Question

Tyrone Shoelaces has invested a huge amount of money into the stock market and doesnât trust just anyone to give him buying and selling information. Before he will buy a certain stock, he must get input from three sources. His first source is Pain Webster, a famous stock broker. His second source is Meg A. Cash, a self-made millionaire in the stock market, and his third source is Madame LaZora, world-famous psychic. After several months of receiving advice from all three, he has come to the following conclusions:

a) Buy if Pain and Meg both say yes and the psychic says no.

b) Buy if the psychic says yes.

c) Donât buy otherwise.

Construct a truth table and find the minimized Boolean function to implement the logic telling Tyrone when to buy.

Answer 1

Solution :

The truth table is :

Pain      Meg       Psych     Buy

   $0$           $0$                $0$            $0$

   $0$           $0$                $1$            $1$

   $0$           $1$                $0$           $0$

   $0$           $1$                 $1$             $1$

   $1$            $0$               $0$            $0$

   $1$            $0$               $1$             $1$

   $1$            $1$                $0$            $1$

   $1$           $1$                  $1$              $1$

The Boolean function :

$\text{F(Pain, \ Meg, \ Psych)}$ = $\overline {\text{PainMeg}}\text{Psych}+\overline{\text{Pain}}\text{MegPsych}+\text{Pain}\overline{\text{Meg}}\text{Psych}+\text{PainMeg}\overline{\text{Psych}}$$+\text{PainMegPsych}$

                              Meg and Psych

                           $00$     01     $11$       10

  Pain         0                 1        1

                   $1$                 $1$        1        $1$

Therefore,

$\text{F(Pain, \ Meg, \ Psych)}$  = Psych + PainMeg