Properties of Boolean Algebra

  • Difficulty Level : Easy
  • Last Updated : 07 Apr, 2022

Switching algebra is also known as Boolean Algebra. It is used to analyze digital gates and circuits It is logical to perform a mathematical operation on binary numbers i.e., on ‘0’ and ‘1’. Boolean Algebra contains basic operators like AND, OR and NOT etc. Operations are represented by ‘.’ for AND , ‘+’ for OR . Operations can be performed on variables that are represented using capital letters eg ‘A’, ‘B’ etc. 

Properties of switching algebra – 

 

  • Annulment law – a variable ANDed with 0 gives 0, while a variable ORed with 1 gives 1, i.e., 

A.0 = 0 
A + 1 = 1 
 

  • Identity law – in this law variable remain unchanged it is ORed with ‘0’ or ANDed with ‘1’, i.e., 

A.1 = A 
A + 0 = A 
 

  • Idempotent law – a variable remains unchanged when it is ORed or ANDed with itself, i.e., 

A + A = A 
A.A = A 
 

  • Complement law – in this Law if a complement is added to a variable it gives one, if a variable is multiplied with its complement it results in ‘0’, i.e., 

A + A’ = 1 
A.A’ = 0 
 

  • Double negation law – a variable with two negations, its symbol gets cancelled out and original variable is obtained, i.e., 

((A)’)’=A 
 

  • Commutative law – a variable order does not matter in this law, i.e., 

A + B = B + A 
A.B = B.A 
 

  • Associative law – the order of operation does not matter if the priority of variables are the same like ‘*’ and ‘/’, i.e., 

A+(B+C) = (A+B)+C 
A.(B.C) = (A.B).C 
 

  • Distributive law – this law governs opening up of brackets, i.e., 

A.(B+C) = (A.B)+(A.C) 
 

  • Absorption law –:-This law involved absorbing similar variables, i.e., 

A.(A+B) = A 
A + AB = A 
 

  • De Morgan law – the operation of an AND or OR logic circuit is unchanged if all inputs are inverted, the operator is changed from AND to OR, the output is inverted, i.e., 

(A.B)’ = A’ + B’ 
(A+B)’ = A’.B’