Consider the following two processors. P$1$ has a clock rate of $4$GHz$,$ average CPI of $0\mathrm{.}9,$ and requires the

execution of $5\mathrm{.}0$E$9$ instructions. P$2$ has a clock rate of $3$GHz$,$ an average CPI of $0\mathrm{.}75,$ and requires the

execution of $1\mathrm{.}0$E$9$ instructions.

a$)$ One usual fallacy is to consider the computer with the largest clock rate as having the highest

performance. Check if this is true for P$1$ and P$2.$

b$)$ Another fallacy is to consider that the processor executing the largest number of instructions will

need a larger CPU time. Considering that processor P$1$ is executing a sequence of $1\mathrm{.}0$E$9$

instructions and that the CPI of processors P$1$ and P$2$ do not change, determine the number of

instructions that P$2$ can execute in the same time that P$1$ needs to execute $1\mathrm{.}0$E$9$ instructions.

c$)$ Common fallacy is to use MIPS $($millions of instructions per second$)$ to compare the performance

of two different processors, and consider that the processor with the largest MIPS has the

largest performance. Check if this is true for P$1$ and P$2.$