Operator precedence in Boolean algebra (digital logic): In a mixed Boolean expression that contains both AND and OR operators, evaluation follows the standard precedence where all AND operations are performed before any OR operations, unless explicit parentheses override the order. Decide whether this precedence rule is stated correctly.

Introduction / Context: Understanding operator precedence in Boolean algebra is essential for correctly reading, simplifying, and implementing digital logic expressions in hardware or HDL code. Just as arithmetic uses multiplication before addition, Boolean algebra relies on a standard evaluation order so that the same expression means the same thing to everyone unless parentheses specify a different grouping.

Given Data / Assumptions:

• Expressions contain AND (·) and OR (+) operators, and possibly NOT (inversion) as well.
• No parentheses are present unless explicitly stated.
• We are discussing algebraic/functional interpretation, not transient hardware timing effects.

Concept / Approach: The conventional precedence in Boolean algebra is: NOT (inversion) first, then AND, then OR. This mirrors arithmetic where unary operators bind most tightly, multiplication/division follow, and addition/subtraction come last. Parentheses always take highest priority and can be used to change the default order when needed for clarity or design intent.

Step-by-Step Solution:

Verification / Alternative check: Evaluate a test expression both ways. For inputs A=0, B=1, C=1: A + B·C → 0 + (1·1) = 1; (A + B)·C → (0 + 1)·1 = 1. For different inputs, the two forms can differ, proving why precedence and parentheses matter and confirming the default rule.

Why Other Options Are Wrong: “Incorrect” contradicts the standard rule. “Depends on propagation delay only” confuses algebraic precedence with hardware timing. “True only for arithmetic” is irrelevant; the rule applies to Boolean algebra specifically.

Common Pitfalls: Ignoring inversion precedence; assuming left-to-right evaluation without rules; forgetting to use parentheses when deviating from the default order.

Final Answer: Correct