gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000010000000000000000000000000000000000000000000000000000 a = 0x0010000000000000 a = x⁵²
b = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1101011111100101000001100011111000000000000000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 11110000010111100001010010000100000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 11011101011001001011110011011000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 110110100101100011111111000111000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1100011010101001111100000000110000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 10110101011011011100110001001100000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1011110100111110100111101010011000000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 101011011001100000111011011100100000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 10001100110101010111000011011010000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1100111001001111111001111000101000000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 10010110111101011001001001010100000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1111101000001110001000101001011000 | - 11101011111100101000001100011111 | 1 ----------------------------------------------------- | 1000111111100101000011000100100 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000001101001010101111101100 c_quotient = 0x000000000034abec c_quotient = x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x²
c_remainder = b0000000000000000000000000000000001000111111100101000011000100100 c_remainder = 0x0000000047f28624 c_remainder = x³⁰ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x¹⁰ + x⁹ + x⁵ + x²