3.1 Boolean Variables & Truth Tables

Boolean algebra differs in a major way from ordinary algebra in that Boolean constants and variables are allowed to have only two possible values, 0 or 1.
Boolean 0 and 1 do not represent actual numbers but instead represent the state of a voltage variable, or what is called its logic level.

Some common representation of 0 and 1 is shown in the following diagram.

Logic 0	Logic 1
False	True
Off	On
Low	High
No	Yes
Open Switch	Close Switch

In Boolean algebra, there are three basic logic operations:
OR, AND and NOT.
These logic gates are digital circuits constructed from diodes, transistors, and resistors connected in such a way that the circuit output is the result of a basic logic operation (OR, AND, NOT) performed on the inputs.

Gate Delay

Real gates have delay. In other words, if you change the value of the inputs, say from 0 and 0 to 0 and 1, then the output takes some small amount of time before it changes. This delay is called gate delay.

This delay is due to the fact that information can travel at most, the speed of light, and in reality, the time it takes to do the computation is not infinitely quick.

This delay limits how fast the inputs can change and yet the output have meaningful values. It also allows certain kinds of circuits to be created that don't follow the rules from the previous section. In particular, flip flops (to be discussed later) can be generated from gates that use cycles.

 Truth Table

A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

In the following two-inputs logic circuit, the table lists all possible combinations of logic levels present at inputs A and B along with the corresponding output level X.

                      

When either input A OR B is 1, the output X is 1. Therefore the "?" in the box is an OR gate.