gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000040000000000000000000000000000000000000000 a = x¹⁶²
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
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10111000110010101111000110111000011101010101101100111111101011101010100010100011101010001111000001010101101011100111011101101100000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110011000101100010011000001100011000110011111110110101000111000110010010010011000110110010011110110011111000110110000111111110000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10110111110000100110111010110011010000000110111110000010001010000001010001011010000101100110001000000110001011110101010110111000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111100000111101011100100000111010101100000101100001000100110101101100001101010101001011011010111100000011000100100001100101010000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11001111100001101001011011101010111010011100101001101110000111011111001110010111111000101111000010011010001001100100001100011000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100010110100100000101011110111111111010111011100100101011110011111110100111010100010010011101111100011010110101010110001010000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10000001001010011111100011010111110001110111000000111110101010100111000110110101001011100111000011010110010011110100111110100100000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001010111101010010111101100011110100010001010010110100000110001011110110000101100111011010011100110000000000100101100100110110000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101111000110110100010010111001110110100010011011110001010000011101101110011101110001000100110011000011001001001101001001111111000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11101111011000111000101010100110111111011111111010011111011010110100010010001111010001011100100111010101101111001011111011011100000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100100101111110101110100010010111010111001101000010101110110011000100010111111111101100001111000110011111100011010100001001110000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10110010010000110100011111111111011100000001100110111011101010011101110110011110110101110101111001010011000101110110111101010100000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111001100111111001000001001011011001100111110100110001000110110001000110101110011001001000100110110101010110100111100111000110000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11100011100011111101110010001011011010100111101110100010000100111011110110110001111010110001001000110011111001111001010001111000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101000010100110000101100111111011111000001111100101000101000010111000110000001010110001100010111010101101010101000001011101010000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11010101001000011111011010010011110011000011000001010000011011100001010001101011101000011000000101100001110011100011101001110100000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11110111111010010000100100111110110100101010011011010110111001101100001011011000100100101011010000111100000110010110011100110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111100001101011101111010001010110001001100001001011100010101000000111011101000001000010110001111011010010101000111000110100010000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110110000101110101101100111110000010101101101111110111110001011110111100100000011011001011000100011110001110011010000000110100000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10011111110010011000011100100000000011110100110110010100111001000100100111000001101010101101011101101000111110010101101111101000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1010100000101010101000010010100000110010010100100011110010101101000010111110001000110010000000010001110101101000100110101111010 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110001111110110011101101001110000100100001101101011011000011111110001111101001010000001110101101111101100100101100011000110011 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111011010000111110111010110010101011 c_quotient = 0x0000000000000000000000000000000000000000000000000000001ed0fbacab c_quotient = x³⁶ + x³⁵ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁸ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁷ + x⁵ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000110001111110110011101101001110000100100001101101011011000011111110001111101001010000001110101101111101100100101100011000110011 c_remainder = 0x0000000000000000000000000000000031fb3b4e121b5b0fe3e940eb7d92c633 c_remainder = x¹²⁵ + x¹²⁴ + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁶ + x¹¹⁵ + x¹¹³ + x¹¹² + x¹⁰⁹ + x¹⁰⁸ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰² + x⁹⁹ + x⁹⁸ + x⁹⁷ + x⁹² + x⁸⁹ + x⁸⁴ + x⁸³ + x⁸¹ + x⁸⁰ + x⁷⁸ + x⁷⁶ + x⁷⁵ + x⁷³ + x⁷² + x⁶⁷ + x⁶⁶ + x⁶⁵ + x⁶⁴ + x⁶³ + x⁶² + x⁶¹ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵¹ + x⁴⁸ + x⁴⁶ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²⁰ + x¹⁷ + x¹⁵ + x¹⁴ + x¹⁰ + x⁹ + x⁵ + x⁴ + x + 1