gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000400000000000000000000 a = x⁸²
b = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 11010101110100110100011101111000011001111010111000010101111110000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 1001111011010010010111110010111011010110101101111010111010001110000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 10001101000001101111100000111011010010000100110110000110001000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 10111101111001001000011010100010001001011100001000100100111110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 100111010111101110111001001101001010010011011111100110010001110000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 1111100000111010001110110111010100000101010010110111010001100000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------- | 110001010000000010100111001101000001001101111101011011011011111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010011000010010100001 c_quotient = 0x000000000000000000000000000984a1 c_quotient = x¹⁹ + x¹⁶ + x¹⁵ + x¹⁰ + x⁷ + x⁵ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000110001010000000010100111001101000001001101111101011011011011111 c_remainder = 0x00000000000000006280539a09beb6df c_remainder = x⁶² + x⁶¹ + x⁵⁷ + x⁵⁵ + x⁴⁶ + x⁴⁴ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁶ + x³⁵ + x³³ + x²⁷ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴ + x³ + x² + x + 1