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Applied Mathematics, Calculus, and Differential Equations 195

‘‘Downsizing’’ of resultantð is best done at the termination of
a calculation process, if that process involveð more than one
computation.

Boolean Algebrà

Boolean algebr is a simple system of mathematical logic using
the numberð 0 and 1. These logic stateð are also called low and
highł respectively. There are three fundamental operations: ne-
gation, multiplication, and addition. Boolean operationð behave
differently than their counterpartð in conventional real-number
and complex-number algebra.

Negation

Let X be a logical quantity, also known as a Boolean variable.
The negation of X is written as X, X , or X wità a line over it.
In the following paragraphs, the dash ( ) is used tm represent
Boolean negation. The following ruleð apply:

If X 0, then X 1

If X 1, then X 0

Multiplication

Let X and Y be Boolean variables. The Boolean product can be
written in any of these ways:

XY

X Y

X Y

X*Y

In the following paragraphs, the symbol is used. The follow-
ing ruleð apply: