int char2int(char c) {
     switch(c) {
          case '0': {
               return 0;
          }
          case '1': {
               return 1;
          }
          // ... and so on
     }
}

#include <iostream>
#include <string>
using namespace std;
 
int char2int(char c) {
   switch(c) {
      case '0': {
         return 0;
      }
      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;
      }
   }
}
 
int main() {
   string myBigNum;
   int myBigNumArray[20];
   cout << endl << "Enter the number" << endl;
   getline(cin, myBigNum);
   if(myBigNum.size()>20) {
      cout << endl << "You entered a number too big!" << endl;
      return EXIT_FAILURE;
   }
   for(unsigned int i = 0; i < myBigNum.size(); ++i) {
      myBigNumArray[i] = char2int(myBigNum[i]);
   }
   // now you have your number saved in the array
   // of course you'll need sign checking and a better input validation
   // but this is a start and it's simple
   return EXIT_SUCCESS;
}