I need assistance with my C++ calculator code...there has to be an easier way

I am writing code for a big integer calculator...this seems to be a hot topic.  The code below is what I have started with.  I am getting stumped when it comes to how to get this program to output a large number without eliminating the extra zeros. ex...100000000 + 100000000.  This program is only a rough draft (not too user friendly).   Essetially it takes input in type char - changes it to sets of 3 int. then adds the sets of 3 int then outputs into someform...this is where I have the problem.  

Thanks for your help..

ps...the extra cout's are for debugging only. I have not removed them because I have not figured out
how to make this thing work yet.
/*
*
*
*******************************************************************************/

#include <iostream>
#include <vector>
#include <string>
#include <sstream>


using namespace std;
int charToInt(char a);

int main()
{
      cout << "Enter a really big number:  ";
      char num;
      vector<char> bigNum;
      vector<char> bigNum1;
      vector<int> bigIntX;
      vector<int> bigIntY;
      vector<int> bigAnswer;
      ostringstream ostr;
      int sum = 0, y = 0, x = 0,
            bigSum = 0, rem = 0,
            repeat = 1;
      
      for(;;)
      {
            cin >> num;
            if (num == '+' ) break;
            bigNum.push_back(num);
      }

      int find = bigNum.size() - 1;
      
      for (int n = 0; n <= find ; n++)
      {
                  char numb = bigNum[find - n];
      
                  x = x * 10;
                  if (x < 1)
                        x++;
                  sum += x * (charToInt(numb));
                  
                  
                  if (repeat == 3)
                  {
                        if ( cin.eof())break;
                        bigIntX.push_back(sum);
                        sum = 0;
                        x = 0;
                        repeat = 0;
                  }

                  
                  if (n == find && repeat != 3 && sum > 0)
                        bigIntX.push_back(sum);

                  cout << repeat;
                  repeat++;

                  
      }
      
      cout << "\nEnter another big number:  ";

      for(;;)
      {
            cin >> num;
            if (num == '+' ) break;
            bigNum1.push_back(num);
      }

      int find2 = bigNum1.size() - 1;
      sum = 0;
      x = 0;
      repeat = 1;

      for (int m = 0; m <= find2 ; m++)
      {
                  char numb = bigNum1[find2 - m];
                        
                  x = x * 10;
                  if (x < 1)
                        x++;
                  sum += x * (charToInt(numb));
                  
                  if (repeat == 3)
                  {
                        if ( cin.eof())break;
                        bigIntY.push_back(sum);
                        sum = 0;
                        x = 0;
                        repeat = 0;
                  }
                  
                  if (m == find2 && repeat != 3 && sum > 0)
                        bigIntY.push_back(sum);

                  cout << repeat << " " << bigIntY.size() << "bsize ";
                  repeat++;
      }
      int sizeBig = 0;

      if (bigIntX.size() >= bigIntY.size())
            sizeBig = bigIntX.size() - 1;
      if (bigIntY.size() > bigIntX.size())
            sizeBig = bigIntY.size() - 1;
      cout << " " << sizeBig << "szbig";

      for (int i = 0; i <= sizeBig ; i++)
            {
                  bigSum = bigIntX[i] + bigIntY[i] + rem;
                  rem = 0;
                  if (bigSum > 1000){
                        bigSum = bigSum - 1000;
                        rem++;}                  
                  
                  if (bigSum < 1){
                        bigAnswer.push_back(0);}
                  else if (bigSum < 10){
                        cout << "not supposed to come out here";
                        bigAnswer.push_back(bigSum);}
                  else if (bigSum < 100){
                        bigAnswer.push_back(bigSum);}
                  else
                        bigAnswer.push_back(bigSum);
                  cout << bigSum << "\n";

      }

      for (int k = sizeBig; k >= 0 ; k--)
            cout << bigAnswer[k];


      
            
                  
      
                        
      
      
}


/****************************************************************************************


****************************************************************************************/
int charToInt(char a)
{
            switch (a)
                  {
                  case '1':
                        return 1;
                  case '2':
                        return 2;
                  case '3':
                        return 3;
                  case '4':
                        return 4;
                  case '5':
                        return 5;
                  case '6':
                        return 6;
                  case '7':
                        return 7;
                  case '8':
                        return 8;
                  case '9':
                        return 9;
                  case '0':
                        return 0;
                  default:
                        cerr << "\nThere was an error in the number entered.";
            }
}