gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000100000000000000000000 a = x⁸⁰
b = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
100000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 110101011101001101000111011110000110011110101110000101011111100000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 10011110110100100101111100101110110101101011011110101110100011100000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 100011010000011011111000001110110100100001001101100001100010000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 101111011110010010000110101000100010010111000010001001001111100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 1001110101111011101110010011010010100100110111111001100100011100000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------- | 11111000001110100011101101110101000001010100101101110100011000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100110000100101000 c_quotient = 0x00000000000000000000000000026128 c_quotient = x¹⁷ + x¹⁴ + x¹³ + x⁸ + x⁵ + x³
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011111000001110100011101101110101000001010100101101110100011000 c_remainder = 0x00000000000000003e0e8edd4152dd18 c_remainder = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁷ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³⁴ + x³² + x³⁰ + x²⁴ + x²² + x²⁰ + x¹⁷ + x¹⁵ + x¹⁴ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁴ + x³