Gate equivalence in digital design A NOR logic gate performs the same overall function as which gate when an inverter is connected to that gate’s output?

Introduction / Context:Gate equivalence is essential when substituting parts or simplifying designs. Recognizing how composite gate configurations replicate standard functions like NOR helps with logic minimization and hardware implementation choices.

Given Data / Assumptions:

• NOR is defined as logical NOT of OR.
• Boolean “+” denotes OR; NOT indicates inversion (complement).
• We compare NOR to a single basic gate followed by an inverter.

Concept / Approach:The NOR function is X = NOT(A + B) for two inputs (and extends similarly for more inputs). That is exactly what occurs if an OR gate’s output is fed into an inverter. Hence, an OR followed by NOT is equivalent to a single NOR gate symbol.

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

Verification / Alternative check:Compare truth tables. For inputs 00, 01, 10, 11, the OR-then-invert sequence gives outputs 1, 0, 0, 0, which is the NOR truth table exactly.

Why Other Options Are Wrong:

• AND then NOT gives NAND, not NOR.
• NAND is NOT(AND); NOR is NOT(OR). They are distinct universal gates.
• “none of the above” is incorrect because OR followed by an inverter is correct.

Common Pitfalls:

• Confusing De Morgan companions: NAND vs. NOR.
• Mixing arithmetic “+” with Boolean “+”; Boolean “+” represents logical OR.

Final Answer:OR