# Definition:Exclusive Or/Truth Table

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## Definition

The characteristic truth table of the exclusive or operator $p \oplus q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \oplus q \\ \hline \F & \F & \F \\ \F & \T & \T \\ \T & \F & \T \\ \T & \T & \F \\ \hline \end{array}$

### Matrix Form

$\begin{array}{c|cc} \oplus & \T & \F \\ \hline \T & \F & \T \\ \F & \T & \F \\ \end{array}$

### Truth Table Number

The truth table number of the exclusive or operator $p \oplus q$ is as follows:

Ascending and descending order:

$0110$ or $\F \T \T \F$