Algebraic Simplification of Logic Circuits

Simplifying logical circuits

Do you take many circuits too complex? If do so, then you can simplify them.

Simplifying by using Boolean algebra

The following rules apply for variables which are used in logical functions. The analogy to the electrical circuit should help you to work out these rules for yourself:

 

First part: Signal a combined with a constant:

Simplifying by using Boolean algebra 1

Simplifying by using Boolean algebra 1


Second part:  Variable combined with itsself

Simplifying by using Boolean algebra - Variable combined with itself

Simplifying by using Boolean algebra - Variable combined with itself


 

Third part: Commutative law

Simplifying by using Boolean algebra - the Commutative law

Simplifying by using Boolean algebra - the Commutative law


Fourth part:      Associative rule

The associative rule tells you how you can summarize single variables, which are linked to each other by, AND 'or' OR '. Summarized variables are indicated by parentheses.

Simplifying by using Boolean algebra - Associative rule

Simplifying by using Boolean algebra - Associative rule

Fifth part:     Distributive laws

The Distributive laws specify how links relate to each other when parentheses are resolved (Law of distribution for calculating with parentheses).

Simplifying by using Boolean algebra - the Distributive laws

Simplifying by using Boolean algebra - the Distributive laws


Sixth part:     The rule of “de Morgan”

The De Morgan's rules are used to transform logic circuits.

Simplifying by using Boolean algebra - De Morgan's law

Simplifying by using Boolean algebra - De Morgan's law

 

 

 

... soon coming more

 

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