OKAY... THIS IS SOMETHING I KNOW REALLY WELL ;).
okay here :),
here are the two states;
1. a low state, witch is basically phisical ground, a binary 0, 0V.
2. a high state, witch is also basic, a phisial scource, a binary 1, common to be 5V.
here are the logic gates;
BUFFER, output is input
NOT gate/INVERTER, output is opposite to input,
AND gate, output is high when all inputs are high,
XOR gate, output is high when ONLY an odd number of inputs are true, also known as if and only if,
XNOR gate, negatave output to a XOR gate, XOR gates output attached to a NOT gate, output is true ONLY if an even number of inputs are true,
universal gates (the ONLY gates that can make any other gate just by using them);
NAND gate, negatave output to the AND gate, AND gate with its output attached to a NOT gate, output is high unless all inputs are high,
NOR gate, negatave output to the OR gate, OR gate with its output attached to a NOT gate, output is high whenever no input is high.
there we go, and klick this link if you want to know the symbols of the opporations and boolean algebera: http://en.wikipedia.org/wiki/Boolean_algebra