Exclusive OR & NOR gates (XOR / XNOR)
We have seen Exclusive OR gates before - XOR and XNOR gates were introduced in Module 3 (gates). As a review:
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.
Symbols:
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XOR: 
2-input XOR gate |
The mathematical symbol for XOR is a
+ inside of a circle:  |
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XNOR: 
2-input XNOR gate |
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Truth Table & Equation:
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| 2-input XOR gate ... two inputs, so 4 rows. (remember 22 = 4)
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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:
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| 2-input XNOR gate .. two inputs, so 4 rows. (remember 22 = 4)
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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!) |
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Examples:
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Parity  |
