For each of the functions below, use a Karnaugh Map to obtain a minimal SOP form. Be sure to:

Circle and list all of the prime implicants.

Indicate which prime implicants are essential.

Indicate any non-essential prime implicants that you use.

Give the cost of your minimal SOP form in terms of both gate count and number of literals.

(4 points) f(a,b,c) = ? m(0,1,3,4,5)

(4 points) f(a,b,c) = ? M(0,1,4,5,7)

(5 points) f(x,y,z,w) = ? m(1,2,5,6,7,11,12,13,14,15)

(5 points) f(x,y,z,w) = ? M(1,3,8,9,10,11,15)

(5 points) f(x,y,z,w) = ? m(0,1,3,4,5,7,9,10,11,13)