gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000100000000000000000000000000000000000000000000000000 a = 0x0004000000000000 a = x⁵⁰
b = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
100000000000000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 11010111111001010000011000111110000000000000000000 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 111100000101111000010100100001000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 110111010110010010111100110110000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 1101101001011000111111110001110000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 11000110101010011111000000001100000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 101101010110110111001100010011000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 10111101001111101001111010100110000000 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 1010110110011000001110110111001000000 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 100011001101010101110000110110100000 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 11001110010011111110011110001010000 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 100101101111010110010010010101000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 11111010000011100010001010010110 | - 11101011111100101000001100011111 | 1 --------------------------------------------------- | 10001111111001010000110001001 |
c_quotient = b0000000000000000000000000000000000000000000011010010101011111011 c_quotient = 0x00000000000d2afb c_quotient = x¹⁹ + x¹⁸ + x¹⁶ + x¹³ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000010001111111001010000110001001 c_remainder = 0x0000000011fca189 c_remainder = x²⁸ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁵ + x¹³ + x⁸ + x⁷ + x³ + 1