$3$a$.$ Consider choosing between two different compilers, A and B$,$ to run the same high$-$level program. The program compiled using compiler A results in $1$ billion instructions and has an execution time of $1\mathrm{.}1$ seconds. The program compiled using compiler B results in $1\mathrm{.}2$ billion instructions and an execution time of $1\mathrm{.}5$ seconds. If the compiled programs run on $1$ GHz processors, what is the average CPI for the programs compiled using compiler A and compiler B$?$

$3$b$.$ Assume the compiled programs using compiler A and B run on two different processors that have different clock cycle times but the same CPIs from part A$.$ If the execution times on the two processors are the same, how much faster is the clock of the processor running compiler A$\text{'}$s code versus the clock of the processor running compiler B$\text{'}$s code?

$4.$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 $5$ billion instructions. P$2$ has a clock rate of $3$ GHz$,$ an average CPI of $0\mathrm{.}75,$ and requires the execution of $1$ billion instructions.

$4$a$.$ One usual fallacy is to consider the computer with the largest clock rate as having the highest performance. Is this true for P$1$ and P$2?$

$4$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 $1$ billion 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 $1$ billion instructions.

$4$c$.$ A common fallacy is to use MIPS to compare the performance of two different processors, and consider that the processor with the largest MIPS has the largest performance. Is this true for P$1$ and P$2?$