Identify the SOP form Which of the following Boolean expressions is correctly written in sum-of-products (SOP) form?

Introduction / Context:Choosing the correct canonical or standard form helps map Boolean expressions directly to hardware. SOP (sum-of-products) is widely used because it implements naturally with an AND–OR structure.

Given Data / Assumptions:

• Products are ANDed literals (e.g., AB, A’C, BCD).
• Sum denotes OR of product terms (e.g., AB + CD + A’C’D).

Concept / Approach:An SOP expression must be an OR of one or more product terms. Each product term contains only literals (possibly complemented) ANDed together, not grouped sums. Parentheses around a product are optional for precedence clarity but should not contain sums inside a product term.

Step-by-Step Solution:Evaluate choices:(A + B)(C + D): product-of-sums (POS), not SOP.(A)B(CD): ambiguous and implies nested product of a product; not a clean OR of products.AB(CD): also a nested product (equivalent to ABCD), but there is no OR between distinct product terms.AB + CD: OR of two product terms → valid SOP.

Verification / Alternative check:Convert any ambiguous product-only expression to a single product of all included literals; SOP must include a sum (the +) at the top level.

Why Other Options Are Wrong:POS vs. SOP: (A + B)(C + D) is clearly POS.Pure products without a top-level sum are not SOP (they are single product terms).

Common Pitfalls:Confusing POS with SOP or assuming parentheses always indicate SOP. Look for a top-level + joining ANDed literal groups.

Final Answer:AB + CD