gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 a = 0x001d2c6f4c15eb24e4bf3371093e4a08 a = 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
b = b00000000000000110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 b = 0x00030401ca8fc6c4fc6848e1e022e7bf b = 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
111010010110001101111010011000001010111101011001001001110010010111111001100110111000100001001001111100100101000001000 | 110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 - 110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010000110001100001000110000110101111011101000000110000011111111101011101000111111000001000001010010111011111110000 | - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110000010001100010100011010111010001010000100010101111111100101101111001011011110111001000011011001011100010001110 | - 110000010000000001110010101000111111000110110001001111110001101000010010001110000111100000001000101110011110111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100011010001111111101110010110010011100000001101000101101011010101110000101000010011100101111100110001 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001011 c_quotient = 0x0000000000000000000000000000000b c_quotient = x³ + x + 1
c_remainder = b00000000000000000000000001100011010001111111101110010110010011100000001101000101101011010101110000101000010011100101111100110001 c_remainder = 0x0000006347fb964e0345ad5c284e5f31 c_remainder = x¹⁰² + x¹⁰¹ + x⁹⁷ + x⁹⁶ + x⁹⁴ + x⁹⁰ + x⁸⁹ + x⁸⁸ + x⁸⁷ + x⁸⁶ + x⁸⁵ + x⁸⁴ + x⁸³ + x⁸¹ + x⁸⁰ + x⁷⁹ + x⁷⁶ + x⁷⁴ + x⁷³ + x⁷⁰ + x⁶⁷ + x⁶⁶ + x⁶⁵ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵⁰ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴³ + x⁴² + x⁴⁰ + x³⁸ + x³⁶ + x³⁵ + x³⁴ + x²⁹ + x²⁷ + x²² + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁴ + x¹² + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁵ + x⁴ + 1