gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000004000000000000000000 a = x⁷⁴
b = b00000000000000000000000000000000000000000000000000000000000000001101111001110000111011101111011111000001100011111011011110011011 b = 0x0000000000000000de70eef7c18fb79b b = x⁶³ + x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁴ + x²³ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁴ + x³ + x + 1
100000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 10111100111000011101110111101111100000110001111101101111001101100000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 1100010100100010011001100011000010000101001000011011000101011010000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 1101101010010100010001100011101000100101011100000011011000001000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 10011100100101010001100110111100100111111111000000110010011000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 1000010111001011111011101001011010111100111111110000101111110110 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 --------------------------------------------------------------------------- | 101101110111011000000000110000101111101011100001011110001101101 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111001000011 c_quotient = 0x00000000000000000000000000000e43 c_quotient = x¹¹ + x¹⁰ + x⁹ + x⁶ + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000101101110111011000000000110000101111101011100001011110001101101 c_remainder = 0x00000000000000005bbb00617d70bc6d c_remainder = x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁶ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁸ + x³⁸ + x³⁷ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²² + x²¹ + x²⁰ + x¹⁵ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁶ + x⁵ + x³ + x² + 1