Boolean expressions are minimized by using Boolean laws and postulates.
MINIMIZATION OF BOOLEAN EXPRESSIONS
Simplify the Boolean expression
=x′y′z′+x′yz+xz′ =x′yz+ z′(x′y′+x)
– 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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