Q$1(7\mathrm{.}5$ marks$).$ Design a controller for the operation of an electric pressure cooker as a Mealy machine. The electric pressure cooker operates in a sequence of states based on its cycles, with the user input indicating when to start, and proceed to different stages of the wash process. The machine transitions through the following states:

Idle State $($SO$)$: The cooker is off, no operation is in progress.

Preheating $($S$1)$: The cooker is heating up and building pressure before cooking begins.

Pressure Cooking $($S$2)$: The cooking process is active, with pressure applied.

Pressure Release $($S$3)$: The cooker is releasing pressure before the cooking is complete.

Complete $($SA$)$: The cooking process is complete, and the cooker returns to the Idle State $($SO$)|$ state after the cycle ends.

Use D$-$flip flops in your design $($below is its corresponding table$).$

$\backslash$table$[[,Q(t+1),$D$],[0,0,0],[0,1,1],[1,0,0],[1,1,1]]$

a$)$ Draw the state diagram based on the above explanation.

b$)$ Draw the state transition table showing all inputs and outputs $($ff any$).$

c$)$ Derive the expressions for the next states. $($Remember this depends on how many flipflops you are considering and how many outputs exists.$)$

Minimize the expressions using K$-$maps.

e$)$ Draw the circuit implementation using D$-$fill flops and other logic gates if needed.