Derive a Boolean expression for a voting machine which allows three persons to v

Question

Derive a Boolean expression for a voting machine which allows three persons to vote.The output is either yes or no dependent on the number of persons voting yes. Two restrictions: 1) No abstain allowed. That is each person has to vote either yes or no. 2) The outcome is yes if two or more yes votes; otherwise, the outcome is no. Normallywhen forming a voting group, like board of trustee, the number of voting members is designated to an odd number to avoid a tie situation. Derive a sum-of-product format fiand then use Karnaugh maps to simplify the expression.

Explanation / Answer

Truth Table

sum-of-product format

The outcome will be true for when either all person say "yes" or any two say "yes"
111 + 110 + 101 + 011;
f(p1,p2,p3) = (7,6,5,3);

Karnaugh maps

We can have two groups (3,7) and (5,6);

Person 1 Person 2 Person 3 Outcome T T T T T T F T F T T T T F T T F F F F T F F F F T F F F F T F

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