gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000001101001010111001101001000001110111000011011011000000110010010010101100111101100100011010101010111001111110110111100011111 a = 0x01a573483b86d8192567b235573f6f1f a = x¹²⁰ + x¹¹⁹ + x¹¹⁷ + x¹¹⁴ + x¹¹² + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁸ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰² + x⁹⁹ + x⁹³ + x⁹² + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁷ + x⁸² + x⁸¹ + x⁷⁹ + x⁷⁸ + x⁷⁶ + x⁷⁵ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶¹ + x⁵⁸ + x⁵⁶ + x⁵⁴ + x⁵³ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴⁴ + x⁴¹ + x³⁷ + x³⁶ + x³⁴ + x³² + x³⁰ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁴ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
b = b00000000000111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 b = 0x001d2c6f4c15eb24e4bf3371093e4a08 b = x¹¹⁶ + x¹¹⁵ + x¹¹⁴ + x¹¹² + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁶ + x¹⁰² + x¹⁰¹ + x⁹⁹ + x⁹⁸ + x⁹⁷ + x⁹⁶ + x⁹⁴ + x⁹¹ + x⁹⁰ + x⁸⁴ + x⁸² + x⁸⁰ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁵ + x⁷³ + x⁷² + x⁶⁹ + x⁶⁶ + x⁶³ + x⁶² + x⁶¹ + x⁵⁸ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁵ + x⁴⁴ + x⁴¹ + x⁴⁰ + x³⁸ + x³⁷ + x³⁶ + x³² + x²⁷ + x²⁴ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁴ + x¹¹ + x⁹ + x³
1101001010111001101001000001110111000011011011000000110010010010101100111101100100011010101010111001111110110111100011111 | 111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 - 111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 | 1 ------------------------------------------------------------------------------------------------------------------------- | 11101111011010110111100111110101101100001101010010101110110111010010100100001010010010111000100110110111100111110011111 | - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 | 1 ------------------------------------------------------------------------------------------------------------------------- | 110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 | - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010100 c_quotient = 0x00000000000000000000000000000014 c_quotient = x⁴ + x²
c_remainder = b00000000000000110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 c_remainder = 0x00030401ca8fc6c4fc6848e1e022e7bf c_remainder = x¹¹³ + x¹¹² + x¹⁰⁶ + x⁹⁶ + x⁹⁵ + x⁹⁴ + x⁹¹ + x⁸⁹ + x⁸⁷ + x⁸³ + x⁸² + x⁸¹ + x⁸⁰ + x⁷⁹ + x⁷⁸ + x⁷⁴ + x⁷³ + x⁷¹ + x⁷⁰ + x⁶⁶ + x⁶³ + x⁶² + x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁴ + x⁵³ + x⁵¹ + x⁴⁶ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³² + x³¹ + x³⁰ + x²⁹ + x²¹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1