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.
Related Topics
Privacy Policy, Terms and Conditions, DMCA Policy and Compliant
Copyright © 2018-2024 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.