eBooks with DRM can be opened and read on up to 5 devices (depending on the publisher's settings).
If you purchased ebooks with DRM and you want to read them on a new or different computer than the one you first opened it on, the only requirement is when you install Adobe Digital Editions on your new computer. Please be sure during setup you use the same Adobe ID used on your previous computer. The same is true for any other device you might try to read your books using Adobe Digital Editions.
You may also need to authorize your computer by opening the Adobe Digital Editions software application on your computer, clicking on "Library", and then on "Authorize computer...".