Consider a counter that counts in the sequence $0,1,2,0,1,2,0,1$dots and keeps counting. The counter counts if the input, $w=0.$ If $w=1,$ the counter stops counting. Answer the following questions:

Draw the state diagram of the counter.

$2-$ Write down the state table of the counter.

$3-$ Assuming the counter starts from the value $2$ and $w=0$ and stays $0,$ what is the value of the counter after $16$ clock cycles?