gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000001100011101000000110100011000111010101111 a = 0x000000c740d18eaf a = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁵ + x³ + x² + x + 1
b = b0000000000000000000000000000000000000000000000000000000101000011 b = 0x0000000000000143 b = x⁸ + x⁶ + x + 1
1100011101000000110100011000111010101111 | 101000011 - 101000011 | 1 ---------------------------------------- | 110011011000000110100011000111010101111 | - 101000011 | 1 ---------------------------------------- | 11011000000000110100011000111010101111 | - 101000011 | 1 ---------------------------------------- | 1111001100000110100011000111010101111 | - 101000011 | 1 ---------------------------------------- | 101001010000110100011000111010101111 | - 101000011 | 1 ---------------------------------------- | 1001000110100011000111010101111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 11000000100011000111010101111 | - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 1100001000011000111010101111 | - 101000011 | 1 ---------------------------------------- | 110001110011000111010101111 | - 101000011 | 1 ---------------------------------------- | 11001101011000111010101111 | - 101000011 | 1 ---------------------------------------- | 1101100111000111010101111 | - 101000011 | 1 ---------------------------------------- | 111100001000111010101111 | - 101000011 | 1 ---------------------------------------- | 10100010000111010101111 | - 101000011 | 1 ---------------------------------------- | 11100111010101111 | - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 1000110110101111 | - 101000011 | 1 ---------------------------------------- | 10110000101111 | - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 10001001111 | - 000000000 | 0 - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 101000011 | - 000000000 | 0 - 101000011 | 1 ---------------------------------------- | 0 |
c_quotient = b0000000000000000000000000000000011111000010111111100000110100101 c_quotient = 0x00000000f85fc1a5 c_quotient = x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²² + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x⁸ + x⁷ + x⁵ + x² + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x0000000000000000 c_remainder = 0