[ubuntu] ubuntu 12.04. 32bit, 64bit question

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http://ubuntuforums.org – I have Ubuntu 12.04 32bit. I'm looking for a new computer but the ones I'm looking at are 64bit. Can I use my current 32bit on it?? I'm asking because I have a saved disk image of the 32bit which has all my folders etc on it. I want to use this disk image, a 32bit, on a 64bit machine but will it work ok? (Hardware)