C:

Create a header file named binary$\_$string.h$.$ The header file should declare the following three functions:

char$*$ unsigned$\_$to$\_$binary$($unsigned x$)$;

unsigned binary$\_$to$\_$unsigned$($char$*$ str$)$;

char$*$ add$\_$binary$($char$*$ str$1,$ char$*$ str$2)$;

Be sure to include a header guard.

Write a C program named binary$\_$string.c$.$ That program should implement the following three functions:

char$*$ unsigned$\_$to$\_$binary$($unsigned x$)$

unsigned$\_$to$\_$binary$()$ takes an unsigned number and returns a c$-$style string of $\text{'}0\text{'}$ and $\text{'}1\text{'}$ characters that represents the binary representation of the argument. For example, unsigned$\_$to$\_$binary$(13)$ should return a pointer to a char array containing $\{\text{'}1\text{'},\text{'}1\text{'},\text{'}0\text{'},\text{'}1\text{'},\text{'}\backslash 0\text{'}\}$ and unsigned$\_$to$\_$binary$(257)$ should return a pointer to a char array containing $\{\text{'}1\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}0\text{'},\text{'}1\text{'},\text{'}\backslash 0\text{'}\}.$ Notice it stores only as many "bits" as necessary $($you can assume a max of $32$ bits $($plus the null character $\text{'}\backslash 0\text{'})).$ Note: unsigned$\_$to$\_$binary$()$ should call malloc$()$ to allocate enough space for the chars.

unsigned binary$\_$to$\_$unsigned$($char$*$ str$)$

binary$\_$to$\_$unsigned$()$ takes a pointer to a c$-$style string that holds a sequence of $\text{'}0\text{'}$ and $\text{'}1\text{'}$ characters and returns the unsigned representation.

char$*$ add$\_$binary$($char$*$ str$1,$ char$*$ str$2)$

add$\_$binary$()$ takes two char$*$ c$-$style binary strings and returns the sum as a binary string. You should not use the functions from the previous parts here. However, if you have helper functions that you wish to reuse, you may do so$,$ so long as they are in the spirit of what this task is asking you to do$.$

Add the "bits" from least significant to most significant, "carrying the one" when necessary. $($You can again assume a max size of $32$ bits. You should discard the overflow bit if the addition exceeds this max size.$)$

So$,$ if your helper functions $($say$)$ convert the entire string to numbers, add them, and turn the entire number back into one string, that does not count as solving this problem. Helper functions that do something useful in the spirit of the task $($like$,$ say, counting the digits of a c$-$style string$)$ would be fine and even encouraged.