gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0001000000000000000000000000000000000000000000000000000000000000 a = 0x1000000000000000 a = x⁶⁰
b = b0000000000000000000000000000000011101011111100101000001100011111 b = 0x00000000ebf2831f b = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1
1000000000000000000000000000000000000000000000000000000000000 | 11101011111100101000001100011111 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 110101111110010100000110001111100000000000000000000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 1111000001011110000101001000010000000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 1101110101100100101111001101100000000000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 11011010010110001111111100011100000000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 110001101010100111110000000011000000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 1011010101101101110011000100110000000000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 101111010011111010011110101001100000000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 10101101100110000011101101110010000000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 1000110011010101011100001101101000000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 110011100100111111100111100010100000000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 1001011011110101100100100101010000000000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 111110100000111000100010100101100000000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 100011111110010100001100010010000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 11001000001011110001111010101110000000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 100011110111011001110110110001000000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 11001001000010011110101110110110000 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 100010111110110110100010101001000 | - 00000000000000000000000000000000 | 0 - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 11000000001111100100001101110110 | - 11101011111100101000001100011111 | 1 ------------------------------------------------------------- | 101011110011001100000001101001 |
c_quotient = b0000000000000000000000000000000000110100101010111110110011011011 c_quotient = 0x0000000034abecdb c_quotient = x²⁹ + x²⁸ + x²⁶ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x¹⁰ + x⁷ + x⁶ + x⁴ + x³ + x + 1
c_remainder = b0000000000000000000000000000000000101011110011001100000001101001 c_remainder = 0x000000002bccc069 c_remainder = x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x¹⁹ + x¹⁸ + x¹⁵ + x¹⁴ + x⁶ + x⁵ + x³ + 1