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Properties of Boolean Algebra

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  • Difficulty Level : Easy
  • Last Updated : 15 Jun, 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 the opening up of brackets, i.e., 

    A.(B+C) = (A.B)+(A.C) 

          (A+B)(A+C) = A + BC 
 

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

    A.(A+B) = A 
    A + AB = A 

           A+ A’B = A+B                                                                                                           ]                                                                                                         A(A’ + B) = AB

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