You are evaluating three processors P$1,$ P$2,$ and P$3$ for a specific task. They

share the same instruction set architecture $($ISA$),$ but have different

performance characteristics:

$$ P$1$: Clock rate $=3\mathrm{.}5$ GHz$,$ CPI $=1\mathrm{.}2$

$$ P$2$: Clock rate $=2\mathrm{.}8$ GHz$,$ CPI $=0\mathrm{.}8$

$$ P$3$: Clock rate $=4\mathrm{.}0$ GHz$,$ CPI $=1\mathrm{.}9$

a$)$ Calculate the MIPS $($Million Instructions Per Second$)$ rating for each

processor.

b$)$ If each processor executes a benchmark program consisting of $5$ billion

instructions, determine the execution time for each.

c$)$ You want to improve P$1\text{'}$s performance to match P$2\text{'}$s execution time for

the same benchmark program. Assuming you can only adjust the clock

rate, what should the new clock rate of P$1$ be$?$