operator=() in base and derived class

Dear members of this group,

recently I came across a problem with repsect to operator=() and
inheritance. Consider the following code snippet:

------------------------------------------------------------
#include <iostream>

using namespace std;

class A
{
public:
  A & operator=(const A &_a) {
    cout << " in A" << endl;
  }
};

class B : public A
{
public:
  B & operator=(const A &_a) {
    cout << " in B" << endl;
    A::operator=(_a);
  }
};

main()
{
  B b1, b2;
  A a;

  b1=b2;

  cout << endl;

  b1=a;
}
----------------------------------------

If you run this program (compiled using gcc 3.3 and 4.1), the output
you get is:

-------------------
 in A

 in B
 in A
------------------

This means:
* for the assignment b1=b2, A::operator=() is invoked
* for b1=a, B::operator=() is invoked.

Now the solution to make the code behave as intended by me is to add
another function

  B & operator=(const B&_B) {
    cout << " in B" << endl;
    A::operator=(_b);
  }

However, I don't understand the reasons for this behaviour and I'd
like to understand that. What are the rationales behind that behaviour?