gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000000000000000000010000000000000000000000000000000000000 a = x¹⁴⁸
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
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 1001011110111001101011110110100000101100110010010001010101100101100110000110000101100111101011111100110010011010001011010010010000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 101110001100101011110001101110000111010101011011001111111010111010101000101000111010100011110000010101011010111001110111011011000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 11100110001011000100110000011000110001100111111101101010001110001100100100100110001101100100111101100111110001101100001111111100000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 101101111100001001101110101100110100000001101111100000100010100000010100010110100001011001100010000001100010111101010101101110000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 11111000001111010111001000001110101011000001011000010001001101011011000011010101010010110110101111000000110001001000011001010100000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 110011111000011010010110111010101110100111001010011011100001110111110011100101111110001011110000100110100010011001000011000110000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 1000101101001000001010111101111111110101110111001001010111100111111101001110101000100100111011111000110101101010101100010100000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 100000010010100111111000110101111100011101110000001111101010101001110001101101010010111001110000110101100100111101001111101001000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 10010101111010100101111011000111101000100010100101101000001100010111101100001011001110110100111001100000000001001011001001101100000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 1011110001101101000100101110011101101000100110111100010100000111011011100111011100010001001100110000110010010011010010011111110000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 111011110110001110001010101001101111110111111110100111110110101101000100100011110100010111001001110101011011110010111110110111000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 1001001011111101011101000100101110101110011010000101011101100110001000101111111111011000011110001100111111000110101000010011100000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 101100100100001101000111111111110111000000011001101110111010100111011101100111101101011101011110010100110001011101101111010101000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 11110011001111110010000010010110110011001111101001100010001101100010001101011100110010010001001101101010101101001111001110001100 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------- | 111000111000111111011100100010110110101001111011101000100001001110111101101100011110101100010010001100111110011110010100011110 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110110100001111101110 c_quotient = 0x00000000000000000000000000000000000000000000000000000000007b43ee c_quotient = x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁴ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + x
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111000111000111111011100100010110110101001111011101000100001001110111101101100011110101100010010001100111110011110010100011110 c_remainder = 0x0000000000000000000000000000000038e3f722da9ee884ef6c7ac48cf9e51e c_remainder = x¹²⁵ + x¹²⁴ + x¹²³ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹³ + x¹¹² + x¹¹¹ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁸ + x¹⁰⁶ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰¹ + x⁹⁷ + x⁹⁵ + x⁹⁴ + x⁹² + x⁹¹ + x⁸⁹ + x⁸⁷ + x⁸⁴ + x⁸³ + x⁸² + x⁸¹ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁵ + x⁷¹ + x⁶⁶ + x⁶³ + x⁶² + x⁶¹ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵³ + x⁵¹ + x⁵⁰ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴¹ + x³⁹ + x³⁸ + x³⁴ + x³¹ + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹⁰ + x⁸ + x⁴ + x³ + x² + x