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 = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1101011111100101000001100011111000000000000000000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 11110000010111100001010010000100000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 11011101011001001011110011011000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 110110100101100011111111000111000000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1100011010101001111100000000110000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 10110101011011011100110001001100000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1011110100111110100111101010011000000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 101011011001100000111011011100100000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 10001100110101010111000011011010000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1100111001001111111001111000101000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 10010110111101011001001001010100000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1111101000001110001000101001011000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1000111111100101000011000100100000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 110010000010111100011110101011100000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1000111101110110011101101100010000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 110010010000100111101011101101100 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------------- | 1000101111101101101000101010010 | - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000001101001010101111101100110110 c_quotient = 0x000000000d2afb36 c_quotient = x²⁷ + x²⁶ + x²⁴ + x²¹ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x¹¹ + x⁹ + x⁸ + x⁵ + x⁴ + x² + x
c_remainder = b0000000000000000000000000000000001000101111101101101000101010010 c_remainder = 0x0000000045f6d152 c_remainder = x³⁰ + x²⁶ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹² + x⁸ + x⁶ + x⁴ + x