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 = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 11010101110100110100011101111000011001111010111000010101111110000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1001111011010010010111110010111011010110101101111010111010001110000000000000000000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10001101000001101111100000111011010010000100110110000110001000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10111101111001001000011010100010001001011100001000100100111110000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100111010111101110111001001101001010010011011111100110010001110000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1111100000111010001110110111010100000101010010110111010001100000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110001010000000010100111001101000001001101111101011011011011111000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10111111011101011001111110110110001111110001000101011110000000100000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 100101110011111111011101011001001100111110010010011100101111010000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 11011000010110110101100010111100001101100111101100000100101100000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1000010111000010011000001010011001110101000111011000110000011110000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1111101111000000010000100100101111001111010000100111010100001000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110000101111010001010101010010011000011101101111011011110110111000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10110000100111000111101101001101000101110011010101011011101000100000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 101010001001100001001110100010000110111100000010011001000111010000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1100100010001000100110011001110110001111110111101001101100101100000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 101001000110010111100010111001010000011001010110101100110010011000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1111101101111110001010000010100000101010100011011100011001100100000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 110000111000100010000001100011100100110011110000000010011011011000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10110010011001011101001011000010100000000000101110010110000100100000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 101000110111111011101000101101100011001111111001010100101011010000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1110011100010010000000010110010011111100001100100100000000101100000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111110110101000011010011000101111110000110001111000001010010011000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 11000011110101010111011111110001110110101111010110001111001100100000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1011001011011110001111100011110110101100000000001001101100011010000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 10100001100100010101101101001010100000111101010101100110100101000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111011001010110011001110100101100011110010000010100100001010110000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 11101100001011010100110011110010011000001110111010100100001001100 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 1110110100101110010010000011101011011000001101101100110100110010 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------------------- | 111011110010100001000001101010111010100110000110000111110001101 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000010011000010010100001110100011001110101101110101111010111 c_quotient = 0x000000000000000000984a1d19d6ebd7 c_quotient = x⁵⁵ + x⁵² + x⁵¹ + x⁴⁶ + x⁴³ + x⁴¹ + x³⁶ + x³⁵ + x³⁴ + x³² + x²⁸ + x²⁷ + x²⁴ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁴ + x² + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000111011110010100001000001101010111010100110000110000111110001101 c_remainder = 0x0000000000000000779420d5d4c30f8d c_remainder = x⁶² + x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵² + x⁵⁰ + x⁴⁵ + x³⁹ + x³⁸ + x³⁶ + x³⁴ + x³² + x³¹ + x³⁰ + x²⁸ + x²⁶ + x²³ + x²² + x¹⁷ + x¹⁶ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x³ + x² + 1