1. Given Y=f(w, x, y, z)= II M(0, 1, 3, 5, 13), a. Write the complete truth table for Y=f(w,x, y, z). b. Write y=f(w, x, y, z) in standard POS form and standard SOP form. c. Write Y=f(w, x,y, z) in sum of min-terms and product of max terms. d. Use a Karnaugh map to derive a minimized POS and minimized SOP. 2. Simplify the following Boolean functions using four variables K-maps and express your answer in minimum sum of products and minimum product of sums. a. F(A,B,C,D)= Em (0, 1, 2, 4, 5)+ d( 3, 6, 7) b. F(X, Y, Z,W) - IIM(0, 6, 8, 13, 14) +d(2, 4, 10) c. F(A, B, C, D)=Em(4, 6, 7, 8, 12, 15) +d( 2, 3, 5, 10, 11, 14) 3. For F(A,B,C,D,E)= A'B'C+A'CE+A'BE+ABE+A'B'CD (Note: A' =) determine a. Truth table. b. Sum of min terms. c. Product of max terms. d. Standard sum of products. e. Standard product of sums. f. Minimum sum of products. g. Minimum products of sums. h. Gate implementation using all NAND gates. i. Gate implementation using all NOR gates.