Where are the 'don't cares' come from? From your table, everything is fully represented. Are you suggesting the mov r7,a are your 'don't cares'? If you're doing SOP, the logic is solved for an output of '1', so your 'don't cares' for output should be '0'.

You like making things hard for yourself don't you! I was solving more complex logic than this by hand when I was 12 - logic minimisation programs had yet to arrive.

As for your objective - do you want the simplest logic equation or do you want the simplest hardware solution? These are not necessarily the same - for example, as a hardware solution, you might use various and,or,nand,nor gates and decoders etc for the solution, whereas for SOP you usually assume a fixed logic solution. What ics do you have at your disposal? I'd start with a 75154 and a handful if 7430's, but if all you've got is 7400's then the logic solution will be different. Then we could add in some 74181's,74182's and some 74161's.... before long we've built a cpu!


Sorry to give you a dose of reality- it really puts a spanner in the works.