gf(2) Polynomial long division

c = a/b

a = b0000000000000000111101111101100100100100100111111111001100111111 a = 0x0000f7d9249ff33f a = 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
b = b0000000000000000000000001100011101000000110100011000111011010101 b = 0x000000c740d18ed5 b = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴ + x² + 1
111101111101100100100100100111111111001100111111 | 1100011101000000110100011000111011010101 - 1100011101000000110100011000111011010101 | 1 ------------------------------------------------ | 1100001001100111110101000100010010011000111111 | - 0000000000000000000000000000000000000000 | 0 - 1100011101000000110100011000111011010101 | 1 ------------------------------------------------ | 10100100111000001011100101001001101111111 | - 0000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000 | 0 - 1100011101000000110100011000111011010101 | 1 ------------------------------------------------ | 1100011101000000110100011000111011010101 | - 1100011101000000110100011000111011010101 | 1 ------------------------------------------------ | 0 |
c_quotient = b0000000000000000000000000000000000000000000000000000000101000011 c_quotient = 0x0000000000000143 c_quotient = x⁸ + x⁶ + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x0000000000000000 c_remainder = 0