Can shellcode run on 32bit, 64bit both windows operating systems?

Is there any way to run 32bit shellcode on 64bit operating system?
I intend to run 32bit shellcode on 64bit process. Is it possible? I am sure that I have to build 32bit, 64bit shellocdes, and run it on equal bits process.
I know, the main point is the size of address, the differences between 0x00000000 and 0x00000000 00000000. My post seems too poor, but how can I express more about my question? Please edit my question and answer me.