Given two processors P$1$ and P$2$ executing the same instruction set. P$1$ has a $2$GHz

clock rate and CPI of $2\mathrm{.}5.$ P$2$ has a $3$GHz clock rate and a CPI of $1\mathrm{.}0.$ Answer the

following questions

a$)$ What is the clock period of P$1$ in picoseconds?

b$)$ If P$2$ takes $10$ seconds to execute the program, what is the number of

instructions in the program $($in billions$)?$

c$)$ Which processor has the highest performance in instructions$/$second $($P$1$ or P$2)?$

Assume for a given program $70\%$ of the executed instructions are arithmetic, $10\%$ are

load$/$store$,$ and $20\%$ are branch.

d$)$ Given the assumption that an arithmetic instruction requires $2$ cycles, a

load$/$store instruction takes $6$ cycles and a branch instruction takes $3$ cycles, find

the average CPI