In Boolean algebra, a “sum-of-products” (SOP) expression is formed by taking several product terms (AND terms) and combining them with a sum (OR). Which description matches SOP?

Introduction / Context:Canonical logic forms simplify design and implementation. Two common normal forms are sum-of-products (SOP) and product-of-sums (POS). Recognizing SOP helps map logic to NAND/NOR realizations and guides minimization with Karnaugh maps or the Quine–McCluskey method.

Given Data / Assumptions:

• An SOP uses product terms (ANDs) as building blocks.
• These product terms are ORed together to form the final expression.
• Variables may appear complemented or uncomplemented in each product term.

Concept / Approach:Product term = AND of literals (e.g., A·B·C’). Sum = OR operation (+). Thus SOP = (product1) + (product2) + … . Examples: F = A’B + AC + BC’. This structure is convenient for two-level logic: first level AND gates, second level OR gate, possibly followed by inversion depending on technology mapping.

Step-by-Step Solution:Identify that “products” means AND terms of literals.Combine these with OR to form the “sum.”Match the description: OR of several AND functions.Select option B.

Verification / Alternative check:Draw a two-level gate diagram: multiple AND gates feeding a single OR gate → classic SOP topology, confirming the description.

Why Other Options Are Wrong:Option A describes POS; C is OR of ORs (not SOP); D is AND of ANDs (a single larger product); “None” is false since B is correct.

Common Pitfalls:Confusing SOP with POS; overlooking that complements in literals do not change the SOP structure, only the content of products.

Final Answer:The OR function of several AND functions