Form identification — which expression is in sum-of-products (SOP) form? Choose the option that correctly represents a sum (OR) of product (AND) terms.

Introduction / Context:Recognizing canonical forms helps in mapping logic to gates or programmable devices. In sum-of-products (SOP), we OR together multiple product terms; in product-of-sums (POS), we AND together multiple sum terms. Identifying SOP vs POS at a glance is a key skill for logic design and optimization.

Given Data / Assumptions:

• '+' means OR, adjacency (e.g., AB) means AND.
• Products are ANDed literals (possibly complemented), sums are ORs of literals.

Concept / Approach:An SOP expression has the structure term1 + term2 + … where each term is a product of literals (e.g., AB, A'B'C). By contrast, POS has the structure (sum1)(sum2)…, where each sum is in parentheses with ORs inside. Complex nestings can be re-expressed, but here we focus on surface form.

Step-by-Step Solution:

Verification / Alternative check:To implement AB + CD in gates: two AND gates feeding a single OR gate, which is the typical SOP structure. This confirms its classification as SOP.

Why Other Options Are Wrong:

• (A + B)(C + D): POS, not SOP.
• (AB)(CD): lacks the final OR; that is an AND of products.
• AB(CD): single product term only.
• (A + B) + (C + D): no product terms; sums being ORed.

Common Pitfalls:

• Confusing internal vs external operators; in SOP the outermost operator is OR.

Final Answer:AB + CD