

AND Function
As both inputs (X1 and X2) are connected to the same neuron the connections must be the same, in this case 1. To model the AND function the threshold on Y is set to 2.
OR Function
This is almost identical to the AND function except the connections are set to 2 and the threshold on Y is also set to 2.
AND NOT Function
Although the truth table for the AND NOT function is shown above it deserves just a small explanation as it is not often seen in the textbooks. The function is not symmetric in that an input of 1,0 is treated differently to an input of 0,1. As you can see from the truth table the only time true (value of one) is returned is when the first input is true and the second input is false.
Again, the threshold on Y is set to 2 and if you apply each of the inputs to the AND NOT network you will find that we have modeled X1 AND NOT X2.
XOR Function
XOR can be modeled using AND NOT and OR;
X1 XOR X2 = (X1 AND NOT X2) OR (X2 AND NOT X1)
(To prove it draw the truth table)
This explains the network shown above. The first layer performs the two AND NOT's and the second layer performs the OR. Both Z neurons and the Y neuron have a threshold of 2.
As a final example of a McCulloch-Pitts network we will consider how to model the phenomenon that if you touch something very cold you initially perceive heat. Only after you have left your hand on the cold source for a while do you perceive cold. This example (from Fausett, 1994) is an elaboration of one originally presented by (McCulloch and Pitts, 1943).
To model this we will assume that time is discrete. If cold is applied for one time step then heat will be perceived. If a cold stimulus is applied for two time steps then cold will be perceived. If heat is applied then we should perceive heat.
Senin, 18 April 2011
Model McP untuk Fungsi Logika
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