Consider two different implementations, M$1$ and M$2,$ of the same instruction set

$($Number of Instructions $=10^9$ i$.$e $1,000,000,000).$ There are three classes of

instructions $($A$,$ B$,$ and C$)$ in the instruction set. M$1$ has a clock rate of $3$ GHz and M$2$ has a clock rate of $4$ GHz$.$ The average number of cycles for each instruction class and their frequencies $($for a typical program$)$ are as follows:

Instruction Class

M$1$ CPI

M$2$ CPI

Frequency

$2$

$2$

$40\%$

B

$1$

$3$

$30\%$

C

$4$

$3$

$30\%$

a$)$ Calculate the average CP$|$ for each machine, M$1$ and M$2$

b$)$ Calculate the execution time for each machine, M$1$ and M$2$ and state which o faster.

c$)$ By how much must we improve the CPI of Class A instructions if we want the program to run $40\%$ times faster on Machine M$1?$

Note: Please show work for all the questions above.