If there's a decimal number $$$2^k$$$ , express it in the form of 1000...

For example: $$$2^4$$$ can be expressed as 10000
So under this definition : 1. Numbers between 10000 and 11111 , any two numbers do the XOR operation , the result will lower than 10000. 2. If 10000 XOR with 1111 , one number smaller than 10000 , we'll get the maximum in the level of $$$2^k$$$ : 11111.