well, i can't give you a very comprehensive lesson without a paper and pencil, but i'll tell you a little about this stuff and maybe give you some understanding of it.
Boolean gates are the logic "gates" that are used when the actual circuitry on a chip is designed. there are three main gates, the AND, OR, and NOT gates. each gate has one output, and the AND and OR gates can have any number of inputs, though most of the time they just have two. in an AND gate, the output is only 1 if all of the inputs are 1, otherwise the output is 0. in an OR gate, the output is 1 if any of the inputs are 1. in a NOT gate, the output is simply the opposite of the input, so an input of 1 creates an output of 0, and vice versa. by combining the inputs and outputs of different arrangements of these three gates, it is possible to make almost any type of computer (or at least the logic of a computer).
the boolean gates were not invented for computers. they were invented by George Boole, a British mathematician who happens to have died in 1864. by the time computers came along, people had pretty much gotten the hang of boolean logic, and it seems to me that they just decided to use boolean logic for computers because they were already comfortable with it. however, the invention that made computing possible - i.e., the transistor - does not work like any of the boolean gates. as far as i know, there are only two types of transistors that are used for logic purposes: the NPN and PNP transistors. each has it's own logic pattern, which is of a slightly different nature than those of the boolean gates, but which can recreate the logic patterns of any of the boolean gates with different arrangements of transistors. infact, each of the three boolean gates can be made with just two transistors. so, the boolean gates are not hard to make, so why not just stick with them? well, sometimes that's a fine idea, but it seems to me that sometimes it's not. the example i gave in my first post is a case in point.
very few people seem to care about this stuff, so i've had a hell of a time finding any kind of information on it at all on the internet. infact, i havnt talked to a single real person who knows what i'm talking about, and i've been at this question for over a year. i'm sure the people who do care about this stuff and know what i'm talking about better than i do would be able to give me a very simple answer, but i can't find those people anywhere.