gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000001010000010000000000000000010000010001010100000001 a = 0x0001410000411501 a = x⁴⁸ + x⁴⁶ + x⁴⁰ + x²² + x¹⁶ + x¹² + x¹⁰ + x⁸ + 1
b = b0000000000000000000100000101010100010100010101000101010100010100 b = 0x0000105514545514 b = x⁴⁴ + x³⁸ + x³⁶ + x³⁴ + x³² + x²⁸ + x²⁶ + x²² + x²⁰ + x¹⁸ + x¹⁴ + x¹² + x¹⁰ + x⁸ + x⁴ + x²
1010000010000000000000000010000010001010100000001 | 100000101010100010100010101000101010100010100 - 100000101010100010100010101000101010100010100 | 1 ------------------------------------------------- | 10001000101000101000101000001000100010001000001 | - 000000000000000000000000000000000000000000000 | 0 - 100000101010100010100010101000101010100010100 | 1 ------------------------------------------------- | 1010000010100010100010101010001000000010001 | - 000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000000000010100 c_quotient = 0x0000000000000014 c_quotient = x⁴ + x²
c_remainder = b0000000000000000000001010000010100010100010101010001000000010001 c_remainder = 0x0000050514551011 c_remainder = x⁴² + x⁴⁰ + x³⁴ + x³² + x²⁸ + x²⁶ + x²² + x²⁰ + x¹⁸ + x¹⁶ + x¹² + x⁴ + 1