NOT operation definition: If a NOT gate has input A and output X, write the correct relationship between X and A.

Introduction / Context:
The NOT gate (inverter) is the simplest logic element that flips a binary value. Accurately expressing the relationship between input and output is central to building and analyzing basic and complex digital systems, from simple oscillators to microprocessor control logic.

Given Data / Assumptions:

• Single input A, single output X.
• Binary logic levels: 0 (LOW) and 1 (HIGH).
• Standard Boolean notation where NOT means logical complement.

Concept / Approach:
By definition, an inverter outputs the complement of its input. This can be denoted several ways: X = NOT A, X = A', or X = Ā. The meaning is identical—X is 1 when A is 0, and X is 0 when A is 1.

Step-by-Step Solution:
Define X = NOT A.Truth evaluation: A=0 ⇒ X=1; A=1 ⇒ X=0.Thus the correct relationship is X = NOT A.

Verification / Alternative check:
Observe the inverter symbol on a schematic: an inversion bubble on the output depicts the NOT operation. Measuring with a logic probe will show output transitions opposite to the input transitions.

Why Other Options Are Wrong:

• X = A implies a buffer, not an inverter.
• X = 0 would mean the output is always LOW, which is not a logic gate function here.
• “none of the above” is invalid because X = NOT A is a correct and standard statement.

Common Pitfalls:

• Confusing overbar notation with subtraction or arithmetic; it strictly means complement.
• Overlooking active-LOW signal naming, which sometimes reads as a “NOT” but refers to assertion level, not necessarily an inverter in the path.

Final Answer:
X = NOT A