gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000101000011
a = 0x0000000000000143
a = x8 + x6 + x + 1

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

  101000011 | 11000001
- 11000001  | 1
  --------- |
   11000001 |
-  11000001 | 1
  --------- |
          0 |

cquotient = b0000000000000000000000000000000000000000000000000000000000000011
cquotient = 0x0000000000000003
cquotient = x + 1

cremainder = b0000000000000000000000000000000000000000000000000000000000000000
cremainder = 0x0000000000000000
cremainder = 0