Processor P$1$ has a clock frequency of $2$ GHz$,$ average CPI of $0\mathrm{.}9,$ and executes $1$

billion instructions to complete a program. Processor P$2$ has a clock frequency of $3$ GHz$,$

average CPI of $0\mathrm{.}8,$ and executes $2$ billion instructions to complete a program.

a$)$ Compute the MIPS rating of P$1$ and P$2$

b$)$ A common fallacy is that a processor with a high clock frequency is better in terms of

performance. Check if this is true by comparing the execution times of the two

processors.