gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000040000000000000000000000000 a = x¹⁰²
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
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 100110011101111110001000000001010001100101000010001111101101110000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 10101010011000001001100000001111001010111100011001000011011001000000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1100110100011110101110000001101101001110110011101011100000010100000000000000000000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 111110001011111000001100111000010011011111010011101111010000000000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1101000101000111001000111000111011101101110010101000100110111000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1110110101000111001111000110001100001011010111001011011010110000000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 10000110101000111110000110000110000111111111011010100111011110000000000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1001010010011000010010110000100100100110101011110111000000101100000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 101100001110111100011110000101110101010000011100110111101000010000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 11111000000000011011010000101011101100010111101110000011110101000000000000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 110100111011100111000000101001001111011101101010011100101110100000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 111110101011000000100101001100111101111001011011011011000011000000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1101100101111111100001001100010101001011111010011100110101111000000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1010110010000010000001100011111000111010010001101001000010110000000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 110000001101101110000100011110010110110111001111000111111011110000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 11000011010001000000011110111110000101101110000000001101001000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 1111101010111100001110111100100110100100000100010010010011100000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ------------------------------------------------------------------------------------------------------- | 11011001010011111111111100101100101000101100000011101110001110 | - 000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110000001010010111101001010011000100010 c_quotient = 0x0000000000000000000001e052f4a622 c_quotient = x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁰ + x²⁸ + x²⁵ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹⁰ + x⁹ + x⁵ + x
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011011001010011111111111100101100101000101100000011101110001110 c_remainder = 0x00000000000000003653ffcb28b03b8e c_remainder = x⁶¹ + x⁶⁰ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵² + x⁴⁹ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁵ + x³³ + x³² + x²⁹ + x²⁷ + x²³ + x²¹ + x²⁰ + x¹³ + x¹² + x¹¹ + x⁹ + x⁸ + x⁷ + x³ + x² + x