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 Xi, i = 0 through 9, respectively, with all other values on variable Xj, j does not equal 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 Xi signals and the clock C has already been designed. The lock opens in response to a sequence of four Xi values, i = 0, ...9, set by the user. The logic for connecting the four selected Xi values to variables Xa, Xb, Xc, and Xd 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 Xa, Xb, Xc, Xd, 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 Xa, Xb, Xc, and Xd, 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.