gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000001001111000101010011001
a = 0x0000000000278a99
a = x21 + x18 + x17 + x16 + x15 + x11 + x9 + x7 + x4 + x3 + 1

b = b0000000000000000000000000000000000000000000000000000000011000001
b = 0x00000000000000c1
b = x7 + x6 + 1

  1001111000101010011001 | 11000001
- 11000001               | 1
  ---------------------- |
   101111100101010011001 |
-  11000001              | 1
  ---------------------- |
    11111110101010011001 |
-   11000001             | 1
  ---------------------- |
      111111101010011001 |
-    00000000            | 0
-     11000001           | 1
  ---------------------- |
        1111111010011001 |
-      00000000          | 0
-       11000001         | 1
  ---------------------- |
          11111110011001 |
-        00000000        | 0
-         11000001       | 1
  ---------------------- |
            111111011001 |
-          00000000      | 0
-           11000001     | 1
  ---------------------- |
              1111001001 |
-            00000000    | 0
-             11000001   | 1
  ---------------------- |
                11001101 |
-              00000000  | 0
-               11000001 | 1
  ---------------------- |
                    1100 |

cquotient = b0000000000000000000000000000000000000000000000000111010101010101
cquotient = 0x0000000000007555
cquotient = x14 + x13 + x12 + x10 + x8 + x6 + x4 + x2 + 1

cremainder = b0000000000000000000000000000000000000000000000000000000000001100
cremainder = 0x000000000000000c
cremainder = x3 + x2