Digital Fundamentals

Digital Logic - XOR & XNOR gate

Input & Output

A XOR gate (eXclusive-OR gate) has two (or more) inputs and one output.

The XOR gate is sometimes called the difference gate - if the inputs are different, the output is 1; if the inputs are the same, the output is 0.

The XNOR (eXclusive-NOR) is sometimes called the equivalence gate - the output is 1 if the inputs are the same, 0 if they are different (the inverse of the XOR).

In theory, an XOR or XNOR gate can have any number of inputs (as long as it has at least two). In practice, we usually use 2-input XOR & XNOR gates.

Symbol:

XOR: 2-input XOR gate The mathematical symbol for XOR is a + inside of a circle:

XNOR: 2-input XNOR gate

Truth Table & Equation:

2-input XOR gate
... two inputs, so 4 rows. (remember 2² = 4)

input output

A B C

0 0 0

0 1 1

1 0 1

1 1 0

Equation: the equation can be written as shown: there will be many times we use techniques to find equations for a circuit. XOR symbols are rarely used in practice; instead, the 2nd equation is typically used:

2-input XNOR gate
.. two inputs, so 4 rows. (remember 2² = 4)

input output

A B C

0 0 1

0 1 0

1 0 0

1 1 1

Equation: the equation can be written as shown: there will be many times we use techniques to find equations for a circuit. XNOR symbols are rarely used in practice; instead, the 2nd equation is typically used:

(note: there is a separate line over each letter A and B in the 2nd equation - not one solid line over both!)

Examples:

2nd module home

next:
Truth Tables, Part II