Boolean Algebra

Boolean Algebra

           In 1885, George Boole's revolutionary paper, "An investigation of the law of thoughts" was published which led to the development of new system, algebra of logic i.e. Boolean Algebra. Boolean algebra is named after the English mathematician George Boole (1815-1864). Boolean algebra is also called as the "Algebra of Logic" as it is the relationship between mathematics and logic. It is a two-valued system (1 & 0) of algebra that represents logical relationship and operations. In the field of computer science, Binary Logic is called as "Digital Logic". 

Digital logic is at the heart of the operation of all modern digital computers because all the computers understand only two languages i.e. 0 and 1. Boolean Algebra is an algebra, which deals with the study of binary variables & logical operations.


'A Boolean algebra deals with binary variables & Logic operation.'

Boolean Expression 

A Boolean expression is a string of symbols representing logical variables and logical operations which is evaluated to give a logical value. Following are the example of Boolean expressios: 

a) A + A'B
b) AB + A'BC + BC'

Boolean Function

A Boolean Function is described by an algebraic expression called Boolean expression which consist of binary variables, the constants 0 & 1 & logical operation symbol. In another word, A logic function is an expression expressed algebriacially with binary variables, logical operation symbols, parenthesis and equal sign, is also known as Boolean function. for example, in the logic function F = A+B, the value of F is 0 if A=0 and B=0 otherwise value of F is 1. The logic function can be represented as logic diagram composed of  AND, OR and NOT gates.

example: F(A,B) = (A+B)+B'

Basic Logical/ Boolean Operation

An operator is a special symbol that indicates the operation to be carried out between two operands. An operation is the action to be carried out upon operands. There are three basic Boolean Operation: AND, OR & NOT operations.