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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