Boolean Algebra

BOOLEAN Algebra was developed by George Boole (1815- 1864), an English mathematician and logician.

The credit for applying the laws of Boolean algebra goes to Claude. E. Shannon, an electrical engineer. Claude. E. Shannon in the year 1938, suggested that Boolean algebra can be applied to problems arising in telephone switching circuits and for this reason Boolean algebra is also known as Switching Algebra.

The other noteworthy persons to realise the significance of this algebra were August De- Morgan, Alfred North -White Head and Beltrand Russell.

 

Perhaps no one at that time might have realised that this abstract algebra was going to result in development of modern high speed digital computers, which have revolutionized the whole world today.

In fact Boolean algebra placed the theory of switching circuits on firm mathematical footings, which resulted in simplification of these circuits by simple mathematical methods.

Before discussing the Boolean algebra and its applications to switching circuits, it is important to have the knowledge of the logical statements and various operations that can be performed on these statements, because Boolean algebra deals with these statements

Logical Statements

  • A computer may be programmed to make decisions based on certain statement.
  • The truth and falsity of statement is know its truth value.
  • A statement is either true or false, but not both.
  • A statement having a truth value is called Logical Statement and
  • The truth-values of a logical statement namely, True(T) or False(F) are also known as Logical Constants.

To understand, the meaning of a Logical Statement. Let us explain it with the following statements.

a)  Please, go to the school.

b)  May God fulfil your desires!

c) What are you doing?

d)  2+2=5  e)  2+2=4

f)  Roses are red.

g)  Violets are blue.

All the above stated statements are meaningful as each one of these conveys a particular meaning. However these statements differ in one respect.

For example, the statements a), b), c) can not be classified as true or false that means we can not say whether these statements are true or false.

On the other hand the statements d) is false, and e), f) & g) are true

In other words, the statements d), e), f) and g) have a truth value which may be true or false.

Hence the statements d), e), f) and g) are logical statements whereas the statements a), b) and c) are not logical statements. Thus, a logical statement may be defined as a meaningful statement, which has truth value as TRUE or FALSE.

An exclamatory statement Is not a logical statement, because such a statement has no truth value.

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Published by

Gagan Deep

FOUNDER & DIRECTOR, ROZY COMPUTECH SERVICES, KUK, KURUKSHETRA (HARYANA), INDIA I am in the profession of teaching in Computer Science since 1996.  In 1996, established a professional setup “Rozy Computech Services” for providing Computer Education, computer hardware and software services. In this span of 21 years , in conjunction with Rozy’s, I also associated in Teaching with different Institutions like Assistant Professor in University College, Kurukshetra University, Kurukshetra, Guest Faculty in Directorate of Distance Education, Kurukshetra University, Visiting Faculty in University Institute of Engineering & Technology, Kurukshetra University and a Resource person in EDUSAT, Haryana. Besides, I am also serving as Guide and Mentor in various private educational institutions. Also written 7 books on computer science.

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