gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000000000004000000000000000000000000000000000 a = x¹³⁴
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
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 10010111101110011010111101101000001011001100100100010101011001011001100001100001011001111010111111001100100110100010110100100100000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 1011100011001010111100011011100001110101010110110011111110101110101010001010001110101000111100000101010110101110011101110110110000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 111001100010110001001100000110001100011001111111011010100011100011001001001001100011011001001111011001111100011011000011111111000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 1011011111000010011011101011001101000000011011111000001000101000000101000101101000010110011000100000011000101111010101011011100000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 111110000011110101110010000011101010110000010110000100010011010110110000110101010100101101101011110000001100010010000110010101000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 1100111110000110100101101110101011101001110010100110111000011101111100111001011111100010111100001001101000100110010000110001100 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------- | 10001011010010000010101111011111111101011101110010010101111001111111010011101010001001001110111110001101011010101011000101 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111101101 c_quotient = 0x00000000000000000000000000000000000000000000000000000000000001ed c_quotient = x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001011010010000010101111011111111101011101110010010101111001111111010011101010001001001110111110001101011010101011000101 c_remainder = 0x00000000000000000000000000000000022d20af7fd772579fd3a893be35aac5 c_remainder = x¹²¹ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹² + x¹⁰⁹ + x¹⁰³ + x¹⁰¹ + x⁹⁹ + x⁹⁸ + x⁹⁷ + x⁹⁶ + x⁹⁴ + x⁹³ + x⁹² + x⁹¹ + x⁹⁰ + x⁸⁹ + x⁸⁸ + x⁸⁷ + x⁸⁶ + x⁸⁴ + x⁸² + x⁸¹ + x⁸⁰ + x⁷⁸ + x⁷⁷ + x⁷⁶ + x⁷³ + x⁷⁰ + x⁶⁸ + x⁶⁶ + x⁶⁵ + x⁶⁴ + x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵² + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁵ + x⁴³ + x³⁹ + x³⁶ + x³³ + x³² + x³¹ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁷ + x⁶ + x² + 1