Classify the Boolean form: For the expression (A + B)(C + D), identify the canonical style of logic representation.

Introduction / Context:Recognizing whether a Boolean expression is in Sum-of-Products (SOP) or Product-of-Sums (POS) form is foundational for logic minimization, mapping to PLDs/CPLDs, and interpreting Karnaugh maps. This recognition influences how you group terms and implement gates.

Given Data / Assumptions:

• Expression is (A + B)(C + D).
• “+” denotes logical OR; adjacency denotes logical AND.
• We classify the overall structural form.

Concept / Approach:SOP means “OR of AND terms” (e.g., AB + A’C). POS means “AND of OR terms” (e.g., (A + B)(C + D)). Since our expression is an AND between two sums, it is POS. Correct identification helps when mapping expressions to gate-level or array-level structures.

Step-by-Step Solution:

Verification / Alternative check:Expanding (A + B)(C + D) yields AC + AD + BC + BD, which is SOP after expansion; however, the original, unexpanded structural form is POS. Structural form is judged before algebraic expansion.

Why Other Options Are Wrong:

• SOP: Not in original structural form.
• LUT / LAB / PLA form: These are implementation terms or device blocks, not canonical expression styles.

Common Pitfalls:Confusing expanded form with original form; assuming only one correct representation exists; overlooking that K-map grouping often moves between SOP and POS depending on 1-cells vs. 0-cells.

Final Answer:POS