$($design as moore$)$Design a sequential logic circuit that controls an electric toothbrush. The toothbrush has a button $($momentary$,$ normally off$)$ for input. Press the button once and the toothbrush turns on at low speed and an LED turns on$.$ Press the button a second time and the toothbrush remains on but the brush now moves at high speed and the LED remains on$.$ Press the button a third time and the toothbrush turns off and the LED turns off. The motor that moves the brush at low or high speed takes two bits input. When the motor receives a $00$ it turns off. When the motor receives a $01$ it turns on at low speed. When the motor receives a $10$ it turns on at high speed. If your design results in unused states, ensure their next state is off. Any outputs from unused states are to be treated as off for their value. Implement your design using JK flip$-$flops. Clearly state if your design is a Mealy or Moore model.

a$)$ State Diagram b$)$ State Table c$)$ Minimized Boolean Equations d$)$ Draw Circuit