Digital Engine Control System automation will be made. There are $K1$ and $K2$ control inputs and $M1$ and $M2$ motor control outputs. When K$1$ input is $1,$ if the M$1$ motor is not running, it will RUN, if it is running, it will continue and the $M2$ motor will be stopped. When K$2$ input is $1,$ if the M$2$ engine is not running it will RUN, if it is running it will continue and the $M1$ engine will be stopped. When both inputs are $"1",MI$ and $M2$ engines will run. If $Ki$ and $K2$ become $0$ at the same time, $M1$ and $M2$ engines will stop. The state of the motors occurs only on CLOCK $($rising edge$)$ edges.

a$)$ In which model can the system be designed? Explain.

b$)$ How many states are there in total in the system? Explain.

c$)$ Create the state transition diagram and table of the system. d$)$ You will implement the system using $T$ flip$-$flops. Implement the required Next State logic circuit using Multiplexers.

e$)$ Design the output circuit.