cin.eof() functionality

I understand that cin.eof() tests the stream format. And while giving input, end of character is not reached when there is wrong in the input. I tested this on my MSV C++ 2010 and am not understanding the strange results. No matter what I give the input, I am getting Format Error message that is present in the program.

#include <iostream>
using namespace std;

int main()
    int i;
    cin>> i;

        cout<< "\n Format Error \n";
        cout<< "\n Correct Input \n";

    return 0;

Results I expected:

Values for i =

  1. 10 => Correct Input but the output is Format Error
  2. 12a => Format Error

Could someone explain where I am going wrong. Thanks.

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