Maybe binary Uno? I'm trying to think of a game which would be nontrivial if converted into binary (lol binary 20 questions, "I'm thinking of a number..." Perhaps it should be binary 1100 questions).
Binary Crossword Puzzles?
How about "binary nim"?
What? No 10 square or 11? No challenge.
I should put this one on my classroom wall.
Binary sudoku would very quickly get very interesting.
hey, anyone remember this? http://www.gocomics.com/foxtrot/2008/09/21/