gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000101110100111001100111011111100001111100100100010110111110000100100010000011101 a = 0x0000000000002e9ccefc3e48b7c2441d a = x⁷⁷ + x⁷⁵ + x⁷⁴ + x⁷³ + x⁷¹ + x⁶⁸ + x⁶⁷ + x⁶⁶ + x⁶³ + x⁶² + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x³⁸ + x³⁵ + x³¹ + x²⁹ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x¹⁷ + x¹⁴ + x¹⁰ + x⁴ + x³ + x² + 1
b = b00000000000000000000000000000000000000000000000000000000101001000001100001001010100011001000110110100110011101001010010010010011 b = 0x00000000000000a4184a8c8da674a493 b = x⁷¹ + x⁶⁹ + x⁶⁶ + x⁶⁰ + x⁵⁹ + x⁵⁴ + x⁵¹ + x⁴⁹ + x⁴⁷ + x⁴³ + x⁴² + x³⁹ + x³⁵ + x³⁴ + x³² + x³¹ + x²⁹ + x²⁶ + x²⁵ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹⁰ + x⁷ + x⁴ + x + 1
101110100111001100111011111100001111100100100010110111110000100100010000011101 | 101001000001100001001010100011001000110110100110011101001010010010010011 - 101001000001100001001010100011001000110110100110011101001010010010010011 | 1 ------------------------------------------------------------------------------ | 111100110101101110001011111000111010010000100101010111010110110000011011101 | - 000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 101001000001100001001010100011001000110110100110011101001010010010010011 | 1 ------------------------------------------------------------------------------ | 10101110100001111000001011011110010100110000011001010011100100010001000101 | - 101001000001100001001010100011001000110110100110011101001010010010010011 | 1 ------------------------------------------------------------------------------ | 1010100111111100100001010010110111101010000000100111001101011000001001 | - 000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001001100 c_quotient = 0x0000000000000000000000000000004c c_quotient = x⁶ + x³ + x²
c_remainder = b00000000000000000000000000000000000000000000000000000000001010100111111100100001010010110111101010000000100111001101011000001001 c_remainder = 0x000000000000002a7f214b7a809cd609 c_remainder = x⁶⁹ + x⁶⁷ + x⁶⁵ + x⁶² + x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵³ + x⁴⁸ + x⁴⁶ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³¹ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁵ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x³ + 1