The binary 0 and 1 states are naturally related to the true and false
logic variables.
We will find the following Boolean algebra useful.
Consider two logic variables *A* and *B* and the result of some Boolean
logic operation *Q*.
We can define

*Q* is true if and only if *A* is true AND *B* is true.

*Q* is true if *A* is true OR *B* is true.

*Q* is true if *A* is false.

A useful way of displaying the results of a Boolean operation is with
a truth table.
We will make extensive use of truth tables later.
If no ``-'' is available on your text processor or circuit
drawing program an ``*N*'' can be used, ie. .

We list a few trivial Boolean rules in table 7.2.

**Table 7.2:** Properties of Boolean Operations.

The Boolean operations obey the usual commutative, distributive and associative rules of normal algebra (table 7.3).

**Table 7.3:** Boolean commutative, distributive and
associative rules.

We will also make extensive use of De Morgan's theorems (table 7.4).

**Table 7.4:** De Morgan's theorems.

Tue Jul 13 16:55:15 EDT 1999