Form identification — which expression is in sum-of-products (SOP) form? Choose the option that correctly represents a sum (OR) of product (AND) terms.
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A(A + B)(C + D)
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B(AB)(CD)
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CAB(CD)
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DAB + CD
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E(A + B) + (C + D)
Answer
Correct Answer: AB + CD
Explanation
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:
Examine AB + CD: two product terms (AB) and (CD) added together ⇒ SOP.(A + B)(C + D): product of sums ⇒ POS.(AB)(CD): product of products ⇒ not SOP.AB(CD): a single product; not a sum of products.(A + B) + (C + D): sum of sums ⇒ not SOP as defined.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