Boolean Algebra: The Foundations of Digital Logic, Summaries of Analog Electronics

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UNIVERSAL GATES - BOOLEAN ALGEBERA is the category of algebra in which the variable’s values are the truth values, true and false , ordinarily denoted 1 and 0 respectively. It is used to analyze and simplify digital circuits or digital gates. It is also called Binary Algebra or logical Algebra. It 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. The important operations performed in Boolean algebra are – conjunction (∧), disjunction (∨) and negation (¬). Hence, this algebra is far way different from elementary algebra where the values of variables are numerical and arithmetic operations like addition, subtraction is been performed on them

Boolean Algebra Operations

The basic operations of Boolean algebra are as follows:  Conjunction or AND operation  Disjunction or OR operation  Negation or Not operation

Associative Law

It states that the order in which the logic

operations are performed is irrelevant as their

effect is the same.  ( A. B ). C = A. ( B. C )  ( A + B ) + C = A + ( B + C) Distributive Law Distributive law states the following conditions:  A. ( B + C) = (A. B) + (A. C)  A + (B. C) = (A + B). ( A + C) AND Law These laws use the AND operation. Therefore they are called AND laws.  A .0 = 0  A. 1 = A  A. A = A OR Law These laws use the OR operation. Therefore they are called OR laws.  A + 0 = A  A + 1 = 1  A + A = A

Inversion Law In Boolean algebra, the inversion law states that double inversion of variable results in the original variable itself.  Boolean Algebra Theorems The two important theorems which are extremely used in Boolean algebra are De Morgan’s First law and De Morgan’s second law. These two theorems are used to change the Boolean expression. This theorem basically helps to reduce the given Boolean expression in the simplified form. These two De Morgan’s laws are used to change the expression from one form to another form. Now, let us discuss these two theorems in detail. De Morgan’s First Law: De Morgan’s First Law states that (A.B)’ = A’+B’.