$1.$ Comparing Performance Characteristics of Two Computing Systems: $(5$ points$)$

Computing system #$1$ has a single issue, scalar, in$-$order pipeline and a system clock rate

of $3$ GHz$.$ It is being used to run a vector multiply$-$add $($axpy$)$ benchmark with a $10,000$

element, $32-$bit, integer data type vector. The benchmark executes at a sustained rate of

$10$ cycles per arithmetic operation $($CPO $=10).$ Assume there is no $($zero$)$ overhead$/$penalty

for memory fetches.

Computing system #$2$ is also a single issue, scalar, in$-$order pipeline machine. It has a

clock rate of $4\mathrm{.}1$ GHz$,$ and different architecture which will execute the benchmark at $8$

cycles per arithmetic operation $($CPO $=8).$

$($a$)$ What will the execution time be for the vector multiply add benchmark when it is run

on computing system #$2?$ Show all the steps used to evaluate the execution time,

and clearly state any additional assumptions you make in your analysis.

$($b$)$ What will the speed up of Computing System #$2$ relative to Computing

System #$1$ be $?$ Show all the steps used to evaluate the execution time, and clearly

state any additional assumptions you make in your analysis.