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:
- SOP consists of product terms (ANDed literals) summed via OR.
- Physical NAND-NAND realizations can implement an SOP function due to De Morgan’s transformations, but the formal SOP definition remains OR of products.
- Terminology refers to algebraic structure, not the gate-level optimization chosen.
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
Discussion & Comments