gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000000000400000000000000000000000000000000000 a = x¹⁴²
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
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 1001011110111001101011110110100000101100110010010001010101100101100110000110000101100111101011111100110010011010001011010010010000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 101110001100101011110001101110000111010101011011001111111010111010101000101000111010100011110000010101011010111001110111011011000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 11100110001011000100110000011000110001100111111101101010001110001100100100100110001101100100111101100111110001101100001111111100000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 101101111100001001101110101100110100000001101111100000100010100000010100010110100001011001100010000001100010111101010101101110000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 11111000001111010111001000001110101011000001011000010001001101011011000011010101010010110110101111000000110001001000011001010100000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 110011111000011010010110111010101110100111001010011011100001110111110011100101111110001011110000100110100010011001000011000110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 1000101101001000001010111101111111110101110111001001010111100111111101001110101000100100111011111000110101101010101100010100000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 100000010010100111111000110101111100011101110000001111101010101001110001101101010010111001110000110101100100111101001111101001000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 10010101111010100101111011000111101000100010100101101000001100010111101100001011001110110100111001100000000001001011001001101100 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 1011110001101101000100101110011101101000100110111100010100000111011011100111011100010001001100110000110010010011010010011111110 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------- | 111011110110001110001010101001101111110111111110100111110110101101000100100011110100010111001001110101011011110010111110110111 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110110100001111 c_quotient = 0x000000000000000000000000000000000000000000000000000000000001ed0f c_quotient = x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x¹⁰ + x⁸ + x³ + x² + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111011110110001110001010101001101111110111111110100111110110101101000100100011110100010111001001110101011011110010111110110111 c_remainder = 0x000000000000000000000000000000003bd8e2a9bf7fa7dad123d172756f2fb7 c_remainder = x¹²⁵ + x¹²⁴ + x¹²³ + x¹²¹ + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁶ + x¹¹⁵ + x¹¹¹ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁵ + x¹⁰³ + x¹⁰¹ + x⁹⁹ + x⁹⁶ + x⁹⁵ + x⁹³ + x⁹² + x⁹¹ + x⁹⁰ + x⁸⁹ + x⁸⁸ + x⁸⁶ + x⁸⁵ + x⁸⁴ + x⁸³ + x⁸² + x⁸¹ + x⁸⁰ + x⁷⁹ + x⁷⁷ + x⁷⁴ + x⁷³ + x⁷² + x⁷¹ + x⁷⁰ + x⁶⁸ + x⁶⁷ + x⁶⁵ + x⁶³ + x⁶² + x⁶⁰ + x⁵⁶ + x⁵³ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁴ + x⁴⁰ + x³⁸ + x³⁷ + x³⁶ + x³³ + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁴ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1