Question

The truth table for the sop expression ab+b c has how many input combinations?



1



2



4



8

Answer 1

hiiii

8 is your answer

Answer 2

The SOP expression will have $3$ input combinations: $F=a'bc+abc'+abc$

Explanation:

1. SOP stands for Sum Of Product and can expressed in form of sum of min-terms that is the input combinations having the output true or $1$.
2. given is the boolean expression, $F=ab+bc$
3. the number of input combination in the truth table is given by, $2^n$ where n is the number of variables in the expression. Here $n=3$
4. Hence $8$ combinations are in the truth table of 'F'.
5. the truth of 'F' is ,                                                                                                     [tex]abc-\ \ \ \ 000\ \ \ \ \ \ \ 001\ \ \ \ \ \ \ 010\ \ \ \ \ \ 011 \ \ \ \ \ \ 100\ \ \ \ \ 101\ \ \ \ \ \ 110\ \ \ \ 111\\ F-\ \ \ \ \ \ 0(m_0)\ \ \ 0(m_1)\ \ \ \ 0(m_2)\ \ \ 1(m_3)\ \ \ 0(m_4)\ \ 0(m_5)\ \ 1(m_6)\ \ 1(m_7)[/tex]    
6. now the min-terms are                                                                                               $m_3=a'bc\ \ \ m_6=abc'\ \ \ m_7=abc$                                                                              
7. hence the SOP expression will have three combinations $F=a'bc+abc'+abc$