We can calculate binary division problems using the same technique as long division in the decimal system. It will be helpful to review some of the basic terms for division. Consider the division problem below.

In this problem, the red 6 is the divisor, the blue 33 is the dividend, the black 5 is the quotient, and the green 3 is the remainder. We will use these same terms to describe how binary division is done.
   5
6|33
  30
   3

Now let's look at a simple division problem in binary: 112 / 102 or 310 / 210. This time 102 is the divisor and 112 is the dividend. The steps below show how to find the quotient which is 1.12.

  1. First, we need to find the smallest part of our dividend that is greater than or equal to our divisor. Since our divisor has two digits, we start by checking the first two digits of the dividend.
      
 10|11
  1. 11 is greater than 10, so we write a 1 in the quotient, copy the divisor below the dividend, and subtract using the borrow method.
     1
 10|11
    10
     1
  1. Since we have no more digits in our dividend, but we still have a remainder, our answer must include a fraction. To finish our problem we need to mark the radix point and append a zero to the dividend.
     1. 
 10|11.0
    10
     1
  1. Now we bring down the extra zero and write it beside our remainder. Then we check to see if this new number is greater than or equal to our divisor. Notice we ignore the radix point in our comparison.
     1. 
 10|11.0
    10
     10
  1. 10 equals the divisor 10, so we write a 1 in the quotient, copy the divisor below the dividend, and subtract. This completes our division because we have no more digits in the dividend and no remainder.
     1.1
 10|11.0
    10
     10
     10
      0

When doing binary division, we need to remember some important rules:

  1. When the remainder is greater than or equal to the divisor, write a 1 in the quotient and subtract.
  1. When the remainder is less than the divisor, write a 0 in the quotient and add another digit from the dividend.

  2. If all the digits of the dividend have been considered and there is still a remainder, mark a radix point in the dividend and append a zero. Remember that some fractions do not have an exact representation in binary, so not all division problems will terminate.

The animation below demonstrates these rules by explaining how to divide 1000012 by 1102. Click on the "Start Tutorial" button to view the animation.

Text-only version