adding two strings as numbers

#include <iostream>
#include <string>
using namespace std;

string remove_zeroes(string a)
{
    string b;
    int length = a.length();
    int n_zero_pos = length;
    for(int i = 0; i < length; i++)
        if(a[i] != '0')
        {
            n_zero_pos = i;
            break;
        }
    if(n_zero_pos == length) return "0";

    for(int i = n_zero_pos; i < length; i++)
        b += a[i];
    return b;
}

string adding(string, string);
string str_reverse(string a)
{
    string b;
    for(int i = a.length()-1; i >= 0; i--)
        b += a[i];
    return  b;
}

int main()
{
    cout << adding("999", "11764") << endl;
    return 0;
}

string adding(string a, string b)
{
    int length = max(a.length(), b.length());
    a = str_reverse(a);
    b = str_reverse(b);
    if(a.length() != b.length())
        ((a.length() > b.length()) ? (b) : (a)).resize(length, '0');
    string c;
    c.resize(length + 1);

    for(int i = 0; i < length; i++)
        c[i] = a[i] - '0' + b[i];

    for(int i = 0; i < length; i++)
        if(c[i] > '9')
        {
            c[i] -= 10;
            c[i+1]++;
        }
    c[length] += '0';
    return remove_zeroes(str_reverse(c));
}