gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000004000000000000000000000000000000000000000000000 a = x¹⁸²
b = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 b = 0x0000000000000000000000000000000065ee6bda0b324559661859ebf3268b49 b = x¹²⁶ + x¹²⁵ + x¹²² + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹³ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰² + x¹⁰⁰ + x⁹⁹ + x⁹⁷ + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁵ + x⁸⁴ + x⁸¹ + x⁷⁸ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵² + x⁵¹ + x⁴⁶ + x⁴⁴ + x⁴³ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹¹ + x⁹ + x⁸ + x⁶ + x³ + 1
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010111101110011010111101101000001011001100100100010101011001011001100001100001011001111010111111001100100110100010110100100100000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011100011001010111100011011100001110101010110110011111110101110101010001010001110101000111100000101010110101110011101110110110000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111001100010110001001100000110001100011001111111011010100011100011001001001001100011011001001111011001111100011011000011111111000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011011111000010011011101011001101000000011011111000001000101000000101000101101000010110011000100000011000101111010101011011100000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111110000011110101110010000011101010110000010110000100010011010110110000110101010100101101101011110000001100010010000110010101000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100111110000110100101101110101011101001110010100110111000011101111100111001011111100010111100001001101000100110010000110001100000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10001011010010000010101111011111111101011101110010010101111001111111010011101010001001001110111110001101011010101011000101000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000000100101001111110001101011111000111011100000011111010101010011100011011010100101110011100001101011001001111010011111010010000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100101011110101001011110110001111010001000101001011010000011000101111011000010110011101101001110011000000000010010110010011011000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10111100011011010001001011100111011010001001101111000101000001110110111001110111000100010011001100001100100100110100100111111100000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110111101100011100010101010011011111101111111101001111101101011010001001000111101000101110010011101010110111100101111101101110000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010010111111010111010001001011101011100110100001010111011001100010001011111111110110000111100011001111110001101010000100111000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011001001000011010001111111111101110000000110011011101110101001110111011001111011010111010111100101001100010111011011110101010000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111100110011111100100000100101101100110011111010011000100011011000100011010111001100100100010011011010101011010011110011100011000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110001110001111110111001000101101101010011110111010001000010011101111011011000111101011000100100011001111100111100101000111100000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10100001010011000010110011111101111100000111110010100010100001011100011000000101011000110001011101010110101010100000101110101000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1101010100100001111101101001001111001100001100000101000001101110000101000110101110100001100000010110000111001110001110100111010000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111011111101001000010010011111011010010101001101101011011100110110000101101100010010010101101000011110000011001011001110011000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11110000110101110111101000101011000100110000100101110001010100000011101110100000100001011000111101101001010100011100011010001000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111011000010111010110110011111000001010110110111111011111000101111011110010000001101100101100010001111000111001101000000011010000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001111111001001100001110010000000001111010011011001010011100100010010011100000110101010110101110110100011111001010110111110100000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101010000010101010100001001010000011001001010010001111001010110100001011111000100011001000000001000111010110100010011010111101000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11000111111011001110110100111000010010000110110101101100001111111000111110100101000000111010110111110110010010110001100011001100000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100001100000011101010001100010111100000100111100110100011010100001110010101101100000111101000010000000001100000111001011110000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100011011111011111110111000111110110111110101110001001100110111101010110101110110100011101101110011000101101111100110111001000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10001100010101100100000101010110111100111001010101011001101110110011010100010111111010010111001100001001001001000100001101100100000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000111100010101001011011100010111001011111000111010011000010011111100100100111010110101010010011101111011010010101010111110110000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100010011001001111110100111000111011101100001110010110010100001001111100111111000000110100111100011100010011111101111010111111000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10000100100111100100011010101111010110101101010110100111111000010110000110011001011111011101011100101110111001001101100011011100000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001111010000101001000100011011010011001011000100101101010100111010110110101001110011100000000011001000101010011100111001001110000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101010101011001111101011000001010001111000001101101000000010101100101110110001100101111110101100111011100011110100010100000111000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11000010110111100111100101100010000100001101001001010101001100111100010111101101110110001111011000010000111000000000010100011100000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001000000101010111011010110000001101011011011011111100000010000100111011101011010110010000111110110101011010001001110001110000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101101111110110001110101101010001111101000010010111001010100010010100011110011000000001110010001000110010011100001011100111001 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111101101000011111011101011001010101110001000111111110001 c_quotient = 0x00000000000000000000000000000000000000000000000001ed0fbacab88ff1 c_quotient = x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴⁸ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³¹ + x³⁰ + x²⁷ + x²⁵ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x⁴ + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101101111110110001110101101010001111101000010010111001010100010010100011110011000000001110010001000110010011100001011100111001 c_remainder = 0x000000000000000000000000000000002dfb1d6a3e84b95128f300e4464e1739 c_remainder = x¹²⁵ + x¹²³ + x¹²² + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁶ + x¹¹⁵ + x¹¹³ + x¹¹² + x¹⁰⁸ + x¹⁰⁷ + x¹⁰⁶ + x¹⁰⁴ + x¹⁰² + x¹⁰¹ + x⁹⁹ + x⁹⁷ + x⁹³ + x⁹² + x⁹¹ + x⁹⁰ + x⁸⁹ + x⁸⁷ + x⁸² + x⁷⁹ + x⁷⁷ + x⁷⁶ + x⁷⁵ + x⁷² + x⁷⁰ + x⁶⁸ + x⁶⁴ + x⁶¹ + x⁵⁹ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁹ + x⁴⁸ + x³⁹ + x³⁸ + x³⁷ + x³⁴ + x³⁰ + x²⁶ + x²⁵ + x²² + x¹⁹ + x¹⁸ + x¹⁷ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁵ + x⁴ + x³ + 1