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In mathematics Boolean Algebra is a branch of algebra in which the variable’s values are the truth values, true and false, usually denoted by binary numbers i.e. 1 and 0 respectively.
Boolean Algebra is used to analyze and simplify the digital (logic) circuits or digital gates . It is also called as Binary Algebra or logical Algebra. Boolean algebra was invented by George Boole. He introduce it in his first book The Mathematical Analysis of Logic in 1854.
Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.
Boolean algebra, symbolic system of mathematical logic that represents relationships between entities—either ideas or objects. The basic rules of this system were formulated in 1847 by George Boole of England and were subsequently refined by other mathematicians and applied to set theory. Today, Boolean algebra is of significance to the theory of probability, geometry of sets, and information theory. Furthermore, it constitutes the basis for the design of circuits used in electronic digital computers.
Boolean Algebra vs Elementary Algebra
In mathematics, although boolean algebra is a branch of algebra but it is different from elementary algebra in two ways.
i) In boolean algebra the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in Elementary Algebra the values of the variables are numbers.
ii) Boolean algebra uses logical operators such as conjunction (and) denoted as ?, disjunction (or) denoted as ?, and the negation (not) denoted as ¬. On the other hand Elementary algebra uses arithmetic operators such as addition, multiplication, subtraction and division.
So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations.
Types of Boolean Laws
There are six types of Boolean Laws.
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