gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000100000101010100010100010101000101010100010100 a = 0x0000105514545514 a = x⁴⁴ + x³⁸ + x³⁶ + x³⁴ + x³² + x²⁸ + x²⁶ + x²² + x²⁰ + x¹⁸ + x¹⁴ + x¹² + x¹⁰ + x⁸ + x⁴ + x²
b = b0000000000000000000001010000010100010100010101010001000000010001 b = 0x0000050514551011 b = x⁴² + x⁴⁰ + x³⁴ + x³² + x²⁸ + x²⁶ + x²² + x²⁰ + x¹⁸ + x¹⁶ + x¹² + x⁴ + 1
100000101010100010100010101000101010100010100 | 1010000010100010100010101010001000000010001 - 1010000010100010100010101010001000000010001 | 1 --------------------------------------------- | 1000100000101000101000000000001010101010000 | - 0000000000000000000000000000000000000000000 | 0 - 1010000010100010100010101010001000000010001 | 1 --------------------------------------------- | 10100010001010001010101010000010101000001 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000000101 c_quotient = 0x0000000000000005 c_quotient = x² + 1
c_remainder = b0000000000000000000000010100010001010001010101010000010101000001 c_remainder = 0x0000014451550541 c_remainder = x⁴⁰ + x³⁸ + x³⁴ + x³⁰ + x²⁸ + x²⁴ + x²² + x²⁰ + x¹⁸ + x¹⁶ + x¹⁰ + x⁸ + x⁶ + 1