Gate equivalence: A NOR gate’s output is logically equivalent to which basic gate combination?

Introduction / Context:
Recognizing functional equivalence among logic gate combinations is essential for logic simplification, hardware substitution, and understanding universal gates. NOR and NAND are universal because they can synthesize any Boolean function, but each also corresponds to a simple “gate plus inverter” form.

Given Data / Assumptions:

• Definition: NOR outputs the logical negation of OR.
• Symbols: “+” denotes OR, an overbar or NOT denotes inversion.
• Truth tables follow standard Boolean algebra.

Concept / Approach:
The NOR operation is X = NOT(A + B). This is precisely the output of an OR gate feeding an inverter. No other single “gate plus inverter” pair matches NOR’s truth table directly.

Step-by-Step Solution:
Start with OR: Y = A + B.Invert: X = NOT(Y) = NOT(A + B).By definition, this equals the NOR function.

Verification / Alternative check:
Compare truth tables for NOR and the OR-then-inverter combination; they match for all four input pairs (00→1, 01→0, 10→0, 11→0).

Why Other Options Are Wrong:

• NAND followed by inverter equals AND (NOT(NOT(A·B)) = A·B).
• AND followed by inverter equals NAND (NOT(A·B)).
• NOR followed by inverter equals OR (double negation cancels).

Common Pitfalls:

• Mixing up De Morgan’s forms: NOR = NOT(OR), NAND = NOT(AND).
• Assuming the order of operations does not matter—here the OR must precede the inverter.

Final Answer:
OR gate immediately followed by an inverter