Windows 7 home Premium 32 bit and Windows Pro 64 bit O/S

64 bit is clearly predominant.   If you take a given computer configuration, one with a 32 bit installation and the other 64, the 64 is about 15% faster

32 bit is limited to a bit more than 3 gigabytes of memory.  64 is limited only by the computer's design.  The difference is how many windows you can open at one time and not degrade performance seriously.

If you will provide details on your current computer, I will offer my advice on what to do next.

1. Laptop or Desktop
2. Age of computer
3. make/model
4. Operating system installed (e.g. Windows 7)
5. Service Pack 1 (SP1) installed? Same place.
6. Capacity of disk drive, how much is in use?  Pie chart shown in Computer
7. Model number of hard drive (click Disk in Device Manager)
8. How much memory is installed? (Right-click on Computer, choose Properties)
9. Please list ALL installed programs.....
10. Security software installed?
11. Speed of Internet service you are using (www.speedtest.net )

Whether a Windows operating system is characterized as 32-bit or 64-bit has no bearing at all on data.  As long as you have application programs that can "understand" the data files, you're good to go. 

For example, if you have *.doc or *.docx files that you created using Microsoft Word on your Windows 7 32-bit system, you will be able to read and edit those files once you install Microsoft Word on a Windows 10 64-bit system. 

That would be the case even if you chose to install the 64-bit version of Word on the Windows 10 system -- but you probably do not want to do that.  Microsoft Office defaults to installing the 32-bit versions of its applications even on systems that are running the 64-bit version of Windows.  See

https://support.office.com/en-us/article/Choose-between-the-64-bit-or-32-bit-version-of-Office-2dee7807-8f95-4d0c-b5fe-6c6f49b8d261

If you had just copied files from your current computer to your external drive, you could just copy them back from the external drive to your new Windows 10 computer.

If you used the "Backup and Restore" routine built into Windows 7 to create your backup, this article explains how to recover your data:  https://www.pcworld.com/article/3034527/windows/restore-a-windows-7-backup-in-windows-10.html

If you used some other application to create your backup, you may need to install that application on your Windows 10 system to recover the data.

I am under the assumption that The only difference between a 32bit and 64bit O/S is the amount of Data transfer is increased and the system runs faster.

Not quite.  As far as most home users are concerned, the main difference between a 32-bit version of Windows and a 64-bit version of Windows is the latter's ability to use more RAM.  The system may or may not "run faster" if it has more RAM; that depends on what you're doing.  And, of course, there won't be any change at all unless you actually install more RAM (assuming that your hardware permits that).

I also understand that EULA has a thing were if you make changes such as your mother board or other components you will not be able to activate your operating system. You will have to call Microsoft to activate your O/S.

If Windows came pre-installed when you bought your computer, you have what's known as an "OEM" license.  This license is limited to the computer on which Windows was first installed.  That means that you can't use the same product key to activate an installation of Windows on a "new computer."

Windows monitors changes in your system hardware, and Microsoft has a secret algorithm that "decides" that you have a "new computer" if too many hardware changes are made.  Outside of Microsoft, no one really knows how many changes are "too many," but it is generally accepted that changing the motherboard will definitely trigger this detection and result in your installation of Windows being flagged as "unauthorized."  There is an exception if you replace a defective motherboard with an identical model (or one that the manufacturer offers as a replacement if the original is no longer available).  If this happens, you will need to "re-activate" Windows by telephone.

I was trying to answer your question:

"I have two directions to take:  One, I am thinking about installing a new hard drive and load my Windows 7 Home Premium 32 bit O/S .Then install all my Data form my external hard drive to my new hard drive.

When I did a back up to my external hard drive I was using the Windows 7 Home Premium 32 bit O/S"

If you are not interested in continuing with Win7, someone else will have to respond to you.

Hello, I don't think you need all that information. All I am looking for is can I install Windows ten pro 64 bit on a new 1 TB W D hard drive and then transfer all my Data to this new hard drive from my external drive.

The information on the external drive was backed up using Windows 7 32 bit O/S, SP1 installed.

Question: will the information on the external back up drive which was created using Windows 7 32 bit O/S transfer to the new hard drive using Windows Pro 1064 bit O/S? Will there be conflicts because of the 32 bit and 64 bit difference? Will my data function under the 64 bit