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

2. 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
 

3. 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

4. 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

5. 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 

6. 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

7. 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

8. 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