gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000001000000000000000000000000000000000000000000000000000000 a = 0x0040000000000000 a = x⁵⁴
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
1000000000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 11000011000001010100101111100100000000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 1110011110001000001100100011101000000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 101011101001001011000001100001100000000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 111100101001110010011011111110000000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 10000100101110111001001000000010000000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 110100011110101100000011111011000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 11000010010101001010001000101010000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 1110010100101011111000011010011000000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 101010111101010101100110101111100000000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 110110001010000110100010001110000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 11010000110000011110000110000010000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 1100000000000001011001101111011000000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 111000011000000001101000000111100000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 10100010100000100111010111001110000 | - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 10010010000110010011100110111000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 ------------------------------------------------------- | 100010110110000110101101000001 |
c_quotient = b0000000000000000000000000000000000000000101110011011110011111001 c_quotient = 0x0000000000b9bcf9 c_quotient = x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹¹ + x¹⁰ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
c_remainder = b0000000000000000000000000000000000100010110110000110101101000001 c_remainder = 0x0000000022d86b41 c_remainder = x²⁹ + x²⁵ + x²³ + x²² + x²⁰ + x¹⁹ + x¹⁴ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁶ + 1