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Chapter: Digital Electronics - Minimization Techniques and Logic Gates

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Minimization of Boolean Expressions

Boolean expressions are minimized by using Boolean laws and postulates.

BOOLEAN EXPRESSION:

Boolean expressions are minimized by using Boolean laws and postulates.

 

 

MINIMIZATION OF BOOLEAN EXPRESSIONS


Simplify the Boolean expression

 

F=x′y′z′+x′yz+xy′z′+xyz′ Given

F=x′y′z′+x′yz+xy′z′+xyz′

 

=x′y′z′+x′yz+xz′(y′+y)

 

=x′y′z′+x′yz+xz′ =x′yz+ z′(x′y′+x)

= x′yz+z′(x′+x)(y′+x)

 

F=x′yz+xz′+z′y′

 

–  Sum-of-Products (SOP) Form

–  Product-of-Sums (POS) Form

–  Each form may contain single variable terms

–  May contain complemented and un-complemented terms

– A SOP and POS expression can’t have a term of more than one variable having an over bar extending over the entire term

 

               Sum-of-Product (SOP) form: When two or more product terms are summed by Boolean addition, the result is a Sum-of-Product or SOP expression

 

               Product-of-Sum (POS) form: When two or more sum terms are multiplied by Boolean multiplication, the result is a Product-of-Sum or POS expression

 

               The Domain of an SOP and POS expression is the set of variables contained in the expression, both complemented and un-complemented.

 

               A SOP and POS expression can have a single variable term such as A

 

               A SOP and POS expression cannot have a term of more than one variable having an over bar extending over the entire term.

 

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