Copying a drive image to move your installed...

Question

I have a computer with a failing hard drive. I'd thought I might copy the image of the disk to another one of the same type and put it back in the same machine. I might also like to do that and run the installed software on another machine.

Is either of those physically possible? If so do you do that? If not why is it that copying the entire disk image would not transfer all the information on it?