gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00100000000000000000000000000000 a = x¹¹⁶
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
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110101011101001101000111011110000110011110101110000101011111100000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 10011110110100100101111100101110110101101011011110101110100011100000000000000000000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 100011010000011011111000001110110100100001001101100001100010000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101111011110010010000110101000100010010111000010001001001111100000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1001110101111011101110010011010010100100110111111001100100011100000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11111000001110100011101101110101000001010100101101110100011000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100010100000000101001110011010000010011011111010110110110111110000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101111110111010110011111101101100011111100010001010111100000001000000000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1001011100111111110111010110010011001111100100100111001011110100000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110110000101101101011000101111000011011001111011000001001011000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 10000101110000100110000010100110011101010001110110001100000111100000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11111011110000000100001001001011110011110100001001110101000010000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100001011110100010101010100100110000111011011110110111101101110000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101100001001110001111011010011010001011100110101010110111010001000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010100010011000010011101000100001101111000000100110010001110100000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11001000100010001001100110011101100011111101111010011011001011000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010010001100101111000101110010100000110010101101011001100100110000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11111011011111100010100000101000001010101000110111000110011001000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100001110001000100000011000111001001100111100000000100110110110000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101100100110010111010010110000101000000000001011100101100001001000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010001101111110111010001011011000110011111110010101001010110100000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11100111000100100000000101100100111111000011001001000000001011000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1111101101010000110100110001011111100001100011110000010100100110000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110000111101010101110111111100011101101011110101100011110011001000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 10110010110111100011111000111101101011000000000010011011000110100000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101000011001000101011011010010101000001111010101011001101001010000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1110110010101100110011101001011000111100100000101001000010101100 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 --------------------------------------------------------------------------------------------------------------------- | 111011000010110101001100111100100110000011101110101001000010011 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000100110000100101000011101000110011101011011101011110101 c_quotient = 0x0000000000000000002612874675baf5 c_quotient = x⁵³ + x⁵⁰ + x⁴⁹ + x⁴⁴ + x⁴¹ + x³⁹ + x³⁴ + x³³ + x³² + x³⁰ + x²⁶ + x²⁵ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x² + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000111011000010110101001100111100100110000011101110101001000010011 c_remainder = 0x00000000000000007616a67930775213 c_remainder = x⁶² + x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵² + x⁵⁰ + x⁴⁹ + x⁴⁷ + x⁴⁵ + x⁴² + x⁴¹ + x³⁸ + x³⁷ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁸ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁴ + x + 1