INVERTER