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Laws of Boolean algebra

The basic Laws of Boolean Algebra can be stated as follows:

  • Commutative Law states that the interchanging of the order of operands in a Boolean equation does not change its result. For example:
    1. OR operator → A + B = B + A
    2. AND operator → A * B = B * A
  • Associative Law of multiplication states that the AND operation are done on two or more than two variables. For example:
    A * (B * C) = (A * B) * C
  • Distributive Law states that the multiplication of two variables and adding the result with a variable will result in the same value as multiplication of addition of the variable with individual variables. For example:
    A + BC = (A + B) (A + C).
  • Annulment law:
    A.0 = 0
    A + 1 = 1
  • Identity law:
    A.1 = A
    A + 0 = A
  • Idempotent law:
    A + A = A
    A.A = A
  • Complement law:
    A + A' = 1
    A.A'= 0
  • Double negation law:
    ((A)')' = A
  • Absorption law:
    A.(A+B) = A
    A + AB = A

De Morgan's Law is also known as De Morgan's theorem, works depending on the concept of Duality. Duality states that interchanging the operators and variables in a function, such as replacing 0 with 1 and 1 with 0, AND operator with OR operator and OR operator with AND operator.

De Morgan stated 2 theorems, which will help us in solving the algebraic problems in digital electronics. The De Morgan's statements are:

  1. "The negation of a conjunction is the disjunction of the negations", which means that the complement of the product of 2 variables is equal to the sum of the compliments of individual variables. For example, (A.B)' = A' + B'.
  2. "The negation of disjunction is the conjunction of the negations", which means that compliment of the sum of two variables is equal to the product of the complement of each variable. For example, (A + B)' = A'B'.

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