$($Q$\mathrm{.}1)$ Consider two different processors, P$1$ and P$2,$ which implement the same instruction set

architecture. The instructions can be divided into four classes according to their CPI:

classes A$,$ B$,$ C$,$ and D$.$ P$1$ has a clock rate $(f_1)$ of $3\mathrm{.}5GHz$ and CPIs of $1,2,3,$ and

$2($associated with the given order of classes$),$ while P $2$ has a clock rate $(f_2)$ of $2\mathrm{.}5GHz$

and CPIs of $3,2,1,$ and $1,$ respectively.

We are given a program Y$,$ which has a dynamic instruction count $($IC$)$ of $2$ million

$({10}^6).$ The instruction distribution is as follows: $15\%$ class $A,20\%$ class $B,55\%$ class

C$,$ and $10\%$ class D$.$

$1.$a$)$ What is the effective CPI for program Y on $P1$ and $P2?$

$1.$b$)$ What is the CPU time when executing program Y on P$1$ and P$2?$ Which processor

is the fastest?

$1.$c$)$ What is the total number of elapsed clock cycles when executing program Y on P$1$

and P$2?$

$1.$d$)$ Defining performance as the number of instructions per second, compute the perfor$-$

mance for P$1$ and P$2.$

$1.$e$)$ We are trying to reduce the CPU time by $30\%,$ but this leads to an increase of $25\%$

on the CPI. What clock rate should we have for each processor?