Boolean Algebra Introduction

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We are already familiar with set theory and mathematical logic from earlier classes. It has already been seen that there is a similarity between the laws stated in set theory and the mathematical logic. The operations 'union', 'intersection' and 'complement' on sets are comparable with the operations like disjunction, conjunction and negation in mathematical logic.

The development of Boolean algebra is a more general theory of set theory and mathematical logic.

An English mathematician, named George Boole invented this new kind of algebra which analyses logic mathematically. This Boolean algebra provided a basic logic for operation on binary numbers 0, 1. Since computers are based on binary system, this branch of mathematics is found to be exactly useful for the internal working of various computers.

Though the development of Boolean algebra was around in 1854, Claude Shannon made use of Boolean algebra in 1938 in designing telephone switching circuits, where a large number of switches are used, forming a network.

Boolean algebra is used in many spheres of activities such as electrical and telecommunication engineering, analysis of propositions, controlling the flow of pulses, mathematical expressions.

Therefore, Boolean algebra is considered to be modern mathematics.

Before we learn the fundamentals of Boolean algebra and its application to switching circuits, let us recall few basic terms.