Logical XOR

Resource type: this resource is a lesson.

Welcome! This is a lesson in the Introductory Discrete Mathematics for Computer Science course here at Wikiversity.

Previous lesson: Logical OR

Introducing the Exclusive OR!

$\oplus$ : This is the XOR operator. It is also called the exclusive OR, to distinguish it from the inclusive OR of the previous lesson. Like the inclusive OR, it is a diadic operator; unlike any other operator, it is true when one and only one input is true.

Let

p

represent the statement: It is raining.

Let

q

represent the statement: I am hungry.

p \oplus q

represents the exclusive disjunction of statements

p

and

q

: It is raining OR I am hungry, But not both.

Truth Table

Its truth table is unique. Here it is!

$p \,\!$	$q \,\!$	$p \oplus q$
T	T	F
T	F	T
F	T	T
F	F	F

Why XOR is Special

XOR is used for adding binary numbers, and is the fundamental arithmetic operation used by computers.

Next Lesson

Your next lesson is called Conditional Operator.

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