Design a sequential circuit to control the motor of a tape player. The logic circuit, shown as follows, has four inputs and three outputs. Four of the inputs are the control buttons on the tape player. The input PL is $1$ if the play button is pressed, the input RE is $1$ if the rewind button is pressed, the input FF is $1$ if the fast forward button is pressed, and the input ST is $1$ if the stop button is pressed. The three outputs of the control circuit are P$,$ R$,$ and F$,$ which make the tape play, rewind, and fast forward, respectively, when $1.$ No more than one output should ever be $ON$ at a time; all outputs off cause the motor to stop. The buttons control the tape as follows: If the play button is pressed, the tape player will start playing the tape $($output $P=1).$ If the play button is held down and the rewind button is pressed and released, the tape player will rewind to the beginning of the current song. If the play button is held down and the fast forward button is pressed and released, the tape player will fast forward to the end of the current song. If rewind or fast forward is pressed while play is released, the tape player will rewind or fast forward the tape. Pressing the stop button at any time should stop the tape player motor.

a$)$ Construct ASM for the tape player control circuit.

b$)$ Realize the control circuit using one hot encoding.