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 = b0000000000000000000000000000000000000000000000000000000101000011 b = 0x0000000000000143 b = x⁸ + x⁶ + x + 1
111101111101100100100100100111111111001100111111 | 101000011 - 101000011 | 1 ------------------------------------------------ | 10101100101100100100100100111111111001100111111 | - 101000011 | 1 ------------------------------------------------ | 1101001100100100100100111111111001100111111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 111001010100100100100111111111001100111111 | - 101000011 | 1 ------------------------------------------------ | 10001001100100100100111111111001100111111 | - 101000011 | 1 ------------------------------------------------ | 101000000100100100111111111001100111111 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 11100100100111111111001100111111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 1000101000111111111001100111111 | - 101000011 | 1 ------------------------------------------------ | 10101110111111111001100111111 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 1111011111111001100111111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 101011001111001100111111 | - 101000011 | 1 ------------------------------------------------ | 11010111001100111111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 1110110101100111111 | - 101000011 | 1 ------------------------------------------------ | 100110011100111111 | - 101000011 | 1 ------------------------------------------------ | 1110000100111111 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 100000010111111 | - 101000011 | 1 ------------------------------------------------ | 1000001111111 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 10001001111 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 101000011 | - 000000000 | 0 - 101000011 | 1 ------------------------------------------------ | 0 |
c_quotient = b0000000000000000000000001100011101000000110100011000111011010101 c_quotient = 0x000000c740d18ed5 c_quotient = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴ + x² + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x0000000000000000 c_remainder = 0