Question $1[40$ pts$]$

Consider a digital combination lock as illustrated in Figure a display that shows the number of keys pressed since the last reset. The lock code below. On its keypad are five digital input buttons for numbers $1-5,$ a reset button R$,$ and is a sequence of four digits. At the initial state, a $0$ is displayed. When a number key is pressed, the display is incremented by $1,$ regardless of the input. Upon the fourth key press, if the input sequence is correct, the display will change to a $0,$ unlocking the system. If an incorrect sequence is entered, the display will change to an E upon the fourth key press, and the user must then press the R button to reset the lock to its initial state. The user can also press the R button anytime to reset the lock. Assume that the code is set to $5152.$

a$)$ Draw the Moore state machine of the combination lock.

b$)$ Draw the Mealy state machine of the combination lock.

Hint: consider the display as well as the lock status $($locked$,$ unlocked$)$ as the output.