Q$3$ Design a module five counter which follows the decimal state sequence $($but using binary values$)024130$dots. The output signal $Z$ is a roll over flag. This counter should produce a $\text{'}1\text{'}$ for one clock period when counter number gets $\text{'}3\text{'}.$ Otherwise, the output $Z$ should be $\text{'}0\text{'}.$

$[25]$

$($a$)$ Derive a State Transition Graph for your design.

$[7]$

$($b$)$ Derive a State Transition$/$Output Table based on the graph in part $($a$).$

$[8]$

$($c$)$ Derive the Excitation equations for your design, assuming D flip$-$flops.

$[6]$

$($d$)$ Derive logic equation for the output $Z.$

$[2]$

$($e$)$ Is your design a self$-$correcting circuit? Why? If not, briefly describe your ideas.$[2]$