gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000001000000000000000000000000000000000000 a = 0x0000001000000000 a = x³⁶
b = b0000000000000000000000000000000000000000001001111000101010011001 b = 0x0000000000278a99 b = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
1000000000000000000000000000000000000 | 1001111000101010011001 - 1001111000101010011001 | 1 ------------------------------------- | 1111000101010011001000000000000000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------------- | 110111101111001010001000000000000 | - 1001111000101010011001 | 1 ------------------------------------- | 10000001101100011101100000000000 | - 1001111000101010011001 | 1 ------------------------------------- | 11111100110111011110000000000 | - 0000000000000000000000 | 0 - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------------- | 1100010111101111000010000000 | - 1001111000101010011001 | 1 ------------------------------------- | 101101111000101011011000000 | - 1001111000101010011001 | 1 ------------------------------------- | 1010011010000010111100000 | - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------------- | 11100010101000100101000 | - 0000000000000000000000 | 0 - 1001111000101010011001 | 1 ------------------------------------- | 1111100100010000011010 | - 1001111000101010011001 | 1 ------------------------------------- | 110011100111010000011 |
c_quotient = b0000000000000000000000000000000000000000000000001001110011101011 c_quotient = 0x0000000000009ceb c_quotient = x¹⁵ + x¹² + x¹¹ + x¹⁰ + x⁷ + x⁶ + x⁵ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000000000000110011100111010000011 c_remainder = 0x000000000019ce83 c_remainder = x²⁰ + x¹⁹ + x¹⁶ + x¹⁵ + x¹⁴ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x + 1