Q$2.$ A program runs in $100$ seconds on a machine with multiply operations $($Booth$)$ responsible for $80$ seconds of this time. In a design modification, only the algorithm implementation for multiplication was changed from the $2-$bit$-$encoding one used in Example $1$ to the $3-$bit$-$encoding one used in Example $2.$ Both examples perform $73$ on $4$ bits. What is the overall percentage speedup for the same program running on the improved processor? $[5$ marks$]$