For each function below, trace through it with reasonably small integer values $($give the trace results as numbers in base $10).$ What does each function do $($give a high$-$level summary$)?$

Requirement: You should assume integers are only $8$ bits for the purpose of this exercise. The sign bit is the leftmost of the $8$ bits.

int mystery$1($int a$,$ int b$)\{$

int c $=$ a $-$ b$,$

d $=($c $>>7)$ & $1,$

mystery $=$ a $-$ c $*$ d;

return mystery;

$\}$

Trace: mystery$1(3,7)$ returns $\_\_\_\_\_\_$

Trace: mystery$1(8,7)$ returns $\_\_\_\_\_\_$

Summary: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

int mystery$2($int x$)\{$

return $($x && $!($x & $($x $-1)))$;

$\}$

Trace: mystery$2(1)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(2)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(3)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(4)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(5)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(6)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(7)$ returns $\_\_\_\_\_\_$

Trace: mystery$2(8)$ returns $\_\_\_\_\_\_$

Summary: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

int mystery$3($int x$,$ int y$)\{$

int s$,$ c;

s $=$ x $^$ y;

c $=$ x & y;

while $($c $!=0)\{$

c $=$ c $<<1$;

x $=$ s;

y $=$ c;

s $=$ x $^$ y;

c $=$ x & y;

$\}$

return s;

$\}$

Trace: mystery$3(5,7)$ returns $\_\_\_\_\_\_$

Trace: mystery$3(2,8)$ returns $\_\_\_\_\_\_$

Summary: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$