During the discussion of Iron Law in the classroom, we pointed out the pittfalls of using of only a subset of the parameters $($e$.$g$.,$ CPI, clock period, instruction count, etc$)$ as a performance metric to compare alternatives. To illustrate this, assume that we have two processors to compare: P$1$ and P$2.$ P$1$ has a clock rate of $4$GHz$,$ average CPI of $1\mathrm{.}8$ and $5,000,000$ instructions to execute a given program. On the other hand, P$2$ has a clock rate of $3$GHz$,$ average CPI of $1\mathrm{.}5$ and $1,000,000$ instructions to execute the same program.a$)[5$ points$]$ One mistake people often do is to consider the processor with the highest clock frequency would have the best performance. Calculate the performance of the given program on both processors and check if this is true for P$1$ and P$1.$b$)[5$ points$]$ Another mistake people often do is to consider that the processor executing more instructions would take longer time to finish. Considering that P$1$ is going to execute $1,000,000$ instructions, calculate the number of instructions that P$2$ is going to execute in the same amount of time $($CPIs remain the same$).$c$)[5$ points$]$ Yet another mistake people often do is to use MIPS $($millions of instructions per second$)$ as a metric to compare the processors and consider the processor with higher MIPS has better performance. Calculate the MIPS of each processor and chech if this is true for P$1$ and P$2.$d$)[5$ points$]$ Why do you think that we have different number of instructions needed on P$1$ and P$2$ for the same program given at the beginning? What are the implications of this on performance expectations for our programs? Please explain.