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As above, i have absolutely no idea how to calculate the quotient (10110110). Some mentioned that there is no need for it, but my exams required me to understand how to get the quotient. Please help thanks.

user3807187
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2 Answers2

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The quotient has $1$'s exactly in the positions where you subtracted the number $110011_2$ from the remainder. That means the ones are corresponding to the (underlined) subtraction steps and $0$s are skipped subtractions (watch the indentation).

          _____________
   110011/1110001100000=10110110
 1        110011       |^^^^^^^^
           010111      | ||||||| 
 0         000000      |-'||||||
            101111     |  ||||||
 1          110011     |--'|||||
             111000    |   |||||
 1           110011    |---'||||
              010110   |    ||||
 0            000000   |----'|||
               101100  |     |||
 1             110011  |-----'||
                111110 |      ||
 1              110011 |------'|
                 011010|       |
 0               000000|-------'
                  11010 = CRC

Now for compactness, the $-0\cdot 110011_2$ steps were omitted, so sometimes the indentation increases by more than $1$.

AlexR
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  • to be honest, i still don't understand how to write the quotient. – user3807187 Mar 04 '15 at 20:50
  • @user3807187 Maybe you should check out some articles about long divison. In this special case, there is no carry though. See that a $1$-bit at a certain position means we subtract $$110011_2$ at that position and a $0$-bit means we "skip" the place and continue with the next (shown by "subtracting" $0\cdot110011_2 = 0$) – AlexR Mar 04 '15 at 20:54
  • hi i managed to understand the question. Thanks! – user3807187 Mar 05 '15 at 13:32
  • @user3807187 After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?. – AlexR Mar 05 '15 at 18:19
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This is exactly like ordinary long division, only simpler, because each stage we just need to check whether the leading bit of the current three bits is 0 or 1. If it's 0, we place a 0 in the quotient and XOR the current bits with 000.

Someone
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