gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000001000000000000000000000000000000 a = 0x0000000040000000 a = x³⁰
b = b0000000000000000000000000000000000000000001001111000101010011001 b = 0x0000000000278a99 b = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
1000000000000000000000000000000 | 1001111000101010011001 - 1001111000101010011001 | 1 ------------------------------- | 1111000101010011001000000000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------- | 110111101111001010001000000 | - 1001111000101010011001 | 1 ------------------------------- | 10000001101100011101100000 | - 1001111000101010011001 | 1 ------------------------------- | 11111100110111011110000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------- | 1100010111101111000010 | - 1001111000101010011001 | 1 ------------------------------- | 101101111000101011011 |
c_quotient = b0000000000000000000000000000000000000000000000000000001001110011 c_quotient = 0x0000000000000273 c_quotient = x⁹ + x⁶ + x⁵ + x⁴ + x + 1
c_remainder = b0000000000000000000000000000000000000000000101101111000101011011 c_remainder = 0x000000000016f15b c_remainder = x²⁰ + x¹⁸ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁸ + x⁶ + x⁴ + x³ + x + 1