This probably sounds really naive. But, a strange discussion came up on Quora about computers possibly weighing more when information is added to them.
I tried looking around but couldn't find a definitive answer. There are a few threads where people have tried to ask something similar.
1) http://www.thenakedscientists.com/forum/index.php?topic=38844.0
Both threads have people arguing about the possibilities, but I'm sure a more definitive, and painfully detailed answer must exist. I hope you have a good laugh and then help me out!
I don't have the rep to post more than two links so I'll just put the original thread in the comments.
Thank you!