Please answer all of the following questions clearly and show your work.$($Q $1\mathrm{.}5,1\mathrm{.}9,1\mathrm{.}14)$

Q$1(10$ points$)$

Consider three different processors $P1,P2,$ and $P3$ executing the same instruction set. P$1$ has a $3GHz$ clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}5GHz$ clock rate and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}0GHz$ clock rate and has a CPI of $2\mathrm{.}2.$

Which processor has the highest performance expressed in instructions per second?

If the processors each execute a program in $10$ seconds, find the number of cycles and the number of instructions.

$3.$ We are trying to reduce the execution time by $30\%$ but this leads to an increase of $20\%$ in the CPI. What clock rate should we have to get this time reduction?

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?

Q$3(20$ points$)$

Assume a program requires the execution of $50{10}^{6}FP$ instructions, $110{10}^6$ INT instructions, $80{10}^6\frac{L}{S}$ instructions, and $16{10}^6$ branch instructions. The CPI for each