Because ARM processors are much less expensive and power-consuming, I want to use them in a PC with PC-type RAM and hard-drive.
Is there a motherboard the allows to use ARM processors with PC-based RAM and hard-drive?
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It's actually totally possible. AMD was supposed to release dev boards based on their new Opteron A1100 octocore ARM APU, but as you can see, there have been severe difficulties with actually getting anyone to ship the darn things.
Another tantalizing possibility is the MP30-AR0 Server Board by Gigabyte. Again, finding anyone willing to ship this stupid thing is the hard part, but it does exist.
Considering Windows 10 works on ARM, Android works on ARM, ChromeOS works on ARM, Linux works on ARM, and some form of Mac's OS works on ARM... I'll leave you to guess why these boards aren't easily available to lowly consumers in an era when CPU power is increasingly irrelevant for most users.
There is no reason you could not have a standard IBM-PC format motherboard using an ARM CPU. Simply obeying the form factor (which nowadays includes not only mounting holes, but a set of backside connectors for video, USB, Net, etc.) as well as being PCI compliant would do it. Clearly the drivers and the software would be custom, but a Linux distro could do that easily, and Windows will soon run on ARM as well.