XOR notation in Boolean algebra: Assess the statement: “The exclusive-OR operation is denoted by a plus sign with a circle around it in Boolean equations.”
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ACorrect
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BIncorrect
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COnly valid in arithmetic sum-of-products, not logic
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DNot enough information is provided
Answer
Correct Answer: Correct
Explanation
Introduction / Context:In symbolic logic and digital design, standard operators use consistent notation across textbooks and datasheets. The exclusive-OR function (XOR) has a distinctive symbol to distinguish it from ordinary OR. Recognizing the correct symbol avoids ambiguity in equations and schematics.
Given Data / Assumptions:
- Standard Boolean operators: + for OR, · for AND, overbar or prime for NOT.
- XOR has a special symbol to avoid confusion with inclusive OR.
- We assume positive logic conventions.
Concept / Approach:The common notation for XOR is a plus inside a small circle, read as “circle plus,” often written as ⊕. In ASCII text, authors may write “XOR” or use the caret ^ symbol, but the circle-plus is the canonical printed symbol in Boolean algebra.
Step-by-Step Solution:
Identify the operator in question: exclusive-OR.Recall canonical symbol: ⊕ (circle-plus).Conclude that the statement is accurate.Verification / Alternative check:Check a typical identity: A ⊕ B = ĀB + AB̄. Here ⊕ is the circle-plus notation, confirming the standard usage.
Why Other Options Are Wrong:
Incorrect: Conflicts with well-established notation.Only valid in arithmetic SOP: The symbol is general for logic, not limited to any form.Not enough information: Symbol conventions are widely standardized.Common Pitfalls:Confusing XOR with OR (+) or with plus in arithmetic; misreading symbols in low-resolution prints.
Final Answer:Correct