gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000004000000000000000000000000000000000000000 a = x¹⁵⁸
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
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010111101110011010111101101000001011001100100100010101011001011001100001100001011001111010111111001100100110100010110100100100000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011100011001010111100011011100001110101010110110011111110101110101010001010001110101000111100000101010110101110011101110110110000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111001100010110001001100000110001100011001111111011010100011100011001001001001100011011001001111011001111100011011000011111111000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011011111000010011011101011001101000000011011111000001000101000000101000101101000010110011000100000011000101111010101011011100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111110000011110101110010000011101010110000010110000100010011010110110000110101010100101101101011110000001100010010000110010101000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100111110000110100101101110101011101001110010100110111000011101111100111001011111100010111100001001101000100110010000110001100000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10001011010010000010101111011111111101011101110010010101111001111111010011101010001001001110111110001101011010101011000101000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000000100101001111110001101011111000111011100000011111010101010011100011011010100101110011100001101011001001111010011111010010000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100101011110101001011110110001111010001000101001011010000011000101111011000010110011101101001110011000000000010010110010011011000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10111100011011010001001011100111011010001001101111000101000001110110111001110111000100010011001100001100100100110100100111111100000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110111101100011100010101010011011111101111111101001111101101011010001001000111101000101110010011101010110111100101111101101110000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010010111111010111010001001011101011100110100001010111011001100010001011111111110110000111100011001111110001101010000100111000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011001001000011010001111111111101110000000110011011101110101001110111011001111011010111010111100101001100010111011011110101010000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111100110011111100100000100101101100110011111010011000100011011000100011010111001100100100010011011010101011010011110011100011000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110001110001111110111001000101101101010011110111010001000010011101111011011000111101011000100100011001111100111100101000111100000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10100001010011000010110011111101111100000111110010100010100001011100011000000101011000110001011101010110101010100000101110101000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1101010100100001111101101001001111001100001100000101000001101110000101000110101110100001100000010110000111001110001110100111010000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111011111101001000010010011111011010010101001101101011011100110110000101101100010010010101101000011110000011001011001110011000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11110000110101110111101000101011000100110000100101110001010100000011101110100000100001011000111101101001010100011100011010001000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111011000010111010110110011111000001010110110111111011111000101111011110010000001101100101100010001111000111001101000000011010 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111101101000011111011101011001010 c_quotient = 0x00000000000000000000000000000000000000000000000000000001ed0fbaca c_quotient = x³² + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁴ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹¹ + x⁹ + x⁷ + x⁶ + x³ + x
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111011000010111010110110011111000001010110110111111011111000101111011110010000001101100101100010001111000111001101000000011010 c_remainder = 0x000000000000000000000000000000003b0bad9f056dfbe2f79036588f1cd01a c_remainder = x¹²⁵ + x¹²⁴ + x¹²³ + x¹²¹ + x¹²⁰ + x¹¹⁵ + x¹¹³ + x¹¹² + x¹¹¹ + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁶ + x¹⁰⁴ + x¹⁰³ + x¹⁰⁰ + x⁹⁹ + x⁹⁸ + x⁹⁷ + x⁹⁶ + x⁹⁰ + x⁸⁸ + x⁸⁶ + x⁸⁵ + x⁸³ + x⁸² + x⁸⁰ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁶ + x⁷⁵ + x⁷³ + x⁷² + x⁷¹ + x⁷⁰ + x⁶⁹ + x⁶⁵ + x⁶³ + x⁶² + x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵² + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x³⁸ + x³⁶ + x³⁵ + x³¹ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁵ + x¹⁴ + x¹² + x⁴ + x³ + x