gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000000010000000000000000000 a = x⁷⁶
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
10000000000000000000000000000000000000000000000000000000000000000000000000000 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 1011110011100001110111011110111110000011000111110110111100110110000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 110001010010001001100110001100001000010100100001101100010101101000000000000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 110110101001010001000110001110100010010101110000001101100000100000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 1001110010010101000110011011110010011111111100000011001001100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 100001011100101111101110100101101011110011111111000010111111011000 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 10110111011101100000000011000010111110101110000101111000110110100 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 1101001000001101110111000110101001110110110111011001111010000010 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ----------------------------------------------------------------------------- | 110001111101001100101001110110110111010100100010100100011001 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011100100001111 c_quotient = 0x0000000000000000000000000000390f c_quotient = x¹³ + x¹² + x¹¹ + x⁸ + x³ + x² + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000110001111101001100101001110110110111010100100010100100011001 c_remainder = 0x00000000000000000c7d329db7522919 c_remainder = x⁵⁹ + x⁵⁸ + x⁵⁴ + x⁵³ + x⁵² + x⁵¹ + x⁵⁰ + x⁴⁸ + x⁴⁵ + x⁴⁴ + x⁴¹ + x³⁹ + x³⁶ + x³⁵ + x³⁴ + x³² + x³¹ + x²⁹ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²² + x²⁰ + x¹⁷ + x¹³ + x¹¹ + x⁸ + x⁴ + x³ + 1