The resulting logic circuit obtained when both inputs of NOR and NAND gates…
2023
The resulting logic circuit obtained when both inputs of NOR and NAND gates are connected together is:
Answer: D. NOT — ConceptIdempotent Boolean laws state A + A = A and A · A = A. NAND and NOR apply a final complement to the corresponding AND or OR result. Therefore, tying…
- A.
AND
- B.
XOR
- C.
OR
- D.
NOT
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Show answer & explanation
Correct answer: D
Concept
Idempotent Boolean laws state A + A = A and A · A = A. NAND and NOR apply a final complement to the corresponding AND or OR result.
Therefore, tying identical inputs first reduces the inner operation to A; the output is then its complement, ¬A.
Application
Let the common input connected to both terminals be A.
For NOR, Y = ¬(A + A) = ¬A by the idempotent OR law.
For NAND, Y = ¬(A · A) = ¬A by the idempotent AND law.
Both outputs complement A, which is the behavior of a NOT gate.
Cross-check
A | Tied-input NOR | Tied-input NAND | NOT A |
|---|---|---|---|
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
The identical truth-table columns confirm that each tied-input circuit is equivalent to a NOT gate.