A sequential circuit for a luggage lock has 10 push buttons labeled0,1,2,3,4,5,6,7,8,9. Each pushbutton 0 through 9 produces a 1on X_i, i=0 through 9 with all other values on variable X_ j, jdoes not equal i, equal to 0. Also, these ten pushbuttons produce apositive pulse on the clock C for clocking the flip-flops in thecircuit. The circuitry that produces the X_i signals and theclock C has already been designed. The lock opens in responseto a sequence of four X_i values, i=0 to 9, set by the user. The logic for connecting the four selected X_i values to variablesX_a, X_b, X_c, and X_d has also been designed. Thecircuit is locked and reset to its initial state by pushingpushbutton LOCK, which provides L, the asynchronous reset signalfor the circuit. The lock is to unlock in response to thesequence X_a, X_b, X_c,X_d, regardless of all past inputs appliedto it since it was reset. The circuit has a single moore typeoutput U which is 1 to unlock the lock and 0 otherwise.

Design the circuit with inputs X_a, X_b, X_c, X_d, reset L, clock Cand output U.
Use a 1-hot code for the state assignment.
Implement using D flipflops, AND gates, OR gates and inverters.