This problem refers to the circuit on the attached figure. Derive the state table and state diagram of the circuit. Tabulate the PLA programming table for the four functions below. Minimize the number of product terms. A(x, y, z) = sigma (1, 2, 5, 6) B(x, y, z) = sigma (0, 1, 3, 7) C(x, y, z) = sigma (2, 5) D(x, y, z) = sigma (1, 2, 3, 6, 7) (a) Simplify the following function, which is given in terms of a Karnaugh map, in SOP (Sum of Products) form: (b) Write the function in POS (Product of Sums) format. (c) Write the complement of the function in POS. Perform this operation 17-5 by performing addition on two numbers which are in signed two's complement format, each being 8 bits long. Show all the steps