A processor with a clock rate of $2\mathrm{.}5$ GHz requires $0\mathrm{.}28$ seconds to execute the $175$ million instructions contained in a program.

a$)$ What is the average CPI $($cycles per instruction$)$ for this program?

b$)(3)$ Suppose that the processor$$s clock rate is increased, but the average CPI for the program rises to $5.$ With this average CPI of $5,$ what value is required for the higher clock rate to achieve an execution time of $0\mathrm{.}175$ seconds?

c$)(5)$ Suppose that the processor$$s clock rate remains $2\mathrm{.}5$ GHz and the CPI remains at $4,$ but the program is rewritten to reduce the number of instructions executed from $175$ million down to $159090910.$ What speedup does the rewritten program provide compared to the original program for which $175$ million instructions were executed? Express your answer to two decimal places.

$7.$ A C$++$ program is translated into machine code that runs on processor A and executes a total of $28$ million instructions. The machine code on processor A contains twelve million instructions with CPI $=2,$ seven million instructions with CPI$=3$ and nine million instructions with CPI$=4.$

The same C$++$ program is translated into machine code that runs on a different processor B$.$ The machine code on processor B executes $32$ million instructions. Ten million of the instructions have CPI $=1,$ seventeen million instructions have CPI$=2$ and five million instructions have CPI$=4.$ Processor A and processor B both run at a $2$ GHz clock rate.

a$)(3)$ What is the peak MIPS rating for the program that runs on processor A$?$ Express your answer to two decimal places.

b$)(3)$ What is the peak MIPS rating for the program that runs on processor B$?$ Express your answer to two decimal places.

c$)(3)$ What is the native MIPS rating for the program that runs on processor A$?$ Express your answer to two decimal places.