gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000000000040000000000000000000000000000000000 a = x¹³⁸
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
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 10111000110010101111000110111000011101010101101100111111101011101010100010100011101010001111000001010101101011100111011101101100000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 1110011000101100010011000001100011000110011111110110101000111000110010010010011000110110010011110110011111000110110000111111110000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 10110111110000100110111010110011010000000110111110000010001010000001010001011010000101100110001000000110001011110101010110111000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 1111100000111101011100100000111010101100000101100001000100110101101100001101010101001011011010111100000011000100100001100101010000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 11001111100001101001011011101010111010011100101001101110000111011111001110010111111000101111000010011010001001100100001100011000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ------------------------------------------------------------------------------------------------------------------------------------------- | 100010110100100000101011110111111111010111011100100101011110011111110100111010100010010011101111100011010110101010110001010000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111011010000 c_quotient = 0x0000000000000000000000000000000000000000000000000000000000001ed0 c_quotient = x¹² + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010110100100000101011110111111111010111011100100101011110011111110100111010100010010011101111100011010110101010110001010000 c_remainder = 0x0000000000000000000000000000000022d20af7fd772579fd3a893be35aac50 c_remainder = x¹²⁵ + x¹²¹ + x¹¹⁹ + x¹¹⁸ + x¹¹⁶ + x¹¹³ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰³ + x¹⁰² + x¹⁰¹ + x¹⁰⁰ + x⁹⁸ + x⁹⁷ + x⁹⁶ + x⁹⁵ + x⁹⁴ + x⁹³ + x⁹² + x⁹¹ + x⁹⁰ + x⁸⁸ + x⁸⁶ + x⁸⁵ + x⁸⁴ + x⁸² + x⁸¹ + x⁸⁰ + x⁷⁷ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁹ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶³ + x⁶² + x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁶ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁷ + x⁴³ + x⁴⁰ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁹ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x¹⁰ + x⁶ + x⁴