The binary magic trick is a set of 6 cards with numbers on them. You show the cards to someone and have them secretly choose a number and then select all of the cards that contain that number. Using your magic powers, you can easily figure out which number they have chosen.
The secret to this magic trick relies on knowledge of binary numbers.
Binary Magic Trick cards (PDF, OpenDocument (.odt)) 

Binary Magic Trick instructions (PDF, OpenDocument (.odt)) 
These kind of magic trick cards have been around for a long time and are of unknown origin (to me at least). The documents with the cards and instructions were created by Gary Kacmarcik.
These documents are licensed under a Creative Commons AttributionShare Alike 3.0 Unported License