I would do something like this;

// Convert from ascii hex representation to binary
// Examples;
//   "00" -> 0
//   "2a" -> 42
//   "ff" -> 255
// Case insensitive, 2 characters of input required, no error checking
int hex2bin( const char *s )
{
    int ret=0;
    int i;
    for( i=0; i<2; i++ )
    {
        char c = *s++;
        int n=0;
        if( '0'<=c && c<='9' )
            n = c-'0';
        else if( 'a'<=c && c<='f' )
            n = 10 + c-'a';
        else if( 'A'<=c && c<='F' )
            n = 10 + c-'A';
        ret = n + ret*16;
    }
    return ret;
}

int main()
{
    const char *in = "0011223344";
    char out[5];
    int i;

    // Hex to binary conversion loop. For example;
    // If in="0011223344" set out[] to {0x00,0x11,0x22,0x33,0x44}
    for( i=0; i<5; i++ )
    {
        out[i] = hex2bin( in );
        in += 2;
    }
    return 0;
}

You'll never convince me that this operation is a performance bottleneck. The efficient way is to make good use of your time by using the standard C library:

static unsigned char gethex(const char *s, char **endptr) {
  assert(s);
  while (isspace(*s)) s++;
  assert(*s);
  return strtoul(s, endptr, 16);
}

unsigned char *convert(const char *s, int *length) {
  unsigned char *answer = malloc((strlen(s) + 1) / 3);
  unsigned char *p;
  for (p = answer; *s; p++)
    *p = gethex(s, (char **)&s);
  *length = p - answer;
  return answer;
}

Compiled and tested. Works on your example.

How can I modify this function so that it returns a string?

You can print to a string variable using sprintf. I assume the hash size is fixed, so you know the size of your string would be number-of-chars-in-hash * 2 + 1. How to return that information is a typical problem in C, you can either return a malloced string that the user must then remember to free, or return a static string that will get replaced with the next call to the function (and makes the function non-reentrable). Personally I tend to avoid returning strings, instead having the function take a char* destination and a size.

(The goal being that I can compare the 2 values later)

Just compare the two hash variables in its raw form, you don't need strings for that.

Convert each character to an unsigned character (so the 0xc0 isn't negative), then convert it to an integer and output as a two digit hexadecimal value.

#include <stdlib.h>
#include <stdio.h>


#define INT(x) ((int)(unsigned char)(x))

int main()
{
     char arr[4];
     arr[0] = 0x11;
     arr[1] = 0xc0;
     arr[2] = 0x0c;
     arr[3] = 0x00;

     char *str;

     str=malloc(32);
     sprintf(str, "%02x%02x%02x%02x",
         INT(arr[0]), INT(arr[1]), INT(arr[2]), INT(arr[3]));

     puts(str);
}

Output is:

11c00c00

For completude, you can also easily do it without calling any heavy library function (no snprintf, no strcat, not even memcpy). It can be useful, say if you are programming some microcontroller or OS kernel where libc is not available.

Nothing really fancy you can find similar code around if you google for it. Really it's not much more complicated than calling snprintf and much faster.

#include <stdio.h>

int main(){
    unsigned char buf[] = {0, 1, 10, 11};
    /* target buffer should be large enough */
    char str[12];

    unsigned char * pin = buf;
    const char * hex = "0123456789ABCDEF";
    char * pout = str;
    int i = 0;
    for(; i < sizeof(buf)-1; ++i){
        *pout++ = hex[(*pin>>4)&0xF];
        *pout++ = hex[(*pin++)&0xF];
        *pout++ = ':';
    }
    *pout++ = hex[(*pin>>4)&0xF];
    *pout++ = hex[(*pin)&0xF];
    *pout = 0;

    printf("%s\n", str);
}

Here is another slightly shorter version. It merely avoid intermediate index variable i and duplicating laste case code (but the terminating character is written two times).

#include <stdio.h>
int main(){
    unsigned char buf[] = {0, 1, 10, 11};
    /* target buffer should be large enough */
    char str[12];

    unsigned char * pin = buf;
    const char * hex = "0123456789ABCDEF";
    char * pout = str;
    for(; pin < buf+sizeof(buf); pout+=3, pin++){
        pout[0] = hex[(*pin>>4) & 0xF];
        pout[1] = hex[ *pin     & 0xF];
        pout[2] = ':';
    }
    pout[-1] = 0;

    printf("%s\n", str);
}

Below is yet another version to answer to a comment saying I used a "trick" to know the size of the input buffer. Actually it's not a trick but a necessary input knowledge (you need to know the size of the data that you are converting). I made this clearer by extracting the conversion code to a separate function. I also added boundary check code for target buffer, which is not really necessary if we know what we are doing.

#include <stdio.h>

void tohex(unsigned char * in, size_t insz, char * out, size_t outsz)
{
    unsigned char * pin = in;
    const char * hex = "0123456789ABCDEF";
    char * pout = out;
    for(; pin < in+insz; pout +=3, pin++){
        pout[0] = hex[(*pin>>4) & 0xF];
        pout[1] = hex[ *pin     & 0xF];
        pout[2] = ':';
        if (pout + 3 - out > outsz){
            /* Better to truncate output string than overflow buffer */
            /* it would be still better to either return a status */
            /* or ensure the target buffer is large enough and it never happen */
            break;
        }
    }
    pout[-1] = 0;
}

int main(){
    enum {insz = 4, outsz = 3*insz};
    unsigned char buf[] = {0, 1, 10, 11};
    char str[outsz];
    tohex(buf, insz, str, outsz);
    printf("%s\n", str);
}

This should work:

    char hex[255] = {0};       // Varible to hold the hex value
    int dec = 1234;            // Decimal number to be converted
    sprintf(hex,"%X", dec);
    printf("%s", hex);         // Print hex value