gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000001000000000000000000 a = x⁷²
b = b00000000000000000000000000000000000000000000000000000000000000000110011001110111111000100000000101000110010100001000111110110111 b = 0x00000000000000006677e20146508fb7 b = x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴¹ + x³² + x³⁰ + x²⁶ + x²⁵ + x²² + x²⁰ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1
1000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------- | 100110011101111110001000000001010001100101000010001111101101110000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------- | 10101010011000001001100000001111001010111100011001000011011001000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------- | 1100110100011110101110000001101101001110110011101011100000010100000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------- | 111110001011111000001100111000010011011111010011101111010000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------- | 1101000101000111001000111000111011101101110010101000100110111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110000001 c_quotient = 0x00000000000000000000000000000781 c_quotient = x¹⁰ + x⁹ + x⁸ + x⁷ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000001101000101000111001000111000111011101101110010101000100110111 c_remainder = 0x00000000000000001a28e471ddb95137 c_remainder = x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵³ + x⁵¹ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴² + x³⁸ + x³⁷ + x³⁶ + x³² + x³¹ + x³⁰ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁶ + x¹⁴ + x¹² + x⁸ + x⁵ + x⁴ + x² + x + 1