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5.0 THE EXCLUSIVE GATES

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The final 2 gates remaining are the XOR (eXclusive OR) and

XNOR (eXclusive NOR) gates. Here they are.


5.1 THE XOR GATE

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The logic behind this gate is that if either A or B is equal

to 1 but not both then the output is equal to 1, here is its

truth table.



 A B | Q

 -------+------

 0 0 | 0

 0 1 | 1

 1 0 | 1

 1 1 | 0



The gate is constructed as follows.



 (A & ~B) | (~A & B)



 (0 & ~0) | (~0 & 0) = 0

 (0 & ~1) | (~0 & 1) = 1

 (1 & ~0) | (~1 & 0) = 1

 (1 & ~1) | (~1 & 1) = 0



5.2 THE XNOR GATE

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The XNOR gate is simply the opposite of the XOR gate, its truth

table looks like the following.



 A B | Q

 -------+------

 0 0 | 1

 0 1 | 0

 1 0 | 0

 1 1 | 1





Its kind of like ~((A & ~B) | (~A & B)).



This is a good time to point out something about boolean algebra,

remember that ~ changes the value of an input to its opposite,

therefore ~(~A) = A and the 2 ~'s simply cancel eachother out.



So XNOR becomes (~A & B) | (A & ~B).