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

Difficulty: Easy

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

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