First of all, the binary remainder method is based on the binary number system. Compared with other number systems, such as decimal or hexadecimal, the binary number system only has two numbers: 0 and 1, which makes the implementation of binary remainder method in computers simpler and more efficient. Computer hardware can directly operate on binary numbers, so the method of using binary remainder can make full use of the computing power of computers.
Secondly, the binary remainder method has the characteristics of modular operation. In modular operation, we can divide one number by another and take the remainder to get an equivalent representation. This feature makes the binary remainder method widely used in cryptography, coding and hashing algorithms. For example, RSA encryption algorithm can encrypt and decrypt information by converting plaintext into binary form and then performing modular operation.
In addition, the binary remainder method also has the nature of power operation. By taking the remainder of a number many times, you can get the power of this number. This property has been applied to fast power algorithm, which can improve the efficiency of power operation.
Finally, the binary remainder method can also be used to solve some discrete mathematical problems. For example, in graph theory, some problems such as shortest path and minimum spanning tree can be solved by representing the vertices of the graph as binary numbers and then taking the remainder.
To sum up, the binary remainder method has the characteristics of binary number system, modular operation, power operation and its application in discrete mathematical problems. These characteristics make it have an important position and application value in computer science and mathematics.