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This is your processor:
It is eight years old.
It will support 64-bit Windows.
However, it is not supported on Windows 10:
This does not mean that Windows 10 will not run. It will. But, you will be not be supported.
Regarding the rest of your configuration, 2gb memory is a bit low, even for 32-bit Windows in today's world.
80gb SSD, is fine, but you are constrained by storage. Again, today's world requires more.
Your graphics card and display are fine.
I have converted machines with configurations like yours to W10, 64-bit, and they work fine, That is, until Microsoft decides differently.
You can stay on 32-bit Windows 10 if you want. If you upgrade to W10, that is what you will have to do. If you do a clean install, you can move to 64-bit W10. However, your memory will then be an issue.