The circuit shown below implements a $1-$bit datapath function in dynamic $($precharge$/$evaluate$)$ logic.

$($a$)$ Write down the Boolean expression for outputs $F$ and $G.$ On which clock phases are they valid?

$($b$)$ To what datapath function could this unit be most directly applied?

$($c$)$ What is the purpose of transistor $M_1?$

$($d$)$ Can the evaluation phase of $F$ be speeded up by rearranging transistors? Can the evaluation of $G$ be speeded up in the same manner? Explain.