Boolean algebra and Logic Circuits

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 Boolean algebra is based on the fundamental concepts described below. 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.

Logical Addition

The symbol ‘+’ is used for logical addition operator. It is also known as ‘OR’ operator. We can define the + symbol (OR operator) by listing all possible combinations of A and B with the resulting value of C for each combination in the equationA+ B = C. Since the variables A and B can have only two possible values (0 or 1). Only four (2 2 ) combinations of inputs are possible (see the table 5.1). The resulting output values for each of the four input combinations are given in the table. Such a table is known as a truth table. Hence, the below figure is the truth table for logical OR operator