$1.$ Consider running a program on a $3$ GHz processor in $10$ seconds.

$1$a$.$ If the CPI is $1\mathrm{.}5,$ what is the number of cycles and the number of instructions?

$1$b$.$ We are trying to reduce the execution time by $30\%$ but this leads to an increase of $10\%$ in the CPI. What clock rate should we have to get this time reduction?

$2.$ Consider running a program on two different processors, P$1$ and P$2,$ that implement the same instruction set architecture. P$1$ has a $2\mathrm{.}5$ GHz clock rate and P$2$ has a $3$ GHz clock rate. The program has $1$ million instructions, divided into three classes: A$,$ B$,$ and C$.10\%$ of the instructions are class A$,20\%$ are class B$,70\%$ are class C$.$ The CPIs of the three classes when running on P$1$ are $1,2,$ and $5,$ respectively. The CPIs of the three classes when running on P$2$ are $2,3,$ and $4,$ respectively.

$2$a$.$ What is the global or weighted average CPI for each processor?

$2$b$.$ What is the number of clock cycles required for each processor?

$2$c$.$Which processor is faster?