BOOLEAN ALGEBRA

BOOLEAN ALGEBRA

A digital computer is made up of various types of simple circuits arranged and grouped according to the rules of symbolic logic. Logic is the science that establishes the validity of thought or reason. As a result of which what is true in one statement will be true in all equivalent statements Gottfried W. Leibnitz (1646 -1716) was the first who tried to develop a general method in which all truths of reason would be reduced to a kind of calculation. But the founder of symbolic logic was George Boole (1806 - 1876) who gave the world a form of mathematical logic now known as Boolean algebra. The significance of these developments was not realized at that time. Boolean algebra find its application to problems in the form of staements having answers either ture or false. It was the binary nature of these true/false problems which linked it with computer developments. The fundamental and simple ideas of logic outlined by Boole and his preducessors provide the foundation for many of the circuit applications in digital computer. But logical design is not limited to this area alone. The same principles have a direct bearing on and an increasing importance in control circuits for other electronic devices, such as digital watches, microwave oven, automatic cameras and instruments used for automatic control of manufacturing processor.

Blooean algebra like any algebra uses algebraic notation to express logical relationship in the same way that ordinary algebra is used to express mathematical relationships. In ordinary algebra an expression such as

x + y = a

consists of variables x, y and a which take numbers as values and symbols for mathematical operations such as (+) for addition. In Boolean algebra the same types of expression used are represented by set of elemetns, a set of operators and a set of rules satisfied by these two logical operators.

Since all electronic devices circuits have two discrete states ON and OFF. therefore we deal with two valued Boolean algebra.

A two valued Boolean algebra has a set with only two elements 0 and 1. A two valued Boolean algebra is also called switching algebra or binary logic. In our subsequent discussion we shall use Boolean algebra for two valued Boolean algebra.

ELEMENTS OF BOOLEAN ALGEBRA

In Boolean algebra an expression is constituted using constants and variables. Boolean Constants, Boolean variables.

continue..ELEMENTS OF BOOLEAN ALGEBRA