gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000100000000000000000000000000000000000000000000000000000000 a = 0x0100000000000000 a = x⁵⁶
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
100000000000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1100001100000101010010111110010000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 111001111000100000110010001110100000000000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 10101110100100101100000110000110000000000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 11110010100111001001101111111000000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1000010010111011100100100000001000000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 11010001111010110000001111101100000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1100001001010100101000100010101000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 111001010010101111100001101001100000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 10101011110101010110011010111110000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 11011000101000011010001000111000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1101000011000001111000011000001000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 110000000000000101100110111101100000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 11100001100000000110100000011110000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1010001010000010011101011100111000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 1001001000011001001110011011100000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 10001011011000011010110100000100 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------------- | 111011101000001111111111111101 |
c_quotient = b0000000000000000000000000000000000000010111001101111001111100101 c_quotient = 0x0000000002e6f3e5 c_quotient = x²⁵ + x²³ + x²² + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x² + 1
c_remainder = b0000000000000000000000000000000000111011101000001111111111111101 c_remainder = 0x000000003ba0fffd c_remainder = x²⁹ + x²⁸ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²¹ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + 1