First off, the XOR gate! XOR is short for "exclusive OR". It has two inputs. If one of the two inputs is triggered, the output is triggered, but if both inputs are triggered at once, the output is off. You can think of it as "one thing or the other, but not both at once."
Then, of course, we have the inverse version of the XOR gate: the XNOR gate. As always, it functions the same way as the XOR gate, but the "on" and "off" states for the output are reversed.
Moving on, let's go over clocks! A clock (or clock generator) is, at its simplest, a circuit that constantly toggles between an on/off state. They can be very fast or slow, depending on the design used. They can be based on torches, pistons, redstone repeaters, among other things.
I'll just be going over a couple of simple designs to start with.
The rapid pulser (or possibly pulsar - I'm afraid the info is a bit inconsistent on this one) or 1-clock is very fast. It's so fast that the redstone torches burn out, but the redundancy allows the clock to remain functional.It's fast enough that trying to use it for something like pushing a column of sand or gravel will result in some of the blocks "popping" and dropping on the ground.
Here's a video illustration of just how quickly it goes!
The 5-Clock is a slower, stabler design. It still goes at a decent pace, but it's slow enough that the torches don't burn out.Clocks can be made faster or slower by adding more or less pairs of torches.
I'll come back to clocks at a later date - they can apparently be made much simpler using repeaters, but I think these illustrate the ideas better. (And I'm having trouble getting repeaters to actually function right now.)
The XOr gate design is lenghtly and not compact at all. Instead, you can utilize secondary power to have the same idea, vertically, so the gate will fit within a 3 by 3 by 3 space. Within a 3 by 3 by 3 space, you can build at least 3 differently structured types of XOr gates that I know of
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