K-map

Question

Consider the boolean expression F(A,B,C,D)=Σm=(0,1,2,5,6,7,8,10,14,15).Find the number of essential prime implicants.

a)1

b)2

c)3

d)4

Comments

b ?

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Thank you for your concern :)

Yes the answer is 2...I had my doubt clear

Answer 1

yes 2 is the ans.

Comments

Yes option b will be the answer.

Number of essential prime implicants is 2 which are quads i.e. set of 4 minterms. 

first quad is consisting of minterms 6,7,14,15 and it is essential prime implicants as minterm 15 cannot be covered by other prime implicants.

Second quad consisting of minterms 0,2,8,10 and it is essential prime implicants as minterm 8 cannot be covered by other prime implicants.

Essential prime implicant is a prime implicant which has atleast one 1 cannot be covered by other prime implicants.

In this k map, except these two quads, all other pairs can be covered by other prime implicants.

The essential prime implicants are shown in the figure as epi.

Answer 2

 

Number of EPI =$2$.

Option $(B)$ is correct.