gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000100000000000000000000000000000000 a = 0x0000000100000000 a = x³²
b = b0000000000000000000000000000000000000000000001101010101111101101 b = 0x000000000006abed b = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
100000000000000000000000000000000 | 1101010101111101101 - 1101010101111101101 | 1 --------------------------------- | 10101010111110110100000000000000 | - 1101010101111101101 | 1 --------------------------------- | 1111111100001101110000000000000 | - 1101010101111101101 | 1 --------------------------------- | 10101001110000011000000000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 --------------------------------- | 1111100101111000010000000000 | - 1101010101111101101 | 1 --------------------------------- | 10110000000101111000000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 --------------------------------- | 1100101011010100010000000 | - 1101010101111101101 | 1 --------------------------------- | 1111110101001111000000 | - 0000000000000000000 | 0 - 0000000000000000000 | 0 - 1101010101111101101 | 1 --------------------------------- | 10100000110010101000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 --------------------------------- | 1110101101101110010 | - 1101010101111101101 | 1 --------------------------------- | 11111000010011111 |
c_quotient = b0000000000000000000000000000000000000000000000000111011011001011 c_quotient = 0x00000000000076cb c_quotient = x¹⁴ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁷ + x⁶ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000000000000000011111000010011111 c_remainder = 0x000000000001f09f c_remainder = x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁷ + x⁴ + x³ + x² + x + 1