Real Chess Board which detects the moves we do We a friend and I play chess we usually don't write down our moves.

It would be great if there would be chess boards which detects our moves.

We could play using a tablet computer, but we prefer to play with a real world chess board.

Are there chess boards which detects the moves we do?

The board does not need to be smart.  For me it would be enough if it could act detect the moves and output the moves like a usb keyboard.
Yes, there are boards that record moves made automatically. This link should give you ample information about so called DGT-boards. 

Because DGT-boards are pretty expensive, maybe you want to take a look at this discussion, in which the Novag Citrine board computer is proposed as a slightly cheaper alternative.

If the Novag is still too expensive, I would look further into the board computers/usb-boards, but those probably don't recognise the pieces automatically, which means they have to pressed on the starting and ending square of each move.