$(60$ points$)$ Performance $-$ CPU Time

a$)(10$ points$)$ Suppose you wish to run a program $P$ with $5^{**}{10}^9$ instructions on a $3GHz$ machine

with a CPI of $2\mathrm{.}3.$ What is the expected CPU time?

b$)(10$ points$)$ Suppose you have the following instruction mix for program $P.$ What is the CPI?

c$)(10$ points$)$ Consider two different processors P$1$ and P$2$ executing the same instruction set

with the clock rates and CPIs given the following table. If the processors each execute a

program in $15$ seconds, find the number of cycles and number of instructions for each

processor.

d$)(10$ points$)$ Using the same settings as c$)$: in terms of CPU time, which processor of P$1$ and P$2$ is

faster, and by how many times?

e$)(20$ points$)$ Using the same settings as c$)$: we are trying to reduce the program execution by

$20\%,$ but this leads to an increase of $25\%$ in the CPI. What clock rate should we have to get this

time reduction. For each processor.