Q$.2$ Consider two different processors, P$1$ and P$2$ executing a program having $5$ billion $(5^{**}{10}^{{?}^{{?}^{?}}9})$ instructions

P$1$ has a $2\mathrm{.}5$ GHz clock rate and a CPI of $1\mathrm{.}5.$

P$2$ has a $3\mathrm{.}5$ GHz clock rate and a CPI of $1\mathrm{.}7.$

Which processor is faster, and by how much?

We are trying to reduce the CPU time of P$1$ by $25\%$ but this leads to an increase of $15\%$ in the CPI. What clock rate should we have to get this time reduction?

Q$\mathrm{.}3$: The clock of the processor runs at $2GHz.$ The following table gives the percentage for each instruction class from a total number of instructions, as well as how many average cycles the instructions take, for the different classes of instructions. The CPU time is exactly $22ms.$

$\backslash$table$[[$Instruction Type,$\%,$CPI$],[$Loads & Stores,$30\%,6$ cycles$],[$Arithmetic Instructions,$50\%,4$ cycles$],[$All Others,$20\%,3$ cycles$]]$

Calculate the total number of instructions.

The hardware expert says that if you double the number of registers, the clock cycle time must be decreased by $20\%.$ What would the new clock speed be $?$