Exclusive-OR

Last updated on April 22nd, 2022 at 08:41 am

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]

Table Of Contents

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 circuit and the Exclusive-OR truth table

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

XOR gate symbol – traditional

And here is the 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: