$1.$ Please draw the state graph for the following finate state machine, and compute the output sequence for the given input sequence. $(16$ points$)$

$($For the output, please ignore the first bit for the inital state.$)$

$($a$)(8$ points$)$

Input:$0011$

$0011$

$($Please draw the time table how to get the output$)$

$($b$)(8$ points$)$

Input:acbbca

acbbca

$($Please draw the time table how to get the

output$)$