We are running programs on a machine where values of type int have a $32-$bit $2\text{'}$s$-$complement

representation. Values of type float use the $32-$bit IEEE format, and values of double use the

$64-$bit IEEE format. We generate arbitrary integer values $x,y,$ and $z,$ and convert them to values

of type double as follows:

$/*$ Create some arbitrary values $*/$

int x $=$ random$()$;

int y $=$ random$()$;

int z $=$ random$()$;

$/*$ Convert to double $*/$

double dx $=($double$)$ x;

double dy $=($double$)$ y;

double dz $=($double$)$ z;

For each of the following expressions, you are to indicate whether or not the expression always

yields $1.$ If it always yields $1,$ describe the underlying mathematical principles. Otherwise, give an

example of arguments that make it yield $0.$

A$.($double$)($float$)x==dx$

B$.$ double