gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x000040000000000000000000 a = x⁷⁸
b = b000000000000000000000000000000000000000000000000111101111101100100100100100111111111001100111111 b = 0x000000000000f7d9249ff33f b = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1
1000000000000000000000000000000000000000000000000000000000000000000000000000000 | 111101111101100100100100100111111111001100111111 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 111011111011001001001001001111111110011001111110000000000000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 110000110101101101101101000000001010101000001000000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 1101001000001001001001100111110101100100110111000000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 10010111010000000000101110001010010111111000110000000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 1100000100110010010111100010101101011001011001100000000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 11011011101011011110101011010010101010010110010000000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 101100011101001100111001001101010110100101101100000000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 10001100000101000011101101010101001101001010011000000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 1111011110011010001111111001010110001111001100100000000000000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 1000011000110110000101001111100000011010000000000000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 111000111101111001100000110011111101001001111110000000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 101000000011101000100010100000010000101000001000000 | - 000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000 | 0 - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 10101111110001100000110000111101111100100110111000 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 1011000000111110010100010100010000000010101000100 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 100011111100111011101011101101111110001100111010 | - 111101111101100100100100100111111111001100111111 | 1 ------------------------------------------------------------------------------- | 11110000001011111001111001010000001000000000101 |
c_quotient = b000000000000000000000000000000000000000000000000000000000000000011001010110101110000000011001111 c_quotient = 0x0000000000000000cad700cf c_quotient = x³¹ + x³⁰ + x²⁷ + x²⁵ + x²³ + x²² + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x⁷ + x⁶ + x³ + x² + x + 1
c_remainder = b000000000000000000000000000000000000000000000000011110000001011111001111001010000001000000000101 c_remainder = 0x0000000000007817cf281005 c_remainder = x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²¹ + x¹⁹ + x¹² + x² + 1