This is one proposition of a C99 base_convert :

#include <stdlib.h>
#include <string.h>

static char *base_convert(const char * str, const int base_in, const int base_out) {
    static const char *alphabet = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
    size_t a, b, c = 1, d;
    char *s = malloc(c + 1);
    strcpy(s, "0");
    for (; *str; ++str) {
        for (a = (char*)memchr(alphabet, *str, base_out) - alphabet, b = c; b;) {
            d = ((char *) memchr(alphabet, s[--b], base_out) - alphabet) * base_in + a;
            s[b] = alphabet[d % base_out];
            a = d / base_out;
        }
        for (; a; s = realloc(s, ++c + 1), memmove(s + 1, s, c), *s = alphabet[a % base_out], a /= base_out);
    }
    return s;
}

Example usage :

#include <stdio.h>

int main() {
    const char a[] = "10000000000000000000000000000000000000000000000000000000"
                     "00000000000000000000000000000000000000000000000000000000"
                     "00000000000000000000000000000000000000000000000000000000"
                     "00000000000000000000000000000000000000000000000000000000";
    char *b = base_convert(a, 2, 10);
    puts(b);
    free(b);
}

It’s magic, example output :

13479973333575319897333507543509815336818572211270286240551805124608