Reading Boolean expressions: When a specification uses the word “NOT” in digital logic, what operation does it indicate?

Difficulty: Easy

Correct Answer: inversion

Explanation:


Introduction / Context:
Boolean expressions are often written in words, symbols, or a mixture of both. Interpreting the word “NOT” correctly is vital for writing and reading truth tables, understanding gate-level schematics, and converting logic requirements into equations.


Given Data / Assumptions:

  • “NOT” is the keyword under examination.
  • We consider standard Boolean algebra and digital circuit conventions.
  • Inputs and outputs take values 0 (LOW) or 1 (HIGH).


Concept / Approach:
“NOT” denotes logical inversion (complementation). If a variable is A, then NOT A is written as Ā, A̅, A', or simply NOT A, and equals 1 when A = 0, and 0 when A = 1. Physically, this is implemented by an inverter gate.


Step-by-Step Reasoning:
Define A ∈ {0,1}.Apply inversion: X = NOT A.Truth: if A=0 ⇒ X=1; if A=1 ⇒ X=0.Therefore, “NOT” means inversion (logical complement).


Verification / Alternative check:
On schematics, an inversion bubble on a gate input or output represents NOT. On timing diagrams, inversion flips HIGH/LOW levels and toggles edge sensitivity where applicable.



Why Other Options Are Wrong:

  • “the same as”: opposite of inversion.
  • “high” or “low”: these are signal levels, not operations. NOT may produce either level depending on the input.


Common Pitfalls:

  • Confusing active-LOW signals (indicated by a bar or a “/” prefix) with normal signals; active-LOW means the function is asserted when the signal is 0, which is a design choice, not a different operation.


Final Answer:
inversion

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