gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000400000000000000000000000000 a = x¹⁰⁶
b = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 11010101110100110100011101111000011001111010111000010101111110000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1001111011010010010111110010111011010110101101111010111010001110000000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 10001101000001101111100000111011010010000100110110000110001000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 10111101111001001000011010100010001001011100001000100100111110000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 100111010111101110111001001101001010010011011111100110010001110000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1111100000111010001110110111010100000101010010110111010001100000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 110001010000000010100111001101000001001101111101011011011011111000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 10111111011101011001111110110110001111110001000101011110000000100000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 100101110011111111011101011001001100111110010010011100101111010000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 11011000010110110101100010111100001101100111101100000100101100000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1000010111000010011000001010011001110101000111011000110000011110000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1111101111000000010000100100101111001111010000100111010100001000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 110000101111010001010101010010011000011101101111011011110110111000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 10110000100111000111101101001101000101110011010101011011101000100000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 101010001001100001001110100010000110111100000010011001000111010000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1100100010001000100110011001110110001111110111101001101100101100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 101001000110010111100010111001010000011001010110101100110010011000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 1111101101111110001010000010100000101010100011011100011001100100000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 110000111000100010000001100011100100110011110000000010011011011000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 10110010011001011101001011000010100000000000101110010110000100100 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------------------- | 101000110111111011101000101101100011001111111001010100101011010 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000010011000010010100001110100011001110101101110 c_quotient = 0x000000000000000000000984a1d19d6e c_quotient = x⁴³ + x⁴⁰ + x³⁹ + x³⁴ + x³¹ + x²⁹ + x²⁴ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁶ + x⁵ + x³ + x² + x
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000101000110111111011101000101101100011001111111001010100101011010 c_remainder = 0x000000000000000051bf745b19fca95a c_remainder = x⁶² + x⁶⁰ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x³⁸ + x³⁶ + x³⁵ + x³³ + x³² + x²⁸ + x²⁷ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁵ + x¹³ + x¹¹ + x⁸ + x⁶ + x⁴ + x³ + x