Q$8.$ points$)$ For Single$-$Step Revolving gates are to be installed at the entrance of a children park.

Specifications are as follows:

a$)$ There are two inputs reset and clock. Reset is used for initializing Finite State Machine $($FSM$)$ to some known state and clock is used for state transition $[$@ rising edge of clock$]$

b$)$ It accepts coins of Dirham. $1$ and Dirham. $2$ only.

c$)$ It gives out a Ticket of value of Dirham$3$ when accumulated sum is $3$ or more.

d$)$ A change of Dirham. $1$ is provided in case of intake of Dirham. $4$ in whatever sequence

e$)$ Opens the gate when ticket inserted

f$)$ Inputs$/$Outputs $=x1$:$x\frac{2}{Y}1$:$Y2$:$Y3$

where

$x1$:$x2=00,-$ No Input

$x1$:$x2=01,-,$ Dirham. $1$ Input

$x1$:$x2=10,-,$ Dirham. $2$ Input

$x1$:$x2=11,-,$ Ticket Input.

Y$1=$ Park Gate Opens.

$Y2=$ Give Ticket.

Y$3=$ Change.

$[$part$-$a$]$ Design a Finite State Machine $($FSM$)$ with minimum number of states.

$[$part$-$b$]$ Draw a compact State Transition Table for the FSM after suitable state assignment.

$[$part$-$c$]$ Find the minimized logical equations for the state variables and Y$1,$ Y$2$ and Y$3$ outputs.