If two D flip$-$flops are used to implement the state machine given below, what is the expression of the D input $($D$1)$ of the flip$-$flop producing Q$1$ and the output $($Z$)$ in terms of input x and present state $($Q$2$Q$1)$

A$.$ D$1=$x$,$Z$=$Q$2.$Q$1$

B$.$ D$1=$x$.$Q$2,$Z$=$Q$2.$Q$1$

C$.$ D$1=$x$.$Q$1^(\text{'}),$Z$=$Q$2.$Q$1$

D$.$ D$1=$x$.$Q$2^(\text{'}),$Z$=$Q$2^(\text{'}).$Q$1^(\text{'})$

E$.$ None of the others