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Basic Laws of Boolean Algebra in Digital Electronics

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The basic Laws of Boolean Algebra in Digital Electronics can be specified as follows:

  1. Commutative Law conditions that the interchanging of the instruction of operands in a Boolean calculation does not modify its result. For example:
    1. OR operator → A + B = B + A
    2. AND operator → A * B = B * A
  2. The associative Law
    1. The 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
  3. Distributive Law
    1. Distributive law states that the multiplication of two variables and adding the result with a variable will result in the same value as the multiplication of the addition of the variable with individual variables. For example:
      A + BC = (A + B) (A + C).
  4. Annulment law:
    A.0 = 0
    A + 1 = 1
  5. Identity law:
    A.1 = A
    A + 0 = A
  6. Idempotent law:
    A + A = A
    A.A = A
  7. Complement law:
    A + A’ = 1
    A.A’= 0
  8. Double negation law:
    ((A)’)’ = A
  9. Absorption law:
    A.(A+B) = A
    A + AB = A

What is Adder

De Morgan’s Law is also known as De Morgan’s theorem, the whole thing depending on the concept of Duality. Duality states that switching the operators and variables in a function, such as replacement 0 with 1 and 1 with 0, AND operator with OR operator, and OR operator with AND operator.

Basic laws of Boolean Algebra

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

Here are some logic gate circuit problems:

  • Draw a logic circuit for (A + B)C.
  • Draw a logic circuit for A + BC + D.
  • Draw a logic circuit for AB + AC.
  • Draw a logic circuit for (A + B)(C + D)C.

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