Design a sequential circuit for a three-number combination lock. The circuit has three inputs w, x, y, and a single output z The lock is opened by giving a series of three-bit binary codes on the system inputs w, x, y. The correct sequence is: wxy = 010, 100, 110 (this is the combination to the lock) Operation of the lock is as follows: Beginning in the "CLOSED" state, entering the code xyz = 001 moves the system to the "1/3-OPEN" state. From there, the next code wxy = 101 moves the system to the "2/3-OPEN"state, but any other entry moves it back to closed. From 2/3-OPEN, the final code wxy = 011 moves the system to the "OPEN" state (and any other entry moves it to closed). When in the open state, the system should generate an output z = 1 (which controls a mechanical system that opens the lock). Finally, the system automatically (for any entry) moves to the closed state. (a) Derive the state diagram for a Moor-type system. Using whatever you determine in this step for parts (b)-(d) (b) represent the states of the system, CLOSED = 00, 1/3-OPEN = 01, 2/3- OPEN = 10, OPEN = 11 are assign the necessary number of bits such as AB = 00, 01, 10, 11. Create the state table that defines the three input variables w, x, y, the current-states (A, B), next-states (A*, B*, and output z. (c) Implement the system using D Flip-flops and whatever combinational gates you may need, and sketch the circuit. (d) Using the method of your choosing, redesign the flip-flop input equations for JK flip-flops, and sketch the circuit. (e) A very simple alternative way to implement the system with JK flip=flops is to replace each D flip-flop in part (c) directly with a JK flip-flop. Show how a JK flip-flop can be wired to emulate the behavior of a D flip-flop