If you'll think back to discrete math, you'll remember that the fundamentals of logical circuits themselves are the basic logic gates.
The first thing we have to establish is this: we're going to be working with logical circuits in a very hands-on way. The long and the short of it is- you can model most all logical circuits in Minecraft, so effectively, whatever you can model with logic gates on paper (i.e. AND, OR, NOR, Adders, etc.) can be modeled in Minecraft as well.
This section will be serve two purposes. We'll have recaps on the functions of the basic gates, along with quick and easy ways to build these gates in Minecraft. If you're totally comfortable with logic gates, feel free to skip the background information and check out the schematics right off the bat.