# Exclusive NOR/X-NOR gate(Equality detector)

Page Contents

## Introduction

The NOTed X-OR is called X-NOR gate.

X-NOR is a two input one output digital circuit. It produces a HIGH output all of its inputs either LOW or HIGH.

It produces a LOW output when one of its inputs is HIGH and other is LOW.

The output is HIGH when inputs are equal so it is called equality detector.

The symbol of X-nor operation is $\odot$

Three input X-NOR gate doesn’t exist. When more than two inputs are to be X-NORed, a number of two input X-NOR gates are used.

The output of X-NOR gate is HIGH when the even number of inputs are HIGH. So it is called as an even function.

#### Equivalent circuit of X-NOR gate:

The expression for X-NOR gate is $X=A\odot&space;B=AB+\overline{A}.\overline{B}$. So the equivalent circuit can be:

#### X-NOR gate as an inverter:

X-NOR gate can be used as an INVERTER.

When we keep one input constant zero and vary another one it will act as an INVERTER.

In that case, when the variable input is LOW:

$0\odot0=0.0+\overline{0}.\overline{0}$

= 0+1.1

= 1

When the variable input is HIGH:

$0\odot1=0.1+\overline{0}.\overline{1}$

= 0 + 0

=0

Please write in the comment box below if you have any questions.