We can divide the binary number 1000012 by 1102 using the same technique as long division in the decimal system.



  1. First, we need to find the smallest part of the dividend that is greater than the divisor 1102. Since our divisor has three digits, we begin by examining the first three digits of the dividend. 1002 is less than 1102 so we need to add another digit from our dividend.
           
 110|100001
  1. Next we try the first four digits of the dividend. Since 10002 is greater than 1102 we know we can do our division.
           
 110|100001
 
  1. 1102 divides 10002 one time, so we write a 1 as the first digit of our quotient, copy the divisor below the dividend, and subtract using the borrow method.
        1  
 110|100001
      110
       10
  1. Now we bring down the next digit of our dividend and write it beside our remainder. Then we check to see if this new number is greater than or equal to our divisor.
        1  
 110|100001
      110
       100
  1. 1002 is less than 1102 so we write a 0 in the quotient and add another digit to our reminder.
        10 
 110|100001
      110
       1001 
  1. 10012 is greater than 1102 so we write a 1 in the quotient and subtract 1102 from 10012.
        101
 110|100001
      110
       1001
        110
         11
  1. Note that we still have a remainder after considering all the digits of the dividend. This means our answer will include a fraction. To finish our problem we need to mark the radix point and append a zero to the dividend.
        101. 
 110|100001.0
      110
       1001
        110
         11
  1. Now we bring down the extra zero and compare the remainder with our divisor. Notice we ignore the radix point in our comparison. 1102 equals 1102 so we write another 1 in the quotient and subtract. This completes our division because we have no more digits in the dividend and no remainder.
        101.1
 110|100001.0
      110
       1001
        110
         110
         110
           0

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