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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=xâ€˛yâ€˛zâ€˛+xâ€˛yz+xyâ€˛zâ€˛+xyzâ€˛ Given

F=xâ€˛yâ€˛zâ€˛+xâ€˛yz+xyâ€˛zâ€˛+xyzâ€˛

=xâ€˛yâ€˛zâ€˛+xâ€˛yz+xzâ€˛(yâ€˛+y)

=xâ€˛yâ€˛zâ€˛+xâ€˛yz+xzâ€˛ =xâ€˛yz+ zâ€˛(xâ€˛yâ€˛+x)

= xâ€˛yz+zâ€˛(xâ€˛+x)(yâ€˛+x)

F=xâ€˛yz+xzâ€˛+zâ€˛yâ€˛

â€“  Sum-of-Products (SOP) Form

â€“  Product-of-Sums (POS) Form

â€“  Each form may contain single variable terms

â€“  May contain complemented and un-complemented terms

â€“ A SOP and POS expression canâ€™t have a term of more than one variable having an over bar extending over the entire term

â€˘               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

â€˘               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

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

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

â€˘               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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