Along input sequence enters a one$-$input one$-$output synchronous sequential circuit, that is required to produce an output symbol z $=1$ whenever the sequence $1111$ occurs. Overlapping sequences are accepted; for example, if the input sequence is $01011111,$ the required output sequence is $00000011.$

$($a$)$ Draw a state diagram.

$($b$)$ Select an assignment and show the excitation and output tables.

$($c$)$ Write down the excitation functions for SR flip$-$flops, and draw the corresponding logic diagram.