Given a function f(a,b,c,d) = Σm(0, 1, 9, 13, 15), Σd(3, 4, 5, 6, 8), find a simplified function f using k-map as; a. Sum of Products (SOP)  b. Product of Sums (POS)  c. Draw the circuits for a & b above and compare them.

Consider the Boolean function F(w, x, y, z) = Σ(1,3,5). Using K-map, derive the SOP and POS of F. Then, implement F with two levels of logic as: a) AND-NOR b) NAND-AND c) OR-NAND d) NOR-OR

Given a digraph D = (V; A; ') with all but one arc (u; v) having non-negative lengths, explain how to determine if D contains a negative circuit in 0 (m + n log n) of time.

Karnaugh maps and standard shapesFor the following function:F(A,B,C,D)= Σm(0,1,2,5,8,9,10) Using the Karnaugh map (See image), the following minimal function is obtained in the form of product of sums: F (A,B,C,D)= (C' + D') (B' + D) (A ' + B') 1-) Identify all prime implicants and/or essential implicants in terms of the function variables