Introduction / Context:
De Morgan's theorems provide equivalences between logic gate implementations, enabling circuit simplification and technology mapping. One classic identity states that a NOR operation can be realized using an AND gate with input inversion (bubbles) and output inversion representation.
Given Data / Assumptions:
- NOR is the complement of OR: A NOR B = NOT(A OR B).
- Bubble notation indicates inversion on inputs or outputs of a logic symbol.
- Gate 'equivalence' is functional equivalence.
Concept / Approach:
- De Morgan 1: NOT(A OR B) = (NOT A) AND (NOT B).
- This means a NOR gate behaves as an AND gate whose inputs are inverted (bubbles on inputs), and typically the symbol shows inversion at inputs rather than an explicit inverter block.
Step-by-Step Solution:
Start from NOR: Y = NOT(A OR B).Apply De Morgan: Y = (NOT A) AND (NOT B).Interpretation: Use an AND gate; place bubbles on both inputs to indicate NOT A and NOT B.Hence: A NOR B is equivalent to a bubbled AND gate.
Verification / Alternative check:
Truth table check for A, B ∈ {0,1} shows equality of outputs for NOR and bubbled-input AND.
Why Other Options Are Wrong:
- XAND: Not a standard logic gate.
- XOR: NOT(A XOR B) is XNOR, unrelated to NOR equivalence above.
- NOR: Statement asks for gate equivalence with bubbling; the gate is AND with bubbles, not NOR itself.
- None of the above: Incorrect because AND is correct.
Common Pitfalls:
- Placing the bubble on the output instead of inputs for this identity.
- Confusing NOR equivalence with NAND equivalence (which relates to OR with input bubbles).
Final Answer:
AND
Discussion & Comments