$10.(5$ points$)$ Trace the execution of the following function by hand $($attach screenshots of your trace work$).$ Then write a program that calls the function, passing it a number entered by the user. What does the function do$?$

$```$

void pb$($int n$)$

$\{$

if $($n $!=0)\{$

pb$($n $/2)$;

putchar$(\text{'}0\text{'}+$ n $\%2)$;

$\}$

$\}$

$```$

$11.(2$ points $($bonus$))$ The Fibonacci numbers are $\backslash (0,1,1,2,3\mathrm{.}5,8,13,\backslash$ldots $\backslash ),$ where each number is the sum of the two preceding numbers. Write a program fragment that declares an array named fib$\_$num bers of length $40$ and fills the array with the first $40$ Fibonacci numbers using iterative approach $($loops$).$ Hint: Fill in the first two numbers individually, then compute the rest.

i$)(3$ points $($bonus$))$ Write a recursive function to solve the above problem.