Question $4$

For the circuit given below, C and X are $2$ inputs which cause the device to operate in $2$ different functions with input C as the selector.

Given that when $\backslash (\backslash$mathrm$\{$C$\}=1\backslash ),$ the device operates as D flip$-$flop; when $\backslash (\backslash$mathrm$\{$C$\}=0\backslash ),$ the device operates as T flip$-$flop. What is the minimum number of NOR gates used to construct the logic circuit? $($Note: fan$-$in for each gate is up to a maximum of $3)$

Please choose one:

a$)9$

b$)6$

c$)7$

d$)8$