Difficulty: Easy
Correct Answer: Incorrect
Explanation:
Introduction / Context: Canonical boolean forms are foundational to logic design, logic minimization, and PLD device mapping. Understanding the exact meaning of Sum-of-Products (SOP) versus Product-of-Sums (POS) is essential, especially when targeting PAL/PLA resources or writing HDL that maps cleanly to product terms.
Given Data / Assumptions:
Concept / Approach: The algebraic definition of SOP is: F = P1 + P2 + ... + Pn, where each Pi is a product term like (a*b*c). While hardware might use NAND gates to implement this efficiently, that does not change the mathematical definition that the top-level operation is OR (sum).
Step-by-Step Solution:
Define product term → AND of literals (e.g., a*b).Define SOP → OR of product terms (e.g., a*b + a*c + b*c).Compare with the statement (NANDed together) → does not match SOP definition → incorrect.Verification / Alternative check:
Convert a NAND-NAND network to its algebraic form; you recover an OR of products after inversion cancellation.Why Other Options Are Wrong:
Correct: Contradicts the canonical definition.Only correct in NAND-NAND implementations: Hardware choice does not redefine SOP algebra.Context-dependent: While gates vary, algebraic naming does not.Common Pitfalls:
Equating gate-level choices (NAND) with algebraic labels (SOP).Forgetting that “sum” means OR in boolean algebra.Final Answer:
Incorrect
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