gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000 a = 0x000000100000000000000000 a = x⁶⁸
b = b000000000000000000000000000000000000000000000000111101111101100100100100100111111111001100111111 b = 0x000000000000f7d9249ff33f b = 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
100000000000000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 11101111101100100100100100111111111001100111111000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 11000011010110110110110100000000101010100000100000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 110100100000100100100110011111010110010011011100000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 1001011101000000000010111000101001011111100011000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 110000010011001001011110001010110101100101100110000000000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 1101101110101101111010101101001010101001011001000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 10110001110100110011100100110101011010010110110000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 1000110000010100001110110101010100110100101001100000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 111101111001101000111111100101011000111100110010000000 | - 111101111101100100100100100111111111001100111111 | 1 --------------------------------------------------------------------- | 100001100011011000010100111110000001101000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0
c_quotient = b000000000000000000000000000000000000000000000000000000000000000000000000001100101011010111000000 c_quotient = 0x00000000000000000032b5c0 c_quotient = x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁸ + x⁷ + x⁶
c_remainder = b000000000000000000000000000000000000000000000000000100001100011011000010100111110000001101000000 c_remainder = 0x00000000000010c6c29f0340 c_remainder = x⁴⁴ + x³⁹ + x³⁸ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁵ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x⁹ + x⁸ + x⁶