Exercises

1. Complete the following table:

   
   
   

2. Invent an algorithm for multiplying two unsigned binary numbers. You may find it easiest to start by thinking about multiplication of decimal numbers (there are other ways as well, but you should start on familiar ground).

3. 1. Invent an algorithm for dividing two unsigned binary numbers. You may find it easiest to start by thinking about long division of decimal numbers.
   2. A user complains that the division algorithm you invented to solve the previous part of this problem is too slow. For her application, she would prefer an algorithm that gets an answer that is ``reasonably close'' to the right answer, but which may take considerably less time to compute. Invent an algorithm that has this property. Find the relationship between ``reasonably close'' and the speed of your algorithm.