Lec-ppt-4/logic/ BOOLEAN ALGEBRA AND LOGIC GATES

Introduction
oBinary logic deals with variables that have two discrete values: 1 for TRUE and 0 for FALSE.
oA simple switching circuit containing active elements such as a diode and transistor can demonstrate the binary logic, which can either be ON (switch closed) or OFF (switch open).
oThe switching functions can be expressed with Boolean equations. Complex Boolean equations can be simplified by a new kind of algebra, which is popularly called Switching Algebra or Boolean Algebra.
BASIC DEFINITIONS
Boolean algebra, like any other mathematical system, may be defined with :
o set of elements, set of operators, and number of assumptions and postulates.
Various algebraic structures are formulated on the basis of the most common postulates, which are described as follows:
1.Closer:
A set is closed with respect to a binary operator if, for every pair of elements of S, the binary operator specifies a rule for obtaining a unique element of S. For example, the set of natural numbers N = {1, 2, 3, 4, ...} is said to be closed with respect to the binary operator plus ( + ) by the rules of arithmetic addition, since for any X,Y ? N we obtain a unique element Z ? N by the operation X + Y = Z.