How to build my own bitcoin system? I want to know whether there exists any software that can let people create their own private personal Bitcoin, and mine their own Bitcoin. 

Or any other software that can let people issue their own digital currency.
Because Bitcoin is open source, the source code is the software for creating new crypto coins.  Depending on what you want out of a new coin, and why you want it, the things you modify will be different.  However, the simple recipe is this:


Fork Bitcoin Core
Change the hard-coded genesis block in the source code
Change the port number that the protocol runs on
Recompile
Start mining, and convince others to join


There are other things you can change as well, such as hashing algorithm, block time, difficulty increase frequency, etc.  It all depends on your goal.