CRC calculate quotient

Question

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.

Answer 1

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 $1$.