Form classification in logic design: Which of the following Boolean expressions is in sum-of-products (SOP) form, meaning an OR of AND terms?

Introduction / Context:
Recognizing SOP form is useful because it directly maps to AND gates feeding an OR gate, or to NAND–NAND structures via DeMorgan's transformations. Many minimization techniques such as Karnaugh maps naturally produce SOP results for straightforward implementation.

Given Data / Assumptions:

• SOP = sum (OR) of product (AND) terms.
• POS = product (AND) of sum (OR) terms.
• Concatenation implies AND, + implies OR.

Concept / Approach:
To decide whether an expression is SOP, check that the outermost operator is addition (OR) and that each term being added is a product of literals (possibly with complements). If so, the expression is SOP. If the outermost operator is multiplication of sums, it is POS instead.

Step-by-Step Solution:
Option a: (A + B)(C + D) is an AND of two sums → POS, not SOP.Option b: AB + CD is an OR of two product terms → SOP.Option c: (A + B + C) is just one sum term → neither SOP nor POS canonical form.Option d: A(B + C) is mixed and not expanded; in expanded form it becomes AB + AC (which would be SOP), but as written it is not in SOP form.

Verification / Alternative check:
Expanding option d gives AB + AC, confirming that SOP indeed looks like an OR of products, as in option b.

Why Other Options Are Wrong:
(A + B)(C + D): POS structure.(A + B + C): only a sum, no product terms.A(B + C): not in finalized SOP until distributed.

Common Pitfalls:
Confusing unexpanded factored forms with SOP. Always ensure each added term is a product, not a sum or mixed factor, to qualify as SOP.

Final Answer:
Y = AB + CD