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In Boolean algebra and digital logic notation, the multiplication (× or ·) symbol corresponds to which logical operation?

Difficulty: Easy

AND
OR
NAND
NOR
None of the above

Correct Answer: AND

Explanation:

Introduction / Context:
Boolean algebra uses symbols that parallel arithmetic: addition corresponds to logical OR, and multiplication corresponds to logical AND. Understanding this mapping is essential when translating between algebraic expressions and logic gate circuits on schematics or HDL code.

Given Data / Assumptions:

We are using standard Boolean algebra conventions.
“+” means OR and “·” (or implied multiplication) means AND.
Complements are indicated by overbar or a prime (X′) to denote NOT.

Concept / Approach:
In Boolean algebra, X·Y (or simply XY) evaluates to 1 only when X=1 and Y=1, exactly matching the AND gate’s truth behavior. Addition “+” yields 1 if either input is 1, matching OR. This correspondence enables direct synthesis from algebraic formulas to gate-level implementations.

Step-by-Step Solution:

Recall truth table: AND outputs 1 only for (1,1). Map algebraic multiplication (·) to that behavior: X·Y = 1 iff X=1 and Y=1. Conclude that the times symbol denotes the AND operation.

Verification / Alternative check:
Standard logic texts and Karnaugh map derivations repeatedly use the product term (AND) nomenclature, confirming the mapping from multiplication to AND.

Why Other Options Are Wrong:

OR is denoted by “+”. NAND and NOR add inversion; they are not the basic multiplication symbol. “None” is invalid because a standard mapping exists.

Common Pitfalls:
Confusing algebraic “+” and “·” with arithmetic meanings; in Boolean algebra, they are logical OR and AND, not numeric addition/multiplication over real numbers.

In Boolean algebra and digital logic notation, the multiplication (× or ·) symbol corresponds to which logical operation?

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