gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x000100000000000000000000 a = x⁸⁰
b = b000000000000000000000000000000000000000000000000111101111101100100100100100111111111001100111111 b = 0x000000000000f7d9249ff33f b = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1
100000000000000000000000000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 11101111101100100100100100111111111001100111111000000000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 11000011010110110110110100000000101010100000100000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 110100100000100100100110011111010110010011011100000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 1001011101000000000010111000101001011111100011000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 110000010011001001011110001010110101100101100110000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 1101101110101101111010101101001010101001011001000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 10110001110100110011100100110101011010010110110000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 1000110000010100001110110101010100110100101001100000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 111101111001101000111111100101011000111100110010000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 100001100011011000010100111110000001101000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 11100011110111100110000011001111110100100111111000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 10100000001110100010001010000001000010100000100000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 1010111111000110000011000011110111110010011011100000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 101100000011111001010001010001000000001010100010000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 10001111110011101110101110110111111000110011101000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 1111000000101111100111100101000000100000000010100 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------------------- | 11111110110101110101100111111010011001101010 | - 000000000000000000000000000000000000000000000000 | 0
c_quotient = b000000000000000000000000000000000000000000000000000000000000001100101011010111000000001100111110 c_quotient = 0x00000000000000032b5c033e c_quotient = x³³ + x³² + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁹ + x¹⁸ + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x
c_remainder = b000000000000000000000000000000000000000000000000000011111110110101110101100111111010011001101010 c_remainder = 0x0000000000000fed759fa66a c_remainder = x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁴ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹⁰ + x⁹ + x⁶ + x⁵ + x³ + x