Exclusive-OR and Exclusive-NOR Gates

The Exclusive-OR Gate

The XOR gate produces a HIGH output only when both inputs are at opposite logic levels. 


Example waveforms for XOR:

Notice that the XOR gate will produce a HIGH only when exactly one input is HIGH.


The Exclusive-NOR Gate

The XNOR gate produces a HIGH output only when both inputs are at the same logic level. 


Example waveforms for XNOR:

Notice that the XNOR gate will produce a HIGH when both inputs are the same. This makes it useful for comparison functions.


Parity Generator/Checker


System Design Applications


Additional Notes

The Exclusive-OR function is one of the most useful of the special logic functions. The Exclusive-OR is sometimes also called the "Either/OR but not Both" function. With only two inputs, the output is true if either of the inputs is true but not both of the inputs. Another way to say this is that the output is true if both of the inputs are the opposite of each other.

Although the Exclusive-OR is a special function, it is most convenient to use the Exclusive-OR in its SOP form (). Although the special symbol Å can be used to identify the Exclusive-OR, there are no rules in the Boolean Algebra to deal with this special formula. If the Exclusive-OR symbol is encountered in a Boolean Expression, it should be converted to its SOP form before any reduction process is started.