Question

Express the boolean function F= (X'+Y)(X+Z)(Y+Z) in SPOS form
(X+Y+Z)(X+Y'+Z)(X'+Y+Z)(X'+Y+Z')
(X'+Y'+Z)(X+Y'+Z)(X'+Y+Z)(X'+Y+Z')
(X'+Y'+Z')(X+Y'+Z)(X'+Y+Z)(X'+Y+Z')
(X+Y+Z)(X+Y'+Z)(X'+Y+Z)(X'+Y'+Z')

Answer 1

given a boolean function, express it in SPOS form

Explanation:

1. SPOS stands for standard product of sum form , it is expressed as product (П) of max terms that is terms having output false ($0$). It is also known as product of max term or canonical conjunctive normal form.
2. Truth Table of the function , $F=(X'+Y)(X+Z)(Y+Z)$ is given as ,                           $X\ Y\ Z\ \ \ F\\f\ f\ f\ \ \ \ f\ \ \ -m_0\\f\ f\ t\ \ \ \ t\ \ \ -m_1\\f\ t\ f\ \ \ \ f\ \ \ -m_2\\f\ t\ t\ \ \ \ \ t\ \ \ -m_3\\t\ f\ f\ \ \ \ f\ \ \ -m_4\\t\ f\ t\ \ \ \ f\ \ \ -m_5\\t\ t\ f\ \ \ \ t\ \ \ -m_6\\t\ t\ t\ \ \ \ t\ \ \ -m_7$        
3. from truth table we get the max terms $m_0,\ m_2,\ m_4,\ m_5$    
4. hence, the expression in SPOS form is given by                                  $F=$Π$(m_0,m_2,m_4,m_5)$                                                                                                       $F=(X'+Y'+Z')(X'+Y+Z')(X+Y'+Z')(X+Y'+Z)$   ---ANSWER