# Laws of Boolean Algebra in DLD Digital Logic Design

**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;

- Commutative Law of addition and multiplication
- Associative Law for addition and multiplication
- 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