LoGates is a game, where you can start learning the basics of binary operations. Most of your favourite logic gates are here: And, Or, Xor, Not.
Try out the different buttons (easy mode, hard mode, help/about, continue) and let's start. When you start playing (either easy or hard) you are given a closed box. Touching the switches results in turning the lights on the other side of the box ON/OFF. Every box has a certain pattern, which you, the player, has to figure out.
With the button in the bottom left corner you can switch to an empty one, so you can start building. The different gates behave differently, but connecting together using wires (just press one "bump" on a gate and release it onto a different kind of "bump", the succesfull connection is shown with a line of moving dots) results in an even more complicated behaviour.
The goal is to make your box behave like the closed one.
WARNING: The ability to win the game lies in the basic understandig of logic gates and binary operations. And even then it may be insanely hard to solve. Just saying.