Find all the prime implicants for the following Boolean functions, and determine which are essential:
F(W,X,Y,Z) = Im(0,2,5,7,8,10,12,13,14,15)
Book solution:
Prime = XZ, WX, X'Z', WZ'
Essential = XZ, X'Z'
The following is my attempt at tackling the problem, but my answer is not matching the book's answer.
Could anyone assist ?
The ordering in the Karnaugh Map should be: \begin{pmatrix} AB/CD & 00 & 01 & 11 & 10 \\ 00 & 0 & 1 & 3 & 2 \\ 01 & 4 & 5 & 7 & 6 \\ 11 & 12 & 13 & 15 & 14 \\ 10 & 8 & 9 & 11 & 10 \end{pmatrix} Thus your map should look like this \begin{pmatrix} WX/YZ & 00 & 01 & 11 & 10 \\ 00 & 1 & 0 & 0 & 1 \\ 01 & 0 & 1 & 1 & 0 \\ 11 & 1 & 1 & 1 & 1 \\ 10 & 1 & 0 & 0 & 1 \end{pmatrix} There you can see that XZ is a prime implicant you missed. Btw as the matrix is symmetrical you see that Y can be omitted and you could simplify the matrix to \begin{pmatrix} WX/Z & 0 & 1 \\ 00 & 1 & 0 \\ 01 & 0 & 1 \\ 11 & 1 & 1 \\ 10 & 1 & 0 \end{pmatrix}