Q$2(20$ points$)$

Assume for arithmetic, load$/$store$,$ and branch instructions, a processor has CPIs of $1,12,$ and $5,$ respectively. Also assume that on a single processor a program requires the execution of $2\mathrm{.}56E9$ arithmetic instructions, $1\mathrm{.}28$E$9$ load$/$store instructions, and $256$ million branch instructions. Assume that each processor has a $2GHz$ clock frequency.

Assume that, as the program is parallelized to run over multiple cores, the number of arithmetic and load$/$store instructions per processor is divided by $0\mathrm{.}7p($where $p$ is the number of processors$)$ but the number of branch instructions per processor remains the same

$1-$ Find the total execution time for this program on $1,2,4,$ and $8$ processors, and show the relative speedup of the $2,4,$ and $8$ processor result relative to the single processor result.

$2-$ If the CPI of the arithmetic instructions was doubled, what would the impact be on the execution time of the program on $1,2,4,$ or $8$ processors?

$3-$ To what should the CPI of load$/$store instructions be reduced in order for a single processor to match the performance of four processors using the original CPI values?