gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000001000000000000000000000000000000000000000000000000 a = 0x0001000000000000 a = x⁴⁸
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
1000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 11000011000001010100101111100100000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 1110011110001000001100100011101000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 101011101001001011000001100001100000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 111100101001110010011011111110000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 10000100101110111001001000000010000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 110100011110101100000011111011000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 11000010010101001010001000101010000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 1110010100101011111000011010011000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 101010111101010101100110101111100000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 110110001010000110100010001110000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 11010000110000011110000110000010 | - 10110000110000010101001011111001 | 1 ------------------------------------------------- | 1100000000000001011001101111011 |
c_quotient = b0000000000000000000000000000000000000000000000101110011011110011 c_quotient = 0x000000000002e6f3 c_quotient = x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x + 1
c_remainder = b0000000000000000000000000000000001100000000000001011001101111011 c_remainder = 0x000000006000b37b c_remainder = x³⁰ + x²⁹ + x¹⁵ + x¹³ + x¹² + x⁹ + x⁸ + x⁶ + x⁵ + x⁴ + x³ + x + 1