gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000010000000000000000000000000000000000000000 a = 0x0000010000000000 a = x⁴⁰
b = b0000000000000000000000000000000000000000001001111000101010011001 b = 0x0000000000278a99 b = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
10000000000000000000000000000000000000000 | 1001111000101010011001 - 1001111000101010011001 | 1 ----------------------------------------- | 11110001010100110010000000000000000000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ----------------------------------------- | 1101111011110010100010000000000000000 | - 1001111000101010011001 | 1 ----------------------------------------- | 100000011011000111011000000000000000 | - 1001111000101010011001 | 1 ----------------------------------------- | 111111001101110111100000000000000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ----------------------------------------- | 11000101111011110000100000000000 | - 1001111000101010011001 | 1 ----------------------------------------- | 1011011110001010110110000000000 | - 1001111000101010011001 | 1 ----------------------------------------- | 10100110100000101111000000000 | - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ----------------------------------------- | 111000101010001001010000000 | - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ----------------------------------------- | 11111001000100000110100000 | - 1001111000101010011001 | 1 ----------------------------------------- | 1100111001110100000110000 | - 1001111000101010011001 | 1 ----------------------------------------- | 101000001011110011111000 | - 1001111000101010011001 | 1 ----------------------------------------- | 1111101001011010011100 | - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ----------------------------------------- | 110010001110000000101 |
c_quotient = b0000000000000000000000000000000000000000000010011100111010111101 c_quotient = 0x000000000009cebd c_quotient = x¹⁹ + x¹⁶ + x¹⁵ + x¹⁴ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + 1
c_remainder = b0000000000000000000000000000000000000000000110010001110000000101 c_remainder = 0x0000000000191c05 c_remainder = x²⁰ + x¹⁹ + x¹⁶ + x¹² + x¹¹ + x¹⁰ + x² + 1