gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000004000000000000000000 a = x⁷⁴
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
100000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 10011001110111111000100000000101000110010100001000111110110111000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 1010101001100000100110000000111100101011110001100100001101100100000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 110011010001111010111000000110110100111011001110101110000001010000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 11111000101111100000110011100001001101111101001110111101000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 110100010100011100100011100011101110110111001010100010011011100 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------- | 111011010100011100111100011000110000101101011100101101101011 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111000000101 c_quotient = 0x00000000000000000000000000001e05 c_quotient = x¹² + x¹¹ + x¹⁰ + x⁹ + x² + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000111011010100011100111100011000110000101101011100101101101011 c_remainder = 0x00000000000000000ed473c630b5cb6b c_remainder = x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁵ + x⁵⁴ + x⁵² + x⁵⁰ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁴ + x³³ + x²⁹ + x²⁸ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x¹¹ + x⁹ + x⁸ + x⁶ + x⁵ + x³ + x + 1