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 = b0000000000000000000000000000000000000111000010101110101001110111 b = 0x00000000070aea77 b = x²⁶ + x²⁵ + x²⁴ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x⁹ + x⁶ + x⁵ + x⁴ + x² + x + 1
111101111101100100100100100111111111001100111111 | 111000010101110101001110111 - 111000010101110101001110111 | 1 ------------------------------------------------ | 101101000010001101010011111111111001100111111 | - 000000000000000000000000000 | 0 - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 10101010111111000011101000111111001100111111 | - 111000010101110101001110111 | 1 ------------------------------------------------ | 1001011101000010111010011011111001100111111 | - 111000010101110101001110111 | 1 ------------------------------------------------ | 111011000011111101001110101111001100111111 | - 111000010101110101001110111 | 1 ------------------------------------------------ | 11010110001000000000010111001100111111 | - 000000000000000000000000000 | 0 - 000000000000000000000000000 | 0 - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 110111011111010100101100101100111111 | - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 1111001010100001100010010100111111 | - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 1001111111100110001111010111111 | - 000000000000000000000000000 | 0 - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 111111010111011011100111001111 | - 111000010101110101001110111 | 1 ------------------------------------------------ | 111000010101110101001110111 | - 000000000000000000000000000 | 0 - 000000000000000000000000000 | 0 - 111000010101110101001110111 | 1 ------------------------------------------------ | 0 |
c_quotient = b0000000000000000000000000000000000000000001001111000101010011001 c_quotient = 0x0000000000278a99 c_quotient = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x0000000000000000 c_remainder = 0