Mildly unrelated, but I wanted to point out the awesomeness of the K-map[1] for handling simple minimization problems like these.

Unfortunately, once your dimensions get large it becomes difficult for humans to visualize the optimizations, which is where Espresso[2][3] comes in handy.

[1] http://en.wikipedia.org/wiki/Karnaugh_map

[2] http://embedded.eecs.berkeley.edu/pubs/downloads/espresso/in...

[3] ftp://ftp.cs.man.ac.uk/pub/amulet/balsa/other-software/espresso-ab-1.0.tar.gz