GATE 2018 CS – Question 59
Consider the minterm list form of a Boolean function $F$ given below.
$$F(P,Q,R,S)=\sum m(0,2,5,7,9,11)+d(3,8,10,12,14)$$
Here, $m$ denotes a minterm and $d$ denotes a don't care term. The number of essential prime implicants of the function $F$ is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 3
Explanation
On the 4-variable Karnaugh map the prime implicants are $\bar Q\bar S$ (covering 0, 2, 8, 10), $QS$ (covering 5, 7 with don't care 3 ... ) and $PS$ (covering 9, 11 with 3 ... ). The prime implicants that are the only cover for some minterm are three in number, so there are 3 essential prime implicants.