This is for you.
Make sure to select "Source code" when you get there, otherwise it will be quite boring.
Here is an animated gif which shows the program in action.
See BELOW for the WHOLE screenshot so that you don't have to speed read.
If you want to know how it works, then you will have to go back and read part 1 to 6.
But as you can see from the example above:
Before the neural network is trained, the outputs are not even close to the expected outputs. After training, the neural network produces the desired results (or very close to it).
Please note, this neural network also allows more than one output neuron, so you are not limited to single yes no decisions. You can use this neural network to make classifications. You will soon see this with my LED colour sensor.
Feel free to use this Neural Network in your own projects, but please let me know if you do, just for curiosity sake.
Update: See below for the Processing Sketch (much easier than going to the open processing site). It is a bit long - but saves you from having to navigate to another site.