gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x010000000000000000000000 a = x⁸⁸
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
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1110111110110010010010010011111111100110011111100000000000000000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1100001101011011011011010000000010101010000010000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 11010010000010010010011001111101011001001101110000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 100101110100000000001011100010100101111110001100000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 11000001001100100101111000101011010110010110011000000000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 110110111010110111101010110100101010100101100100000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1011000111010011001110010011010101101001011011000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 100011000001010000111011010101010011010010100110000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 11110111100110100011111110010101100011110011001000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 10000110001101100001010011111000000110100000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1110001111011110011000001100111111010010011111100000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1010000000111010001000101000000100001010000010000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 101011111100011000001100001111011111001001101110000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 10110000001111100101000101000100000000101010001000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1000111111001110111010111011011111100011001110100000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 111100000010111110011110010100000010000000001010000000000 | - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 1111111011010111010110011111101001100110101000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 100100001110011111010110010110010101100111110000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ----------------------------------------------------------------------------------------- | 11001110011111011110010110001101010101011001111 |
c_quotient = b000000000000000000000000000000000000000000000000000000110010101101011100000000110011111000010001 c_quotient = 0x000000000000032b5c033e11 c_quotient = x⁴¹ + x⁴⁰ + x³⁷ + x³⁵ + x³³ + x³² + x³⁰ + x²⁸ + x²⁷ + x²⁶ + x¹⁷ + x¹⁶ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁹ + x⁴ + 1
c_remainder = b000000000000000000000000000000000000000000000000011001110011111011110010110001101010101011001111 c_remainder = 0x000000000000673ef2c6aacf c_remainder = x⁴⁶ + x⁴⁵ + x⁴² + x⁴¹ + x⁴⁰ + x³⁷ + x³⁶ + x³⁵ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²³ + x²² + x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁷ + x⁶ + x³ + x² + x + 1