Windows 7: Windows 7 32 to 64 question

Hi, I have a copy of windows 7 professional x32 and i read that the cd keys are interchangeable for either x32 or x64 as long as it is the same type. The cd key that i bought i got online from the store but i want to install it on a new hard drive. I have my 32 bit cd key but i cant find my 64 bit cd key.

My question is: will my professional x32 digital cd key be accepted and valid if i download and install a professional x64 ISO onto a new hard drive. They are both full version cd keys and of the same type. I just read i believe that a x32 digital cd key wont be valid with a x64 ISO dvd.

Sorry if this is confusing just ask and ill try to be more clear.

A retail CD key is valid for both x32 and x64 versions

Even though one of the cd keys was bought digitally?

Yes, if both are retail versions

When you purchased the Win 7 DVD, you should have gotten a key that would work with either 32 or 64 bit. Why did you buy a second key and where did you buy it from? Hopefully you won't say Ebay.