Q$5$: Compute the run time of the following program

Line No Interpretation Program Instructions Number of cycles per instruction

$1$ Initialization Index $=01$ cycle

$2$ A Label; not an instruction Label: Start $0$ cycle

$3$ Lines $1-6$ are a FOR LOOP If Index $<1000,000,000$ then $2$ cycle

$4$ Sum $=$ Sum $+$ Index; $1$ cycle

$5$ Index $=$ Index $+1$; $1$ cycle

$6$ GoTo Label $1$ cycle

$7$ End

a$.$ Find the no of cycles required for the First iteration of the For loop. $[10$ pts$]$

Note you have to include the cycle count of Initialization.

No$.$ of cycles for first iteration of FOR loop $=1($for initialization$)+2($for if condition comparison$)+1($for calculating sum$)+1($for updating index variable$)+1($for going back to label$)=6$ cycles

b$.$ What is the total number of cycles used by the above program? $[10$ pts$]$

Total no$.$ of cycles $=$ no$.$ of cycle for initialization of index variable $+($no$.$ of iterations of FOR loop $*$ number of cycles in one iteration FOR loop$)=1+(1,000,000,000*5)=5,000,000,001$ cycles $=5*109$ cycles

c$.$ Calculate the time taken by above program in nano seconds for $1$ Ghz$,2$ GHz and $500$ MHz CPUs? $[30$ pts$]$

$($i$)$ Time taken in $1$ GHz CPU $=($time taken to complete one cycle $*$ total no$.$ of cycles$)=1*5,000,000,001=5,000,000,001$ nano$-$seconds $=5$ seconds $($approx$.)$

$($ii$)$ Time taken in $2$ GHz CPU $=0\mathrm{.}5*5,000,000,001=2,500,000,000\mathrm{.}5$ nano$-$seconds $=2\mathrm{.}5$ seconds $($approx$.)$

$($iii$)$ Time taken in $500$ MHz $=2*5,000,000,001=10,000,000,002$ nano$-$seconds $=10$ seconds $($approx$.)$