Definition check: In digital logic, a “variable” denotes a symbol representing a logical quantity that can assume the value 1 or 0. Evaluate this statement.

Introduction / Context:
Precise terminology is essential in Boolean algebra and digital systems. A variable is a placeholder for a logical value that can change according to inputs, states, or time. Understanding this definition underpins work with truth tables, K-maps, and HDL descriptions.

Given Data / Assumptions:

• The logical domain is binary: {0, 1}.
• Variables may be complemented (~A) or uncomplemented (A).
• Expressions are composed using OR (+), AND (*), and NOT (~).

Concept / Approach:
A Boolean variable represents a logical quantity that can be either 0 (false/LOW) or 1 (true/HIGH). This is distinct from multi-valued logic systems (e.g., ternary or 4-state simulation), which extend beyond basic Boolean algebra typically taught in introductory courses.

Step-by-Step Solution:

Verification / Alternative check:
Truth tables treat each variable as taking 0 or 1, enumerating 2^n combinations for n variables. HDL signals in simple combinational contexts also behave as binary variables under idealized models.

Why Other Options Are Wrong:

• Incorrect: Conflicts with the standard definition in Boolean logic.
• Ambiguous as stated: The statement specifies values clearly (0 or 1).
• Cannot be determined: No further information is needed; it is definitional.

Common Pitfalls:
Conflating Boolean variables with arithmetic variables that can take many integer values. In logic, the domain is strictly binary unless otherwise noted (e.g., X/Z states in simulation models).

Final Answer:
Correct