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 = b0000000000000000000000000000000000000000000100000101010100100111 b = 0x0000000000105527 b = x²⁰ + x¹⁴ + x¹² + x¹⁰ + x⁸ + x⁵ + x² + x + 1
111101111101100100100100100111111111001100111111 | 100000101010100100111 - 100000101010100100111 | 1 ------------------------------------------------ | 11101010111000000011100100111111111001100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 1101000010010010000000100111111111001100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 101001000111011001110100111111111001100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 1001101101111101001100111111111001100111111 | - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 1100111010100000010111111111001100111111 | - 000000000000000000000 | 0 - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 100110000001001011001111111001100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 110101011101111110111111001100111111 | - 000000000000000000000 | 0 - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 10101110111011010000111001100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 101100010001000011011001100111111 | - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 1100111011100111100001100111111 | - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 100110001001110101111100111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 110100011010001000100111111 | - 000000000000000000000 | 0 - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 10100110000101100011111111 | - 100000101010100100111 | 1 ------------------------------------------------ | 100100101111110000011111 | - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 100000101010100100111 | - 000000000000000000000 | 0 - 000000000000000000000 | 0 - 100000101010100100111 | 1 ------------------------------------------------ | 0 |
c_quotient = b0000000000000000000000000000000000001111010011001101011001101001 c_quotient = 0x000000000f4cd669 c_quotient = x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²² + x¹⁹ + x¹⁸ + x¹⁵ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁶ + x⁵ + x³ + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x0000000000000000 c_remainder = 0