gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000010000000000000000000000000000000000000000000 a = x¹⁷²
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
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001011110111001101011110110100000101100110010010001010101100101100110000110000101100111101011111100110010011010001011010010010000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101110001100101011110001101110000111010101011011001111111010111010101000101000111010100011110000010101011010111001110111011011000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111011110110001110001010101001101111110111111110100111110110101101000100100011110100010111001001110101011011110010111110110111000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001001011111101011101000100101110101110011010000101011101100110001000101111111111011000011110001100111111000110101000010011100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 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c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110110100001111101110101100101010111000100011 c_quotient = 0x00000000000000000000000000000000000000000000000000007b43eeb2ae23 c_quotient = x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁸ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁵ + x²³ + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁵ + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100011110001010100101101110001011100101111100011101001100001001111110010010011101011010101001001110111101101001010101011111011 c_remainder = 0x0000000000000000000000000000000023c54b7172f8e984fc93ad5277b4aafb c_remainder = x¹²⁵ + x¹²¹ + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁴ + x¹¹² + x¹¹⁰ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰² + x¹⁰¹ + x¹⁰⁰ + x⁹⁶ + x⁹⁴ + x⁹³ + x⁹² + x⁸⁹ + x⁸⁷ + x⁸⁶ + x⁸⁵ + x⁸⁴ + x⁸³ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁵ + x⁷² + x⁷¹ + x⁶⁶ + x⁶³ + x⁶² + x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁵ + x⁵² + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴³ + x⁴² + x⁴⁰ + x³⁸ + x³⁶ + x³³ + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + x + 1