Multiplication in Binary Calculation

On the term test 1, I found that for addition and multiplication in binary calculation, I got them mixed up.

For instance, for multiply 15 with 19, I used to think in this way :  

1 1 1 1

 X   1 0 0 1 1

_______________

         1 0 0 0 1 0    

That’s wrong. Binary multiplication should multiply non-negative integers first, and then use additional operations. So the answer for this question should be:

      1 1 1 1

X  1 0 0 1 1

__________________

       1 1 1 1

     1 1 1 1

   0 0 0 0

0 0 0 0

    +  1 1 1 1

____________________

      1 0 0 0 1 1 1 0 1