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 = 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
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 10011001110111111000100000000101000110010100001000111110110111000000000000000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010101001100000100110000000111100101011110001100100001101100100000000000000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110011010001111010111000000110110100111011001110101110000001010000000000000000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11111000101111100000110011100001001101111101001110111101000000000000000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110100010100011100100011100011101110110111001010100010011011100000000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 111011010100011100111100011000110000101101011100101101101011000000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1000011010100011111000011000011000011111111101101010011101111000000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 100101001001100001001011000010010010011010101111011100000010110000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 10110000111011110001111000010111010101000001110011011110100001000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1111100000000001101101000010101110110001011110111000001111010100000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11010011101110011100000010100100111101110110101001110010111010000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11111010101100000010010100110011110111100101101101101100001100000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110110010111111110000100110001010100101111101001110011010111100000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 101011001000001000000110001111100011101001000110100100001011000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11000000110110111000010001111001011011011100111100011111101111000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100001101000100000001111011111000010110111000000000110100100000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 111110101011110000111011110010011010010000010001001001001110000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1101100101001111111111110010110010100010110000001110111000111000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1010110100000001110110010111000101110011000011111000101010110000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 110000111101110000111010111001111111111101011101001010111011110000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 11110011001111111110111001010111001111111100001101001101001000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 111111110100000010101001010101101100110110001001010010010011100000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1100111010111101101101010101000100000100101000010101100101011000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 --------------------------------------------------------------------------------------------------------------------- | 1001010010011100010101001110001000000000000100011000110110 | - 000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000001111000000101001011110100101001100010001010011000101010 c_quotient = 0x0000000000000000007814bd2988a62a c_quotient = x⁵⁴ + x⁵³ + x⁵² + x⁵¹ + x⁴⁴ + x⁴² + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³⁴ + x³² + x²⁹ + x²⁷ + x²⁴ + x²³ + x¹⁹ + x¹⁵ + x¹³ + x¹⁰ + x⁹ + x⁵ + x³ + x
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000001001010010011100010101001110001000000000000100011000110110 c_remainder = 0x00000000000000000252715388004636 c_remainder = x⁵⁷ + x⁵⁴ + x⁵² + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴⁰ + x³⁸ + x³⁶ + x³³ + x³² + x³¹ + x²⁷ + x¹⁴ + x¹⁰ + x⁹ + x⁵ + x⁴ + x² + x