AOI realization – does complementing the output of an AND–OR network produce an AND–OR–Invert (AOI) circuit?

Introduction / Context:
AOI (AND–OR–Invert) gates are common library elements in standard-cell ASICs and TTL/CMOS logic families. They are formed when a two-level AND–OR structure is followed by a single inversion at the output. This item checks whether you recognize that adding a final inversion to an AND–OR network yields an AOI function.

Given Data / Assumptions:

• Network consists of first-level AND gates feeding a second-level OR gate.
• We apply a single inversion to the overall output.
• Ideal Boolean behavior is assumed.

Concept / Approach:
Let the AND–OR network compute S = (P1) + (P2) + ... where each Pi is a product term (e.g., A * B, C * D * E). Adding an inversion gives Y = NOT(S), which by definition is an AOI structure. Using De Morgan’s law, Y = NOT(P1 + P2 + ...) = NOT(P1) * NOT(P2) * ..., demonstrating the dual NAND–NOR interpretation and motivating why AOI (and OAI) forms are efficient in transistor networks.

Step-by-Step Solution:

Verification / Alternative check:
Standard cell libraries list AOI21, AOI22, etc., where the suffix indicates how many inputs feed the first-level ANDs. Datasheets and timing libraries confirm they are implemented by inverting the output of an AND–OR combination.

Why Other Options Are Wrong:
Input inversion is not required to form AOI (that would be OAI variants or different polarities). Limiting to “two-level SOP only” is misleading—AOI refers specifically to two levels plus inversion, which is exactly the structure described. Wired-logic is unrelated to the functional definition.

Common Pitfalls:
Confusing AOI with OAI (OR–AND–Invert). Also, forgetting that a single output inverter transforms SOP to POS complements via De Morgan’s law.

Final Answer:
Correct