gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000001000000000000000000000000000000000000000000000000 a = 0x0001000000000000 a = x⁴⁸
b = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
1000000000000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 110101111110010100000110001111100000000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 1111000001011110000101001000010000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 1101110101100100101111001101100000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 11011010010110001111111100011100000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 110001101010100111110000000011000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 1011010101101101110011000100110000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 101111010011111010011110101001100000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 10101101100110000011101101110010000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 1000110011010101011100001101101000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 110011100100111111100111100010100 | - 11101011111100101000001100011111 | 1 ------------------------------------------------- | 1001011011110101100100100101010 | - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000110100101010111110 c_quotient = 0x0000000000034abe c_quotient = x¹⁷ + x¹⁶ + x¹⁴ + x¹¹ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x
c_remainder = b0000000000000000000000000000000001001011011110101100100100101010 c_remainder = 0x000000004b7ac92a c_remainder = x³⁰ + x²⁷ + x²⁵ + x²⁴ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹¹ + x⁸ + x⁵ + x³ + x