$1\mathrm{.}5[4]$ $$1\mathrm{.}6>$ 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.

c$.$ 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?

$1\mathrm{.}6[20]$ $$1\mathrm{.}6>$ Consider two different implementations of the same instruction

set architecture. The instructions can be divided into four classes according to

their CPI $($class A$,$ B$,$ C$,$ and D$).$ P$1$ with a clock rate of $2\mathrm{.}5$ GHz and CPIs of $1,2,3,$

and $3,$ and P $2$ with a clock rate of $3$ GHz and CPIs of $2,2,2,$ and $2.$

Given a program with a dynamic instruction count of $1\mathrm{.}0$E$6$ instructions divided

into classes as follows: $10\%$ class A$,20\%$ class B$,50\%$ class C$,$ and $20\%$ class D$,$

which implementation is faster?

a$.$ What is the global CPI for each implementation?

b$.$ Find the clock cycles required in both cases.