Q$1(7\mathrm{.}5$ marks$).$ Design a controller for the operation of a washing machine as either Moore or Mealy machine. The washing machine 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$)$: When the machine is off, no operation is in progress.

$-$ Fill Water $($S$1)$: The machine begins filling water after receiving the start signal. The fill water process will continue until the tank is full.

$-$ Wash $($S$2)$: After the water is filled, the machine proceeds to the washing cycle, where the clothes are washed.

$-$ Rinse $($S$3)$: Once the washing is done, the machine enters the rinse cycle, where it fills the tank with clean water and rinses the clothes.

$-$ Spin $($S$4)$: After rinsing, the machine enters the spin cycle to remove excess water from the clothes.

$-$ Complete $($S$5)$: Finally, after the spin cycle is completed, the washing machine returns to the Idle State $($SO$).$

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

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

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

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

d$)$ Minimize the expressions using K$-$maps.

e$)$ Draw the circuit implementation using $\backslash (\backslash$mathbf$\{$D$\}\backslash )-$ flip flops and other logic gates if needed.