Consider three different processors P$1,$ P$2,$ and P$3$ executing the same instruction

set.

P$1$ has a $3$ GHz clock rate and a CPI of $1\mathrm{.}5$

P$2$ has a $2\mathrm{.}5$ GHz clock rate and a CPI of $1\mathrm{.}0$

P$3$ has a $4\mathrm{.}0$ GHz clock rate and has a CPI of $2\mathrm{.}2.$

a$.$ Which processor has the highest performance expressed in instructions per second?

b$.$ If the processors each execute a program in $10$ seconds, find the number of cycles

and the number of instructions for each processor.

c$.$ For processor P$1,$ we are trying to reduce the execution time by $30\%$ but this leads to

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

reduction?