F(V, W, X, Y, Z) = Π M(0, 3, 6, 9, 11, 19, 20, 24, 25, 26, 27, 28, 29, 30) · Π D(1, 2, 12, 13)(a) Find two minimum sum-of-products expressions for F.(b) Underline the essential prime implicants in your answer and tell why each oneis essential.

The First answer is

VWXZ+VWXY+WYZ+VXY+VWZ+XYZ

The second possible answer is:

VWXZ+VWYZ+WYZ+VXY+VWZ+XYZ

Step-by-step explanation:

First we draw the k-maps for the function . There are two k-maps, one with V as zero while the other is V as 1. Then we combine the entries in power of 2. Remember that the function is given in maxterms form.Max-terms are those whose value is 0. So all the values other than max-values are either 1 or don't care. So we will keep these terms 0 and other as 1. The k-maps are attached in the files below. The essential prime implicants are those which are repeated in all the possible solutions.In this case Essential prime implicants are :

VWXZ+WYZ+VXY+VWZ+XYZ

http://www.32x8.com/sop5A-B-C-D-Em_4-5-7-8-10-14-15-16-17-18-21-22-23-31d_1-2-12-13option-0899788976571894282724?fbclid=IwAR2BaNgaMe0FXK1AEcwzLb1tkw5Oo-DIn-w0QNxE6ck9nYOSS1GnGtWC4SU

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

666666666666666666666

6

6

6

6

6

6

6

66

6

6

6

66

6

66answer:

step-by-step explanation: