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 = b00000000000000000000000000000000000000000000000000000000000000000110011001110111111000100000000101000110010100001000111110110111 b = 0x00000000000000006677e20146508fb7 b = x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴¹ + x³² + x³⁰ + x²⁶ + x²⁵ + x²² + x²⁰ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1001100111011111100010000000010100011001010000100011111011011100000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 101010100110000010011000000011110010101111000110010000110110010000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11001101000111101011100000011011010011101100111010111000000101000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1111100010111110000011001110000100110111110100111011110100000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11010001010001110010001110001110111011011100101010001001101110000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11101101010001110011110001100011000010110101110010110110101100000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 100001101010001111100001100001100001111111110110101001110111100000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 10010100100110000100101100001001001001101010111101110000001011000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1011000011101111000111100001011101010100000111001101111010000100000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 111110000000000110110100001010111011000101111011100000111101010000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1101001110111001110000001010010011110111011010100111001011101000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1111101010110000001001010011001111011110010110110110110000110000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11011001011111111000010011000101010010111110100111001101011110000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 10101100100000100000011000111110001110100100011010010000101100000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 1100000011011011100001000111100101101101110011110001111110111100000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 110000110100010000000111101111100001011011100000000011010010000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11111010101111000011101111001001101001000001000100100100111000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 110110010100111111111111001011001010001011000000111011100011100000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 101011010000000111011001011100010111001100001111100010101011000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------------------------------------- | 11000011110111000011101011100111111111110101110100101011101111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000111100000010100101111010010100110001000101001 c_quotient = 0x000000000000000000001e052f4a6229 c_quotient = x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x³⁴ + x³² + x²⁹ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²² + x¹⁹ + x¹⁷ + x¹⁴ + x¹³ + x⁹ + x⁵ + x³ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011000011110111000011101011100111111111110101110100101011101111 c_remainder = 0x000000000000000030f70eb9ffd74aef c_remainder = x⁶¹ + x⁶⁰ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁸ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁴ + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x³ + x² + x + 1