Q$10.$ Design a Finite State Machine $($FSM$)$ with one input and one output. The circuit should read one$-$bit

data at every rising edge of the clock. According to the data input, the circuit will produce the

following output. On reset, its output will be $100.$

If the input bit sequence is $11$ then the output will be $000.$

If the input bit sequence is $00$ then the output will be $001.$

If the input bit sequence is $111$ then the output will be $010.$

If the input bit sequence is $000$ then the output will be $011.$

Otherwise, the output will be $100.$

$($a$)$ Sketch the state transition diagram.

$($b$)$ Write the state transition and output tables with binary encodings.

$($c$)$ Write the Boolean equations for the next$-$state and output logic.

$($d$)$ Sketch the circuit schematic for the FSM$.$