problem in calculating size of derived classes

Code:

class base
   { 
    private :
                int b;
   };
class derived : public base
    {
     private :
                int j;
    };
void main()
{
cout<<endl<<sizeof(derived)<<endl<<sizeof(base);
}

Output:
4
2
I think size of derived=sizeof(j)+sizeof(b).
Am I right or wrong?If I am wrong then please tell me how the size of derived class is
calculated.If I am right then tell me
Why the sizeof derived class is 4 when it is not inheriting the private member b of class base?