I would think that you will at least need to know how to create some perceptron.
If you don't find the textbook clear, check wikipedia. Although it seems many of the stuff regarding AI is directly taken out of it.
Think of the neuron as a trigger. You give it's bias weight/threshold a value. And then you give the input weights values. When these inputs trigger they will or will not "trip" the threshold, ie be greater than it. If it is then the neuron "fires". So if you look at those simple binary ones:
AND has two inputs with weights of 1 and the bias weight of 1.5.
If only one input fires:
1 < 1.5 doesn't fire.
if both inputs fire:
1 + 1 > 1.5 the neuron fires. Thus AND has happened.
Now look at the Summed Weights part and see if that makes sense. Think of what will happen if you link a bunch of these together.
Hope this helps a bit.