Mathematics | Properties of Boolean algebra

Switching algebra is also known as Boolean Algebra. It is used to analyze digital gates and circuits It is logic to perform mathematical operation on binary numbers i.e., on ‘0’ and ‘1’. Boolean Algebra contains basic operators like AND, OR and NOT etc. In this operations can be performed on variables which are represented using capital letter 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 remain unchanged when it is ORed or ANDed, 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 negation 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 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)
    A+(B.C) = (A+B).(A+C)

  • Absorption law –:-This law involved absorbing the 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’

  • GATE CS Corner Questions

    Practicing the following questions will help you test your knowledge. All questions have been asked in GATE in previous years or in GATE Mock Tests. It is highly recommended that you practice them.

    1. GATE CS 2013, Question 65
    2. GATE CS 2009, Question 6
    3. GATE CS 2007, Question 85

    References –
    Boolean algebra – Wikipedia
    De Morgan’s laws – Wikipedia

    This article is contributed by Vaishali Bhatia. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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