1.

Boolean algebra is not new. The symbolic operations utilized in digital computers are

based on the investigations of the 19th century mathematician George Boole, and the

resulting algebraic system is called Boolean algebra in his honor. Computer designers, in

search of a system which would enable them to combine and manipulate binary numbers,

found that Boolean algebra lent itself well to the "two valued" digital-computer elements

and allowed the simplification of binary expressions quickly and efficiently.

The

objective of using Boolean algebra in the study of digital computes is to determine the

"truth value" of a combination of two or more statements. Boole's logic is based upon the

premise that a statement is either true or false. True statements have a value of 1, while

false statements have a value of 0.

Boole's logic is based upon the premise that a statement is either

or

.

true

2.

To understand Boolean notations, a person must ignore the common usage of the

false

arithmetic multiplication (x) and addition (+) connectives, since their use in logical

operations is quite different from the arithmetic usage. In arithmetic, the symbol "x"

means "multiply," and the symbol "+" means "add." In Boolean algebra, the arithmetic

symbol "x" means AND, and the arithmetic symbol "+" means OR. For example, the

expression A+B is read A or B; the expression AxB is read A and B. In ordinary

arithmetic, digits represent arithmetic quantities; whereas, in Boolean algebra, digits

represent conditions, such as ON-OFF, OPEN-CLOSED, etc.

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