Consider three different processors $P1,P2,$ and $P3$ executing the same instruction set. $P1$ has a

$3\mathrm{.}1$ GHz clock rate and a CPI $($cycles per instruction$)$ of $1\mathrm{.}6.$ P$2$ has a $2\mathrm{.}4GHz$ clock rate and a CPI

of $1\mathrm{.}2.$ P$3$ has a $4\mathrm{.}0GHz$ clock rate and has a CPI of $1\mathrm{.}8.$

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.

c$.$ We are trying to reduce the execution time by $20\%$ but this leads to an increase of $10\%$

in the CPI. What clock rate should we have to get this time reduction?