Installed Vista on a Harddrive in my old computer, I want to switch it to a different computer which has no os. If I switch the harddrive to it will windows vista show up on the computer with no os?

I’ve heard a lot of bad reviews about installing windows 7 on an external hardrive. Some people say you can’t other say you can but it would be crappy. If we can, what am I supposed to do for my windows 7 to run perfectly on an external hardrive. Do I have to format the external HD? What’s a good external HD? I would really appreciate your help.