What data structures would you use to represent a chessboard for a computer chess program?
Well, not sure if this helps, but Deep Blue used a single 6-bit number to represent a specific position on the board. This helped it save footprint on-chip in comparison to it's competitor, which used a 64-bit bitboard.
This might not be relevant, since chances are, you might have 64 bit registers on your target hardware, already.