Decoder realization with minimal gates: can a single AND gate plus two inverters act as a functional “basic decoder,” i.e., uniquely select one-of-N outputs from coded inputs?

Introduction / Context:
Decoders expand a coded input (e.g., 2 bits) into one-of-N outputs (e.g., 4 lines). This item probes whether an extremely small gate set—one AND gate and two inverters—can truly perform the generic decoder function, which requires producing uniquely asserted output lines for each input code.

Given Data / Assumptions:

• “Basic decoder” refers to standard one-of-N selection (e.g., 2-to-4, 3-to-8).
• Inputs are the coded lines; outputs are mutually exclusive selects.
• No ROM or PLA structures are assumed.

Concept / Approach:
A k-to-2^k decoder uses product terms (minterms) of the inputs and their complements. For k = 2, four AND terms are required, each AND-ing either the true or complemented inputs. Two inverters provide complements, but a single AND gate cannot generate all required minterms. Thus, the proposed gate count is insufficient for one-of-N decoding.

Step-by-Step Solution:

Verification / Alternative check:
Truth table inspection shows that a single AND gate yields only one of the minterms; additional AND gates are needed to cover all code combinations.

Why Other Options Are Wrong:
Applies: overclaims capability.
Applies only with enable: an enable simply gates all outputs; it does not create missing minterms.
Applies only for one-to-two decoding: even 1-to-2 decoding typically uses a buffer and an inverter (or two ANDs with enable), not a lone AND plus two inverters to realize “decoder” semantics.

Common Pitfalls:
Confusing “some decoding” (one minterm) with a full decoder; underestimating the number of product terms needed.

Final Answer:
Does not apply