gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000010000000000000000000000000000000000000000000000000000000000 a = 0x0400000000000000 a = x⁵⁸
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
10000000000000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 110000110000010101001011111001000000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 11100111100010000011001000111010000000000000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1010111010010010110000011000011000000000000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1111001010011100100110111111100000000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 100001001011101110010010000000100000000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1101000111101011000000111110110000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 110000100101010010100010001010100000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 11100101001010111110000110100110000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1010101111010101011001101011111000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1101100010100001101000100011100000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 110100001100000111100001100000100000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 11000000000000010110011011110110000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1110000110000000011010000001111000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 101000101000001001110101110011100000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 100100100001100100111001101110000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1000101101100001101011010000010000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 11101110100000111111111111110100 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------------- | 1011110010000101010110100001101 |
c_quotient = b0000000000000000000000000000000000001011100110111100111110010101 c_quotient = 0x000000000b9bcf95 c_quotient = x²⁷ + x²⁵ + x²⁴ + x²³ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁴ + x² + 1
c_remainder = b0000000000000000000000000000000001011110010000101010110100001101 c_remainder = 0x000000005e42ad0d c_remainder = x³⁰ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²² + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁸ + x³ + x² + 1