Boolean Algebra laws

Chapter 3: The Basic of Logic Design

Boolean Algebra laws:

As well as the logic symbols "0" and "1" being used to represent a digital input or output. Laws or rules for Boolean Algebra expressions have been invented to help reduce the number of logic gates needed to perform a particular logic operation resulting in a list of functions or theorems known commonly as the Laws of Boolean.

Examples of these individual laws of Boolean, rules and theorems for Boolean Algebra are given in the following table.

These are the laws of Boolean Algebra, you should learn these.

·         Commutative laws

·         Associative laws

·         Distributive laws

·         Identity laws

·         Zero and one laws

·         Inverse laws

·         De Morgan’s laws

Commutative laws:

1.      A ∙ B = B ∙ A,    The order in which two variables are AND’ed makes no difference.

2.      A + B = B + A,    The order in which two variables are OR’ed makes no difference.

Associative laws:

• - This law allows the removal of brackets from an expression and regrouping of the variables.

1.      A + (B+C) = (A+B) + C

2.      A(BC)=(AB)C

 Distributive laws:

·         This law permits the multiplying or factoring out of an expression.

1.      A(B+C)=AB+AC

Identity laws:

1.      A + 0 = A,   A variable OR’ed with 0 is always equal to the variable.

2.      A . 1 = A,    A variable AND’ed with 1 is always equal to the variable.

Zero and one laws:

1.      A ∙ 0 = 0, A variable AND’ed with 0 is always equal to 0.

2.      A + 1 = 1,    A variable OR’ed with 1 is always equal to 1.

Inverse laws:

1.      A∙A’ = 0

2.      A+A’ = 1

De Morgan’s laws:

1.  Two separate terms NOR´ed together is the same as the two terms inverted (Complement) and AND´ed for example, A’+B’ = A’∙ B’.

2. Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and OR´ed for example, A’∙B’ = A’ +B’.

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