gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00400000000000000000000000000000 a = x¹¹⁸
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
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1011110011100001110111011110111110000011000111110110111100110110000000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110001010010001001100110001100001000010100100001101100010101101000000000000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110110101001010001000110001110100010010101110000001101100000100000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1001110010010101000110011011110010011111111100000011001001100000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100001011100101111101110100101101011110011111111000010111111011000000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10110111011101100000000011000010111110101110000101111000110110100000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1101001000001101110111000110101001110110110111011001111010000010000000000000000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110001111101001100101001110110110111010100100010100100011001000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110011010001111000111001011001011010010101101001001100000101100000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100110110111011010111100100100110010011100110100001111100001100000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10001010000011001010010011001001110011010111011100010011000001100000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1010100011111000100101000111110000011001111100010100100100111010000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111011010001000011110101000101111011000011111101111111010100001000000000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1100110110000000011011111000000111000101110010010010101101100100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1001111110000100000010111011000000100010001101001110011111111000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100000111110100111001010100011111100011101110110101000001100011000000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10111011001100100100100011110000000011011111001000101110101110100000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1100101010000101010011000000111110011000111110110011001001000010000000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1010011110101101000101111100001011001011101001000010111011001000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111100111011101111110010011010100001010001010111001100101010011000000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1011011100101100011100100111011101010111011000100001010011110100000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110100101011100100111001000000010010110111011011010001101101111000000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 11001100100111010111111101101110110001010100111100010100010100000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10010111011011001000110011001000001001100000010100011110010110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1001001000111000110001000111111111001111000101010101001110000110000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100110001001000001010101000100000001110100110101110010000011101000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10001101110000010111011111001111101110010111010011111111010000100000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1010011101100011001100100111000011110001111101101001000110110010000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111100100010011110111001000011100110000011110010010011000101001000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1011000101011101010111111110011010000101111101111110111100100100 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110111100101101101100010001000101000100011110000101100010111111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000011100100001111000100100111101001111001101100010011111101 c_quotient = 0x000000000000000000e43c49e9e6c4fd c_quotient = x⁵⁵ + x⁵⁴ + x⁵³ + x⁵⁰ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x³⁸ + x³⁵ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁴ + x²³ + x²² + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹⁰ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000110111100101101101100010001000101000100011110000101100010111111 c_remainder = 0x00000000000000006f2db111447858bf c_remainder = x⁶² + x⁶¹ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴⁴ + x⁴⁰ + x³⁶ + x³² + x³⁰ + x²⁶ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁴ + x¹² + x¹¹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1