I am trying to solve a EE problem and am unsure whether I doing it correctly. The problem is:
Find all the prime implicants for the following Boolean functions, and determine which are essential: F(A,B,C,D) = Σm(1, 2, 4, 6, 8, 10, 11, 13, 15)
Here is what I did.
If anyone can just lead me in the right direction, I'd really appreciate it. Thanks!
Your Karnaugh map is correct.
You circled $0100$ and $0110$. This corresponds to the prime implicant $\overline W ~ X ~ \overline Z$, which is essential since it is the only prime implicant that covers $0100$.
You circled $1000$ and $1010$. This corresponds to the prime implicant $W ~ \overline X ~ \overline Z$, which is essential since it is the only prime implicant that covers $1000$.
You circled $0001$. This corresponds to the prime implicant $\overline W ~ \overline X ~ \overline Y ~ Z$, which is essential since it is the only prime implicant that covers $0001$.
You circled $1101$ and $1111$. This corresponds to the prime implicant $W ~ X ~ Z$, which is essential since it is the only prime implicant that covers $1101$.
There are two remaining uncovered minterms:
To cover $1011$, we can use either of the nonessential prime implicants $W~ Y~ Z$ or $W~ \overline X ~ Y$.
To cover $0010$, we can use either of the nonessential prime implicants $\overline X ~ Y ~ \overline Z$ or $\overline W ~ Y~ \overline Z$.