A simple neural network for parity problem using 4 bitwise inputs and outputs, the network is trying to identify the parity problem, that is, if there are odd number of 1 bits the output is 1 and 0 elsewhere. All activation functions are sigmoid, and matrix are used with numpy library in order to speed the calculations.
Please note that this a terrible network, and it usually gets stuck in local minimas even learning rate is very small. This could help you understand what neural networks do if you ever want to implement them yourself. Otherwise, please save yourself from the burder of wasted hours in pointless training sessions for this example.
I tried to write it as readable as possible. Hope it helps!