Redstone circuits/Piston

Why Pistons?
Simply, pistons do not fizzle out like redstone torches so it is possible to create cuircuits with only pistons, wire and repeaters as these can run at 1/3 of the speed.

The Principle
Power is transmitted in several ways which are useful to pistons. The first thing to note are two types of solid block, transparent and opaque. This has nothing to do with your texture pack. Transparent blocks are like glass. most blocks are opaque. if a block is on top of a redstone torch, any wire connected to it will be powered. if, however, the block is transparent, the torch will not power the wires.

when a repeater is directed at a block, it will pass power into that block just like the torch does when it is below. power will not be transmitted with transparent blocks. There is another related detail:

The two above will work however

will not work = Simple logic gates =

if you don't understand these, look at Redstone circuits

NOT Gate
The torch on the left is the input. The piston is sticky and the output is on the right and could be reversed.

OR Gate
The three wires at the top are the input, you can have any number of them. the wire at the bottom is the output and can come from any direction. again the piston is sticky

AND Gate
Note that the piston is again a sticky one. if you are atatching one input to a clock, i would suggest the top one as it will be faster and reduce noise

Multiple input AND gate Note that all the blocks along the top are inputs

IMPLIES Gate
This is equivalent to an and gate with one of the inputs inverted and is faster with pistons.

XOR Gate
This one is superb, it is far far smaller and more efficient than the redstone equivalent It does, however rely on pistons so it is = More Complex Gates =