# RF remote with three buttons

I am trying to create an RF remote that has 6 buttons but the RF encoder only has 4 inputs. Is this possible and preferably I would not like to use a separate chip.

This is what I am using:

http://www.farnell.com/datasheets/56726.pdf

It has 4 inputs, which means you can input $2^4$ combinations of these inputs. To translate button presses to binary numbers, a priority encoder is needed, such as this one.