gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000010000000000000000000000000000000000 a = 0x0000000400000000 a = x³⁴
b = b0000000000000000000000000000000000000000000001101010101111101101 b = 0x000000000006abed b = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
10000000000000000000000000000000000 | 1101010101111101101 - 1101010101111101101 | 1 ----------------------------------- | 1010101011111011010000000000000000 | - 1101010101111101101 | 1 ----------------------------------- | 111111110000110111000000000000000 | - 1101010101111101101 | 1 ----------------------------------- | 1010100111000001100000000000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ----------------------------------- | 111110010111100001000000000000 | - 1101010101111101101 | 1 ----------------------------------- | 1011000000010111100000000000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ----------------------------------- | 110010101101010001000000000 | - 1101010101111101101 | 1 ----------------------------------- | 111111010100111100000000 | - 0000000000000000000 | 0 - 0000000000000000000 | 0 - 1101010101111101101 | 1 ----------------------------------- | 1010000011001010100000 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ----------------------------------- | 111010110110111001000 | - 1101010101111101101 | 1 ----------------------------------- | 1111100001001111100 | - 0000000000000000000 | 0 - 1101010101111101101 | 1 ----------------------------------- | 10110100110010001 |
c_quotient = b0000000000000000000000000000000000000000000000011101101100101101 c_quotient = 0x000000000001db2d c_quotient = x¹⁶ + x¹⁵ + x¹⁴ + x¹² + x¹¹ + x⁹ + x⁸ + x⁵ + x³ + x² + 1
c_remainder = b0000000000000000000000000000000000000000000000010110100110010001 c_remainder = 0x0000000000016991 c_remainder = x¹⁶ + x¹⁴ + x¹³ + x¹¹ + x⁸ + x⁷ + x⁴ + 1