Not on the same disk, but definitely in the same box (especially if you get it retail). Oem copy will be licensed for either 32bit or 64bit but the disk you get with only be one of the other... the cdkey you get however will work with both.
As a home computer, home premium is 100% fine. However, personally for me, i prefer at least Pro for Windows. Other than the obvious, i thought they removed lots of advanced stuff like many of the MMC snapins, among other things from home premium?
From the winsuper site:
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Windows 7 Professional
The leap from Windows 7 Home Premium to Professional is quite a bit less profound, though of course certain people will simply have to get this version because it includes key business-oriented features like support for Active Directory-based domains. Windows 7 Professional users also gain access to Windows XP Mode, a fully-licensed version of Windows XP with Service Pack 3 that runs in a virtual machine under Windows Virtual PC and lets you solve any lingering compatibility issues caused by the big upgrade to Windows 7.
Additionally, Windows 7 Professional supports more RAM than does Windows 7 Home Premium, at least in 64-bit guise: 192 GB vs. just 16 GB for its lower-end cousin. It provides automated network backup capabilities to Windows Backup (arguably a key differentiator for individuals) as well as support for the Encrypting File System (EFS). It adds Remote Desktop host functionality, so that you can remotely control the PC from another PC, and Offline Files support, so you can access network-based documents while disconnected from that network. And Windows Mobility Center provides a unique presentation mode feature that isn't present in Windows 7 Home Premium.
Windows 7 Professional isn't as much of a slam-dunk as Windows 7 Home Premium, but then you either need it or you don't. Some of the discretionary advantages--I'm particularly fond of automated network backup functionality, for instance--could be a deciding factor. But for those who don't need domain support, Windows 7 Professional is overkill that doesn't really justify the price hike.
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