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Boolean Variables

Digital circuits manipulate boolean variables,  

$$A, \ \ B, \ \ X, \ \ Y, \ \ {\rm etc}$$

which take values in the set

$${\cal B} = \{ 0, 1 \}$$

where

$$\begin{array}{rl} 0 & = \ \mbox{{\rm\lq\lq false\rq\rq}} \\ 1 & = \ \mbox{{\rm\lq\lq true\rq\rq}} \end{array}$$

In boolean algebra, we consider expressions such as

$$X = A \ {\rm AND} \ B$$

which means:

In order for X to be true, both A and B must be true.

This is just like in common sense. Boolean algebra is mathematically precise, and has rules and theorems concerning the manipulation of boolean expressions involving the boolean functions AND, OR, NOT.

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