Exclusive-NOR

Two special logic circuits that occur quite often in digital systems are the exclusive-OR and exclusive-NOR circuits. In this post, we will talk about Exclusive-NOR. [ Read about Exclusive-OR here ]

Exclusive-NOR

The circuit that produces a HiGH output whenever the two inputs are at the same level is called the Exclusive-NOR. The exclusive-NOR circuit (abbreviated XNOR) operates completely opposite to the XOR circuit.

output expression of Exclusive-NOR

Consider the logic circuit of Figure 1. The output expression of this Exclusive-NOR circuit is:

output expression of Exclusive-NOR
output expression of Exclusive-NOR

Exclusive-NOR circuit and the Exclusive-NOR truth table

In the next figure (figure 1), you see the Exclusive-OR circuit and the Exclusive-OR truth table;

figure 1: Exclusive-NOR circuit and the Exclusive-NOR truth table
figure 1: Exclusive-NOR circuit and the Exclusive-NOR truth table

XNOR gate symbol – traditional

And here is the traditional XNOR gate symbol.

figure 2: traditional XNOR gate symbol
figure 2: traditional XNOR gate symbol

The accompanying truth table shows that x = 1 for two cases: A = B = 1 (the first term of the output expression) and A = B = 0 (the second term of the output expression).

In other words: This XNOR circuit produces a HiGH output whenever the two inputs are at the same levels.

This is the exclusive-NOR circuit, which will hereafter be abbreviated XNOR.

It should be apparent that the output of the XNOR circuit is the exact inverse of the output of the XOR circuit. The traditional symbol for an
XNOR gate is obtained by simply adding a small circle at the output of the XOR symbol

shorthand way for XNOR gate output

An XNOR gate has only two inputs; there are no three-input or four-input XNOR gates.

A shorthand way that is sometimes used to indicate the XNOR output expression is:

This shorthand expression of XNOR is simply the inverse of the XOR operation.

The characteristics of an XNOR gate

The characteristics of an XNOR gate are summarized as follows:

1 ) It has only two inputs and its output is

2 ) Its output is HIGH only when the two inputs are at the same levels.

ICs containing XNOR gates

Several ICs are available that contain XNOR gates. Those listed below are quad XNOR chips containing four XNOR gates.

Each of these XNOR chips, however, has special output circuitry that limits its use to special types of applications. Very often, a logic designer will
obtain the XNOR function simply by connecting the output of an XOR to an INVERTER.

Exclusive-NOR
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