Laws of Boolean Algebra in DLD Digital Logic Design

By Prof. Fazal Rehman Shamil
Last modified on May 27th, 2019

What are Laws of Boolean Algebra?

The basic laws of Boolean Algebra are the same as ordinary algebra and hold true for any number of variables. Some of these laws are discussed below;

  1. Commutative Law of addition and multiplication
  2. Associative Law for addition and multiplication
  3. Distributive Law

What is Commutative Law of Addition?

According to commutative law of addition, if X OR Y are two variables, then X OR Y are same as Y OR X.

           X + Y = Y + X

What is Commutative Law of Multiplication?

According to commutative law of multiplication, if X AND Y are two variables, then X AND Y are same as Y AND X.

      X.Y= Y.X

What is Associative Law of Addition?

According to associative law of addition, if X OR (Y  OR  Z) are three variables, then X OR (Y  OR  Z) are same as (X + Y) + Z.

X + (Y + Z) = (X + Y) + Z

What is Associative Law of Multiplication?

According to associative law of multiplication, if X AND (Y  AND  Z) are three variables, then X AND (Y  AND  Z) are same as (X AND Y) AND Z

X.(Y.Z) = (X.Y).Z

What is Distributive Law?

According to distributive law, if X AND (Y  OR  Z) are three variables, then X AND (Y  OR  Z) are same as (X AND Y) OR (X AND Z).

X.(Y + Z) = X.Y + X.Z

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