gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000010000000000000000000000000000000000000000 a = 0x0000010000000000 a = x⁴⁰
b = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 ----------------------------------------- | 1101011111100101000001100011111000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------- | 11110000010111100001010010000100000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------- | 11011101011001001011110011011000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------- | 110110100101100011111111000111000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------- | 1100011010101001111100000000110 | - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000001101001010 c_quotient = 0x000000000000034a c_quotient = x⁹ + x⁸ + x⁶ + x³ + x
c_remainder = b0000000000000000000000000000000001100011010101001111100000000110 c_remainder = 0x000000006354f806 c_remainder = x³⁰ + x²⁹ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁸ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x¹¹ + x² + x