gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00100000000000000000000000000000 a = x¹¹⁶
b = b00000000000000000000000000000000000000000000000000000000000000001101111001110000111011101111011111000001100011111011011110011011 b = 0x0000000000000000de70eef7c18fb79b b = x⁶³ + x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁴ + x²³ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁴ + x³ + x + 1
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10111100111000011101110111101111100000110001111101101111001101100000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100010100100010011001100011000010000101001000011011000101011010000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1101101010010100010001100011101000100101011100000011011000001000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10011100100101010001100110111100100111111111000000110010011000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1000010111001011111011101001011010111100111111110000101111110110000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 101101110111011000000000110000101111101011100001011110001101101000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 11010010000011011101110001101010011101101101110110011110100000100000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100011111010011001010011101101101110101001000101001000110010000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100110100011110001110010110010110100101011010010011000001011000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1001101101110110101111001001001100100111001101000011111000011000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 100010100000110010100100110010011100110101110111000100110000011000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10101000111110001001010001111100000110011111000101001001001110100000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1110110100010000111101010001011110110000111111011111110101000010000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 11001101100000000110111110000001110001011100100100101011011001000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10011111100001000000101110110000001000100011010011100111111110000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1000001111101001110010101000111111000111011101101010000011000110000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 101110110011001001001000111100000000110111110010001011101011101000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 11001010100001010100110000001111100110001111101100110010010000100000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10100111101011010001011111000010110010111010010000101110110010000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1111001110111011111100100110101000010100010101110011001010100110000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10110111001011000111001001110111010101110110001000010100111101000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1101001010111001001110010000000100101101110110110100011011011110000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 110011001001110101111111011011101100010101001111000101000101000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 100101110110110010001100110010000010011000000101000111100101100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10010010001110001100010001111111110011110001010101010011100001100000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1001100010010000010101010001000000011101001101011100100000111010000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 100011011100000101110111110011111011100101110100111111110100001000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10100111011000110011001001110000111100011111011010010001101100100 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 1111001000100111101110010000111001100000111100100100110001010010 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------------------------------------------------- | 10110001010111010101111111100110100001011111011111101111001001 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000111001000011110001001001111010011110011011000100111111 c_quotient = 0x000000000000000000390f127a79b13f c_quotient = x⁵³ + x⁵² + x⁵¹ + x⁴⁸ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁶ + x³³ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁵ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000010110001010111010101111111100110100001011111011111101111001001 c_remainder = 0x00000000000000002c5757f9a17dfbc9 c_remainder = x⁶¹ + x⁵⁹ + x⁵⁸ + x⁵⁴ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁶ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³² + x³¹ + x²⁹ + x²⁴ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x³ + 1