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.
IT0342
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