Question $9(20$ points$)$

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Consider three different processors P$1,$ P$2,$ and P$3$ executing the same instruction set. P$1$ has a $3\mathrm{.}00$ GHz clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}50$ GHz clock rate and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}00$ GHz clock rate and has a CPI of $2\mathrm{.}2.$

a$.$ Find execution time for each processor $\{$The first three answer boxes in order of processor number, only write the rounded $($up$)$ time in seconds in format of d$.$d; e$.$g$.0\mathrm{.}7\}$ for a program with $2\mathrm{.}00$e$+9(2$e$+09$ is a notation for $2$x$(10^9)=2,000,000,000)$ instructions. Which one is the fastest $\{$The fourth answer box just the number of fastest processor, $1,2,$ or $3\}?$

b$.$ If the processors each execute a program in $10$ seconds, find the number of instructions that they are running $\{$The answer boxes $5,6,$ and $7$ for processor $1,2,$ and $3$ respectively, in the format of d$.$dde$+$dd; e$.$g$.1\mathrm{.}79$e$+10\}?$ We are trying to reduce the execution time by $20\%$ but this leads to an increase of $10\%$ in the CPI. What clock rate in GHz should we have to get for this time reduction for each processor $\{$The last three answer boxes in order of processor numbers in format of d$.$d; e$.$g$.3\mathrm{.}1\}?$