OR vs EX-OR vs EX-NOR Logic Gates: A Comparison

This article explores the differences between OR, EX-OR (XOR), and EX-NOR logic gates, including their truth tables and logic symbols.

OR Logic Gate

The OR gate is a fundamental electronic circuit. It produces a “true” or high output (represented by 1) if one or more of its inputs are true. The OR operation is often represented by a plus sign (+).

OR Gate Symbol and Truth Table

Figure: OR gate logic symbol

The following truth table summarizes the behavior of the OR gate:

Table: OR gate truth table

In essence, the output $Output$ of an OR gate with inputs $Input_1$ and $Input_2$ can be represented as:

$Output = Input_1 + Input_2$

EX-OR (XOR) Logic Gate

The Exclusive-OR (EX-OR or XOR) gate is a circuit that outputs “true” only if exactly one of its two inputs is true. If both inputs are true, or both are false, the output is false. The EX-OR operation is denoted by an encircled plus sign (⊕).

EX-OR Gate Symbol and Truth Table

Figure: EX-OR gate logic symbol

Here’s the truth table for the EX-OR gate:

Table: EX-OR gate truth table

Mathematically, the EX-OR operation can be described as:

$Output = Input_1 \oplus Input_2$

EX-NOR Logic Gate

The Exclusive-NOR (EX-NOR) gate is the inverse of the EX-OR gate. It outputs “true” if both inputs are the same (either both true or both false), and “false” if the inputs are different. The EX-NOR symbol is an EX-OR gate with a small circle at the output, indicating inversion.

EX-NOR Gate Symbol and Truth Table

Figure: EX-NOR gate logic symbol

The EX-NOR gate’s truth table is as follows:

Table: EX-NOR gate truth table

The EX-NOR operation can be represented as:

$Output = \overline{Input_1 \oplus Input_2}$

This indicates that the output is the inverse (or complement) of the EX-OR operation.