Boolean complement rule: Evaluate the statement: “In Boolean algebra, the complement of 1 is 0.” Support your answer with truth-level reasoning.
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ACorrect
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BIncorrect
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COnly true in active-LOW systems
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DNot enough information is provided
Answer
Correct Answer: Correct
Explanation
Introduction / Context:Complements are fundamental in Boolean algebra and digital logic. The complement (logical NOT) flips a truth value: what is true becomes false and vice versa. This concept is directly realized in hardware by inverters.
Given Data / Assumptions:
- Binary logic levels: 0 and 1 represent false and true, respectively.
- NOT operation: produces the complement of its input.
- Positive logic is assumed (1 = TRUE, 0 = FALSE).
Concept / Approach:By the definition of complement in Boolean algebra, NOT(1) = 0 and NOT(0) = 1. This identity underlies De Morgan’s laws, inverter gates, and expressions using overbars or primes.
Step-by-Step Solution:
Start with input 1 (TRUE).Apply NOT → output becomes 0 (FALSE).Therefore, the complement of 1 is 0.Verification / Alternative check:Truth table of an inverter: input 0 → output 1; input 1 → output 0. The mapping is unambiguous.
Why Other Options Are Wrong:
Incorrect: Contradicts Boolean definition.Only true in active-LOW systems: Active-LOW changes naming conventions, not the algebraic NOT operation.Not enough information: The rule is universal in Boolean algebra.Common Pitfalls:Confusing logic polarity (active-HIGH/LOW) with the meaning of NOT; assuming electrical inversion always implies voltage inversion rather than logic inversion.
Final Answer:Correct