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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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