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 = 0 through 9, respectively, with all other values on variable X ,j ≠ i, equal to 0. Also, these ten pushbuttons produce a positive pulse on the clock C for clocking the flip-flops in the circuit. The circuitry that produces the X j signals and the clock C has already been designed. The lock opens in response to a sequence of four X 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 1-hot code for the state assignment. Implement the circuit with D flip-flops and AND gates, OR gates, and inverters.