$4.$ Implement the following finite state machine using D flip$-$flops to store the state bits $\backslash (\backslash$mathrm$\{$Q$\}\_\{1\}\backslash$mathrm$\{$Q$\}\_\{0\}\backslash ).$ Express your answer using three Boolean functions in sum$-$of$-$products form $($call the input bit A $)$:

$-$ A function for the $\backslash ($ D $\backslash )$ input of state bit $\backslash ($ Q$\_\{1\}\backslash ).$

$-$ A function for the $\backslash ($ D $\backslash )$ input of state bit $\backslash ($ Q$\_\{0\}\backslash ).$

$-$ A function for the output bit $\backslash ($ Z $\backslash ).$

c