Logic equivalence: a NOR gate is functionally equivalent to an OR gate followed by which single element?

Difficulty: Easy

Correct Answer: Inverter (NOT)

Explanation:


Introduction / Context:
Composite logic functions can be described by combining simpler gates. Recognizing these equivalences helps with circuit minimization and technology mapping. NOR, a universal gate, is defined as the logical negation of OR.


Given Data / Assumptions:

  • NOR outputs 1 only when all inputs are 0; otherwise outputs 0.
  • We are asked to express NOR as an OR stage followed by one additional element.
  • Standard logic gate behavior and naming are assumed.


Concept / Approach:
By definition, NOR(X, Y) = NOT(OR(X, Y)). Therefore, implement OR first, then invert its output using a single NOT (inverter). This identity is used widely when decomposing complex gates into primitive cells or CMOS pull-up/pull-down networks.


Step-by-Step Solution:

Form the intermediate signal S = OR(X, Y). Apply inversion: Z = NOT(S). Conclude Z equals NOR(X, Y).


Verification / Alternative check:
Truth table comparison confirms that for inputs (0,0) → OR=0 → NOT=1; for any case with a 1 input → OR=1 → NOT=0, matching NOR behavior exactly.


Why Other Options Are Wrong:

AND or XOR following OR does not invert the logic and thus cannot produce NOR. “XAND” is not a standard logic element. “None” is invalid because the inverter is correct.


Common Pitfalls:
Confusing NOR with NAND (which equals AND followed by NOT). Keep the pairings straight: NOR = OR then NOT; NAND = AND then NOT.


Final Answer:
Inverter (NOT)

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