Is there a simple way to do this without doing Demorgans law a bajillion times?

Thanks again!

 

DeMorgan's isn't too bad for this. Just work outside in. From there you can get an SOP form of the function, plug that into a K-map and find the minimal cost circuit from there.

 

I'd make a truth table then use a K-map to simplify.

 

Minimal cost generally means using the same logic gate over and over. Since you can get ICs with several of the same gate on them, fewer gates doesn't necessarily mean cheaper; fewer ICs does.

 

Too true... Generally you might want to use only NANDs as they can substitute any gate, including NOT.

 

Generally you might want to use only NANDs as they can substitute any gate, including NOT.

... or only NORs