(Design Problem) The Standard Master Combination Lock (the kind you find on gym lockers) has a dial with the numbers 0 through 39 on it. It works as follows. You reset it by spinning it clockwise past 0 a few times. Then you turn it counterclockwise to the first number in the combination, positioning the dial so that the number is directly under an indicator arrow. Then you spin the dial clockwise again, past 0 once, to the second number of the combination. Finally you spin the dial counterclockwise a second time directly to the last number of the combination. At this point the lock should open.

(a) Define the system's inputs and outputs. Consider signals that indicate clockwise or counterclockwise motion, the number where the dial is currently positioned, etc.

(b) Draw a finite state diagram for this subsystem, showing states, transition arcs, and logical conditions under which the machine moves from one state to the next.