In a product-of-sums (POS) realization, the logic network forms OR terms (sums) first and then combines those terms to drive the final output. Which logic gate generates the final output stage in a canonical POS circuit?

Introduction / Context:
Canonical logic forms—sum-of-products (SOP) and product-of-sums (POS)—guide how we implement Boolean functions using two-level logic. Understanding which gate finishes the computation in each form is essential for reading schematics, performing K-map minimization, and mapping functions to AOI/OAI cells in VLSI flows.

Given Data / Assumptions:

• POS means an AND of sum terms.
• Each sum term is an OR of literals (variables or complements).
• We consider the straightforward, non-inverted canonical form.

Concept / Approach:
By definition, a POS expression has the structure F = (S1) * (S2) * … where each Si = (l1 + l2 + …). The network first creates each OR term (sum) and then combines all sum terms using an AND gate. In practical CMOS libraries, an OAI (OR–AND–INVERT) gate may implement the complement efficiently, but the canonical POS form’s final combining operation is still the AND of those sums.

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