gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000010000000000000000000000000000000000000000000000000000 a = 0x0010000000000000 a = x⁵²
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
10000000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 110000110000010101001011111001000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 11100111100010000011001000111010000000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1010111010010010110000011000011000000000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1111001010011100100110111111100000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 100001001011101110010010000000100000000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1101000111101011000000111110110000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 110000100101010010100010001010100000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 11100101001010111110000110100110000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1010101111010101011001101011111000000000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1101100010100001101000100011100000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 110100001100000111100001100000100000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 11000000000000010110011011110110000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 1110000110000000011010000001111000 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 101000101000001001110101110011100 | - 10110000110000010101001011111001 | 1 ----------------------------------------------------- | 100100100001100100111001101110 | - 00000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000001011100110111100111110 c_quotient = 0x00000000002e6f3e c_quotient = x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁴ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x
c_remainder = b0000000000000000000000000000000000100100100001100100111001101110 c_remainder = 0x0000000024864e6e c_remainder = x²⁹ + x²⁶ + x²³ + x¹⁸ + x¹⁷ + x¹⁴ + x¹¹ + x¹⁰ + x⁹ + x⁶ + x⁵ + x³ + x² + x