gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000100101010011000010001101001010100000001110 a = 0x00000254c234a80e a = x⁴¹ + x³⁸ + x³⁶ + x³⁴ + x³¹ + x³⁰ + x²⁵ + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹¹ + x³ + x² + x
b = b0000000000000000000000001100011101000000110100011000111010101111 b = 0x000000c740d18eaf b = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁵ + x³ + x² + x + 1
100101010011000010001101001010100000001110 | 1100011101000000110100011000111010101111 - 1100011101000000110100011000111010101111 | 1 ------------------------------------------ | 10100100111000001011100101001001010110010 | - 1100011101000000110100011000111010101111 | 1 ------------------------------------------ | 1100011101000000110100011000111111101100 | - 1100011101000000110100011000111010101111 | 1 ------------------------------------------ | 101000011 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000111 c_quotient = 0x0000000000000007 c_quotient = x² + x + 1
c_remainder = b0000000000000000000000000000000000000000000000000000000101000011 c_remainder = 0x0000000000000143 c_remainder = x⁸ + x⁶ + x + 1