A processor running at $1\mathrm{.}8$ GHz executes a program with the following instruction mix:

$-50\backslash \%$ Integer $\backslash ($ A L U$($C P I$=1)\backslash )$

$-15\backslash \%$ Floating point $($CPI $=4)$

$-\backslash (20\backslash \%\backslash )$ Load $\backslash (/5\backslash )$ tore $($CPI $=2)$

$-15\backslash \%$ Control flow $($CP$)=2$

The program needs to execute $5$ million instructions.

Calculate the following and make sure if entering decimals that they are rounded to two decimal places:

$1.$ The average CPI

$($percentages x CPI$)$

$2.$ Total execution time in milliseconds

ms $($instructions $\backslash (\backslash$times $\backslash )$ CPI x clock period$)$

$3.$ If floating point CPI is improved to $2,$ what percentage improvement in execution time would we achieve?

Important Note About Units in CPU Calculations

Before solving CPU performance problems, it's crucial to understand how to handle units properly:

When given a processor frequency in GHz $,$ convert it to a clock period in nanoseconds $($ ns $)$:

$-$ Clock Period $=\backslash (1/\backslash )$ Frequency

$-$ Example: For $\backslash (7\backslash$mathrm$\{$GHz$\}\backslash$rightarrow $1/7\backslash$mathrm$\{$GHz$\}=0\mathrm{.}143\backslash$mathrm$\{$~ns$\}\backslash )$

$-$ This conversion is important because execution time calculations multiply clock period $\backslash (\backslash$times $\backslash )$ CPI $\backslash (\backslash$times $\backslash )$ instruction count

$-$ Using GHz would give incorrect results due to the scale of the numbers involved

When reporting final answers follow these guidelines:

$-$ Use nanoseconds $($ns$)$ for calculations to maintain precision

$-$ For innal answers:

$-$ Use microseconds $(\backslash (\backslash$mu $\backslash$mathrm$\{$s$\}\backslash ))$ if the result is between $1,000$ ns and $999,999$ ns

$-$ Use milliseconds $($ ms $)$ if the result is $1,000,000$ ns or more

$-$ Keep nanoseconds if the result is less than $1,000$ ns