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Setting the weights for a neural network

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Adjust the weights and threshold values in the artificial neuron network in Figure 10th edition: 11.18; 9th edition: 10.19 so that its output is 1 when both inputs are the same (both 0 or both 1) and 0 when the inputs are different (one being 0 while the other is 1).

book:
Glenn Brookshear, Computer Science: an overview (Tenth Edition-2008), Addison Wesley/Pearson, World: ISBN: 0-321-54428-5, ISBN 13: 978-0-321-54428-5/US: ISBN: 0321524039, ISBN 13: 9780321524034

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Solution Summary

This solution explains how to set the weights for neural network to implement an XNOR function.

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The goal is to create a network that generates a 1 when both outputs are 0 or 1 and a 0 otherwise. We can adjust the weights and the threshold values of each layer in the network to make these changes.

First we will define our terms and the equations.

We can call the inputs i1 and i2. The weights in the first network layer we will call w11 and w12. The threshold for level one we will call t1. The output from layer 1 we will call o1. Similarly for the second layer we will have w21, w22, w23, t2, and o2.

o1 is defined to be 1 if the weighted sum of the inputs is ...

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