AND–OR–INVERT (AOI) standard cells and networks are commonly used to implement minimized sum-of-products efficiently. AOI gates are primarily designed to simplify the implementation of which canonical logic form?

Introduction / Context:
Many standard-cell libraries include complex gates like AOI (AND–OR–INVERT) and OAI (OR–AND–INVERT) because they reduce transistor count and delay compared to building the same logic strictly from basic gates. Recognizing which canonical form each complex gate targets helps map minimized expressions directly to efficient hardware.

Given Data / Assumptions:

• AOI topology: multiple AND gates feed an OR gate, followed by an inversion.
• Target expressions: minimized two-level SOP forms (sum of products).
• Goal: identify which canonical form AOI matches most naturally.

Concept / Approach:
A two-level SOP is of the form F = Σ(products) = (A*B) + (C*D) + … . AOI realizes the complemented SOP: F' = [(A*B) + (C*D) + …]'. In CMOS, AOI gates can be highly efficient because the pull-down (or pull-up) networks implement the inverted sum directly with fewer transistors. By placing or removing bubbles (De Morgan transformations), an AOI gate effectively implements the intended SOP with minimal staging, often as a NAND–NAND equivalent.

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