$1\mathrm{.}13$ Section $1\mathrm{.}11$ cites as a pitfall the utilization of a subset of the performance equation as a performance metric. To illustrate this, consider the following two processors. P$1$ has a clock rate of $4GHz,$ average $\frac{C}{P}$I of $0\mathrm{.}9,$ and requires the execution of $5\mathrm{.}0$E$9$ instructions. P$2$ has a clock rate of $3GHz,$ an average CPI of $0\mathrm{.}75,$ and requires the execution of $1\mathrm{.}0E9$ instructions.

$1\mathrm{.}13\mathrm{.}1[5]$$$$1\mathrm{.}6,1\mathrm{.}11>$ 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$2.$

$1\mathrm{.}13\mathrm{.}2[10]($:$$$1\mathrm{.}6,1\mathrm{.}11$:$)$ Another fallacy is to consider that the processor executing the largest number of instructions will need a larger CPU time. Considering that processor $P1$ is executing a sequence of $1\mathrm{.}0E9$ instructions and that the CPI of processors $P1$ and P$2$ do not change, determine the number of instructions that $P2$ can execute in the same time that $P1$ needs to execute $1\mathrm{.}0E9$ instructions.

$1\mathrm{.}13\mathrm{.}3[10]$$$$1\mathrm{.}6,1\mathrm{.}11$: A 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 $P1$ and $P2.$