A sequential circuit for a luggage lock has ten pushbuttons labeled 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each pushbutton 0 through 9 produces a 1 on X_i, i = 0 through 9, respectively, with all other values on variable X_j, j ≠ i, equal to 0. Also, these ten pushbuttons produce a positive pulse on the clock C for clocking the lip- lops in the circuit. The circuitry that produces the X_i signals and the clock C has already been designed. The lock opens in response to a sequence of four X_i values, i = 0, . . . , 9, set by the user. The logic for connecting the four selected X_i values to variables X_a, X_b, X_c, and X_d has also been designed. The circuit is locked and reset to its initial state by pushing pushbutton Lock, which provides L, the asynchronous reset signal for the circuit. The lock is to unlock in response to the sequence X_a, X_b, X_c, X_d, regardless of all past inputs applied to it since it was reset. The circuit has a single Moore type output U which is 1 to unlock the lock, and 0 otherwise. Design the circuit with inputs X_a, X_b, X_c, and X_d, reset L, clock C, and output U. Use a one- hot code for the state assignment. Implement the circuit with D lip- lops and AND gates, OR gates, and inverters.