gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000001000000000000000000000000000000 a = 0x0000000040000000 a = x³⁰
b = b0000000000000000000000000000000000000000000001101010101111101101 b = 0x000000000006abed b = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
1000000000000000000000000000000 | 1101010101111101101 - 1101010101111101101 | 1 ------------------------------- | 101010101111101101000000000000 | - 1101010101111101101 | 1 ------------------------------- | 11111111000011011100000000000 | - 1101010101111101101 | 1 ------------------------------- | 101010011100000110000000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ------------------------------- | 11111001011110000100000000 | - 1101010101111101101 | 1 ------------------------------- | 101100000001011110000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ------------------------------- | 11001010110101000100000 | - 1101010101111101101 | 1 ------------------------------- | 11111101010011110000 | - 0000000000000000000 | 0 - 0000000000000000000 | 0 - 1101010101111101101 | 1 ------------------------------- | 101000001100101010 | - 0000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000001110110110010 c_quotient = 0x0000000000001db2 c_quotient = x¹² + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁵ + x⁴ + x
c_remainder = b0000000000000000000000000000000000000000000000101000001100101010 c_remainder = 0x000000000002832a c_remainder = x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁵ + x³ + x