Exclusive-OR

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-OR. [ Read about exclusive-NOR here]


Exclusive-OR

The circuit that produces a HiGH output whenever the two inputs are at opposite levels is called the Exclusive-OR.
This is the exclusive-OR circuit, which will hereafter be abbreviated XOR.

output expression of Exclusive-OR

Consider the logic circuit of Figure 1 below. The output expression of this Exclusive-OR circuit is:

Exclusive-OR output expression
Exclusive-OR output expression

Exclusive-OR circuit and the Exclusive-OR truth table

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

figure 1: Exclusive-OR circuit and the Exclusive-OR truth table
figure 1: Exclusive-OR circuit and the Exclusive-OR truth table

XOR gate symbol – traditional

And here is the traditional XOR gate symbol.

figure 2: traditional XOR gate symbol
figure 2: traditional XOR gate symbol

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

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

This is the exclusive-OR circuit, which will hereafter be abbreviated XOR.
This particular combination of logic gates occurs quite often and is very useful in certain applications.

In fact, the XOR circuit has been given a symbol of its own, shown in Figure 2 above. This symbol is assumed to contain all of the logic contained in the XOR circuit and therefore has the same logic expression and truth table.

This XOR circuit is commonly referred to as an XOR gate, and we consider it as another type of logic gate.

shorthand way for XOR gate output

An XOR gate has only two inputs; there are no three-input or four-input XOR gates. A shorthand way that is sometimes used to indicate the XOR output expression is:

The characteristics of an XOR gate

The characteristics of an XOR 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 different levels.

ICs containing XOR gates

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

Exclusive-OR
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