You've probably heard that all computers really understand is 1s and 0s. But how are those 1s and 0s made so useful?
The answer is the use of logic gates. Just like gates in real life, logic gates are something binary numbers pass through. However, when the 1s and 0s pass through these gates, they are judged according to set rules. A bit (binary digit) may go in a 1, but it might wind up as a 0, or remain a 1, depending on the rules applied.
The 3 most basic operations performed on bits are NOT, AND and OR. These sound complex, but are fairly easy to understand. However, since I like to make mathematical concepts fun, here's an excellent example of these logic processes in action, through the use of dominoes and marbles:
As noted in the wikipedia article on logic gates, there are additional operations referred to as NAND (NOT + AND), NOR (NOT +OR), XOR (Exclusive OR), and XNOR (NOT + Exclusive OR), but we'll save discussion of these for another time.
A good way to learn about the logic gates more directly would be to build some yourself. If you're a hands-on type, you might like to do this by printing out and building these AND, NOT and OR logic goats. The finished AND and OR logic goats are demonstrated below (including their internal workings):
However, if you'd like to play with logic gates more directly, and figure out what you can do with them, I highly recommend playing with Logicly, a free logic gate simulator that runs in your browser.
It's amazing to think that just 2 digits and a few simple rules about how to process those digits are responsible for the awesome power of computers, but hopefully this will help bring a little more understanding, and thus a little more computer power, into your hands.