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Principles of Boolean Algebra

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Published on Nov 29, 2010

Principles of Boolean AlgebraAlgebra of logic is a mathematical device used to record, calculat, simplify, and transform logical propositions. Algebra of logic was developed by George Boole and therefore was named Boolean algebra. It started as a speculative science, accessible only to a narrow circle of scientists. That was until Englishman George Boole bet in the nineteenth century he would create a science completely detached from reality and without any practical application. He turned mathematical logic into algebra of propositions. Boolean algebra is the algebra of two values - true and false. For example, the statement "6 is an even number" is true, and the statement "The Neva flows into the Caspian Sea" is false. These 2 elements - true and false - are called constants and they are assigned, respectively, logical 1 and logical 0. In the algebra of logic, propositions can be combined to give new propositions. These new propositions are called functions of the initial propositions of the logical variables A, B, C, each of which can take 0 or 1.Depending on the values of variables and operations, a function can be either 1, or 0. The values of functions are determined by the truth table of this function. A truth table is a table used to establish a correspondence between all possible configurations of logical variables in a logical function and the values of these functions. All possible logical functions of variables can be formed with the help of 3 main operations:Logical disjunctionLogical conjunction and negationLogical disjunction is an operation also known as OR. The function is true if at least 1 operand is true. OR corresponds to the mathematical operation of union of sets. Logical conjunction is an operation also known as AND. The function is true if both operands are true. It corresponds to the mathematical operation of intersection of sets. Negation is an operation also known as logical complement. The function is true if the variable is false or vice versa. Of course, like any other science, Boolean algebra has many laws, axioms, rules, etc. But I can safely say that all the computer technology is based on logical constants 1 and 0 and logical operations AND, OR, NOT. Boole made a scientific revolution, and he didn't even know about it. The new concept of logic that he introduced were later used as a basis for the data processors construction. History has shown that Boole lost the bet. It was Boolean algebra, unlike other types of logic, that was most widely applied in engineering.

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