Gate universality and functional completeness: Determine whether one can build a logical AND function using only NOR gates (i.e., express A * B solely with NORs).

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context: NOR and NAND gates are universal, meaning any Boolean function can be implemented using only one of these gate types. Understanding equivalences via De Morgan’s theorems is a staple of digital logic design and optimizations in standard-cell libraries.Given Data / Assumptions: Target: implement AND using only NOR. Available primitive: 2-input NOR (and inverter via tying inputs). Boolean identities and De Morgan’s laws are applicable. Concept / Approach: From De Morgan: A * B = (A' * B') = (A' + B')'. A NOR gate computes (X + Y)'. If we can obtain A' and B', then a single NOR of A' and B' yields (A' + B')' = A * B. Inverters can be made by tying both inputs of NOR together (X NOR X = X').Step-by-Step Solution: Generate A' using NOR: A NOR A = A'.Generate B' using NOR: B NOR B = B'.Compute AND: (A' NOR B') = (A' + B')' = A * B.Thus, AND is realizable using only NOR gates. Verification / Alternative check: Truth table inspection confirms the equivalence for all input pairs (00, 01, 10, 11). Why Other Options Are Wrong: Incorrect: Conflicts with NOR universality.Only if A = B / Only with XOR assistance: Unnecessary constraints; the construction works for all inputs and requires no XOR. Common Pitfalls: Forgetting that tying NOR inputs provides inversion.Confusing NOR-only with OR-only implementations; OR alone is not universal without inversion. Final Answer: Correct

Gate universality and functional completeness: Determine whether one can build a logical AND function using only NOR gates (i.e., express A * B solely with NORs).

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