gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000010000000000000000000 a = x⁷⁶
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
10000000000000000000000000000000000000000000000000000000000000000000000000000 | 110011001110111111000100000000101000110010100001000111110110111 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 1001100111011111100010000000010100011001010000100011111011011100000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 101010100110000010011000000011110010101111000110010000110110010000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 11001101000111101011100000011011010011101100111010111000000101000000000000 | - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 1111100010111110000011001110000100110111110100111011110100000000000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 11010001010001110010001110001110111011011100101010001001101110000 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 110011001110111111000100000000101000110010100001000111110110111 | 1 ----------------------------------------------------------------------------- | 11101101010001110011110001100011000010110101110010110110101100 | - 000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111100000010100 c_quotient = 0x00000000000000000000000000007814 c_quotient = x¹⁴ + x¹³ + x¹² + x¹¹ + x⁴ + x²
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000011101101010001110011110001100011000010110101110010110110101100 c_remainder = 0x00000000000000003b51cf18c2d72dac c_remainder = x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁶ + x⁵⁴ + x⁵² + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁶ + x³⁵ + x³¹ + x³⁰ + x²⁵ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁸ + x⁷ + x⁵ + x³ + x²