Boolean algebra and Logic Circuits

Boolean algebra deals with binary number system. It is very useful in designing logic circuits used in processors of computer system. In this chapter, you will learn about this algebra and elementary logic gates used to build up logic circuits of different types for performing necessary arithmetic operations. These logic gates are the building blocks of all logic circuits in a computer. You will also learn how to use Boolean algebra for designing simple logic circuits used frequently by arithmetic logic unit and almost all computers.

In mid 1800, George Boole (1815-1864), an English mathematician, developed algebra for simplifying the representation and manipulation of propositional logic. It is known a Boolean algebra after its developer’s name. Later, in the year 1938. Claude E. Shannon proposed the use of Boolean algebra in the design of relay switching circuits. The basic techniques described Shannon were adopted almost universally for the design and analysis of switching circuits. Owing to analogous relationship between the action of relays and modern electronic circuits, the same techniques are still used in the design of modern computers. Boolean algebra provides an economical and straightforward approach to the design of relay and other types of switching circuits. Just as an ordinary algebraic expression is simplified by using basic theorems , the expression describing a given switching circuit network is also simplified by using Boolean algebra. Today, Boolean algebra is used extensively in designing electronic circuitry of computers.

Fundamental concepts of Boolean Algebra

Use of Binary Digits In a normal algebraic expression, a variable can take any numerical value. For example, in the expression 3A+ 7B = C, each of the variables. A, B, and C may have from the entire field of real numbers. Since, Boolean algebra deals with binary number system, the variables used in Boolean equations may have only possible values (0 or 1). For example, in the Boolean equation A + B = C, each of the variables A, B, and C may have only the values 0 or 1.