Problem $2[$Datapath design$]$ For the datapath shown in Figure $1,$ the timing parameters are given in Table $1.$

$($a$)$ Determine the minimum clock period, $T_{\text{m}\text{i}\text{n}}$

$($b$)$ You can scale the logic unit by a scaling factor S $,$ such that its delay reduces by the same factor, i$.$e$.,$

$t_{p{L}_{\text{s}\text{c}\text{a}\text{l}\text{l}\text{e}\text{d}}}=\frac{t_{pL}}{S}$

What is the maximum scaling factor you can use, and the resulting maximum frequency of operation?

$\frac{?}{\text{b}\text{a}\text{r}}(i{)}_{\text{d}\text{o}\text{t}\text{s}}$dots.

Figure $1$: Datapath for Question $2$

Table $2$: Timing parameters

$\backslash$table$[[$Parameter$,$Min,Max$],[t_{c2Q},50$ ps$,100$ ps$],[t_{pL},200$ ps$,800$ ps$],[t_{su},100$ ps$,],[t_{\text{h}\text{o}\text{l}\text{d}},100$ ps$,]]$