gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

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 = b0000000000000000000010001011001011101101101010110001011000000000 b = 0x000008b2edab1600 b = x⁴³ + x³⁹ + x³⁷ + x³⁶ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁶ + x¹² + x¹⁰ + x⁹
111101111101100100100100100111111111001100111111 | 10001011001011101101101010110001011000000000 - 10001011001011101101101010110001011000000000 | 1 ------------------------------------------------ | 11111001111011111111110001011101001001100111111 | - 10001011001011101101101010110001011000000000 | 1 ------------------------------------------------ | 1110010110000010010011011101100010001100111111 | - 10001011001011101101101010110001011000000000 | 1 ------------------------------------------------ | 110111010101100100101110110100111101100111111 | - 10001011001011101101101010110001011000000000 | 1 ------------------------------------------------ | 10101100111011111110100011000101011100111111 | - 10001011001011101101101010110001011000000000 | 1 ------------------------------------------------ | 100111110000010011001001110100000100111111 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000011111 c_quotient = 0x000000000000001f c_quotient = x⁴ + x³ + x² + x + 1
c_remainder = b0000000000000000000000100111110000010011001001110100000100111111 c_remainder = 0x0000027c1327413f c_remainder = x⁴¹ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³⁴ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁴ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1