gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000 a = 0x000000001000000000000000 a = x⁶⁰
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
1000000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 111011111011001001001001001111111110011001111110000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 110000110101101101101101000000001010101000001000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 1101001000001001001001100111110101100100110111000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 10010111010000000000101110001010010111111000110000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 1100000100110010010111100010101101011001011001100000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 11011011101011011110101011010010101010010110010000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 101100011101001100111001001101010110100101101100 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------- | 10001100000101000011101101010101001101001010011 |
c_quotient = b000000000000000000000000000000000000000000000000000000000000000000000000000000000011001010110101 c_quotient = 0x0000000000000000000032b5 c_quotient = x¹³ + x¹² + x⁹ + x⁷ + x⁵ + x⁴ + x² + 1
c_remainder = b000000000000000000000000000000000000000000000000010001100000101000011101101010101001101001010011 c_remainder = 0x000000000000460a1daa9a53 c_remainder = x⁴⁶ + x⁴² + x⁴¹ + x³⁵ + x³³ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁵ + x¹² + x¹¹ + x⁹ + x⁶ + x⁴ + x + 1