A method for determining the first m digits $0.$b$1$b$2$b$3...$bm of the binary representation of a real number

x in $(0,1)$ is the following algorithm:

c $<-$ x

for j from $1$ to m do

b$[$j$]<-$ floor$(2*$c$)$

c $<-2*$c $-$ b$[$j$]$ where floor$($x$)$ is the greatest integer less than or equal to the real number x$,$ and $*$ represents

multiplication.

$($a$)$ Explain how this algorithm works.

$($b$)$ Write a C function that implements this algorithm. The prototype of your function should be

void get$\_$binary$($double x$,$ int$*$ b$,$ int m$)$;

where x is the real number in double precision floating point representation, b is the starting

address of an array of integers, and m is the number of digits we want to obtain. You will need

to include the header file $$math$.$h$$; also include the $$stdio$.$h$$ header:

#include

#include

Test your function with the following $$main$$ function:

int main$()\{$

int b$[30]$;

get$\_$binary$(0\mathrm{.}1,$ b$,30)$;

for$($int i $=0$; i $<30$; i$++)\{$

printf$("\%$d$",$ b$[$i$])$;

$\}$

return $0$;

$\}$

PLEASE NOTE: Even though the pseudo$-$code representation of the algorithm indexes the array of

digits starting at $1,$ C$/$C$++$ always starts indexing at $0.$ Make sure to write your code so that the

calculations are performed correctly.