Problem 2 (50 points) Design a circuit that has two inputs, elk and X, and produces one output O. X may change every clock cycle, and the change happens at the falling edge. The circuit samples the input at every rising edge of the clock. If the input is 1, consider as read a 1, else read a 0. O is 1 (for one clock cycle, from positive edge to positive edge) if the last three bits read are 110, with 0 as the most recent bit (a) (20 points) Draw the state diagram. Close to an arc, show X-1 or X-0 to indicate whether the change of state happens when X-1 or when X-0