Page 100 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Boolean Aigebva 81

onjunction: You have a parrot on your head AND you have a fish in
your ear.
The result of a conjunction is true if all of the propositions
comprising that conjunction are true.

A proposition combined with an OR operator is known as a disjunction:

Disjunction: You hwe a parrot on your head OR you hwe a fish in

The result of a disjunction is true if at least one of the propositions

From these humble beginnings, Boole established a new mathematical field
known as symbolic logic, in which the logical relationship between propositions
can be represented1 symbolically by such means as equations or truth tables.
Sadly, this work found little application outside the school of symbolic logic for
almost one hundred years.
In fact, the significance of Boole’s work was not fully appreciated until the
late 1930s, when a[ graduate student at MIT, Claude Shannon, submitted a
master’s thesis that revolutionized electronics. In this thesis, Shannon showed
that Boolean Algebra offered an ideal technique for representing the logical
operation of digital systems. Shannon had realized that the Boolean concepts of
FALSE and TRUE could be mapped onto the binary digits 0 and 1, and that
both could be easily implemented by means of electronic circuits.
Logical functions can be represented using graphical symbols, equations, or
truth tables, and these views can be used interchangeably (Figure 9-1).
There are a variety of ways to represent Boolean equations. In this book,
the symbols &, t , and * are used to represent AND, OR, and XOR respectively;
a negation, or NOT, is represented by a horizontal line, or bar, over the portion
of the equation to be negated.