Form identification (SOP vs. others): Determine whether the Boolean expression A'B + AB' is in sum-of-products (SOP) form. Justify your classification.
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ACorrect
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BIncorrect
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CIt is product-of-sums (POS), not SOP
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DIt is neither SOP nor POS
Answer
Correct Answer: Correct
Explanation
Introduction / Context:Being able to recognize canonical forms accelerates simplification and hardware mapping. SOP (sum-of-products) means an OR (sum) of one or more product terms, where each product term is an AND of literals (variables or their complements).
Given Data / Assumptions:
- Expression: F = A'B + AB'.
- Literal is a variable or its complement (e.g., A or A').
- Product term is a logical AND of literals; sum is a logical OR of product terms.
Concept / Approach:Check each term: A'B is a product (A' AND B). AB' is also a product (A AND B'). The entire expression is the sum (OR) of these two products. Therefore it fits SOP.
Step-by-Step Solution:
Identify product terms: P1 = A'B; P2 = AB'.Identify the outer operator: OR, combining P1 and P2.Conclude: F = P1 + P2 is in SOP form.Verification / Alternative check:Attempt POS recognition: POS requires a product (AND) of sum terms like (A + B)(A' + B'); our expression does not match that template, confirming SOP classification.
Why Other Options Are Wrong:
Incorrect: The structure clearly matches SOP.It is POS: Incorrect operator ordering.Neither SOP nor POS: It is a standard SOP example (an XOR-like form).Common Pitfalls:Confusing SOP with POS; overlooking that literals can be complemented and still be part of valid product terms; assuming canonical form must include all variables in every term (not required for non-canonical SOP).
Final Answer:Correct