Boolean Algebra: Consensus theorem trouble.

I have a few homework problems that are really troubling me in my logic's course. On these I really don't even understand were too begin. These problems are in regard to the consenses theorem.

The problem calls for simplifying each the following expressions using only the consensus theorem (or its dual):

a)BC'D' + ABC' + AC'D + AB'D + A'BD' (reduce to three terms)

b)A'BC' + BC'D' + A'CD + B'CD + A'BD

c)(B + C + D)(A + B + C)(A' + C + D)(B' + C' + D')

And info or ideas would greatly be appreciated.

Thanks,

Mckay

Mckayman,

a)BC'D' + ABC' + AC'D + AB'D + A'BD' (reduce to three terms)

Click to expand...

I will do the first one for you, then you can do the rest.

[A'BD'+ABC'+BC'D']+[ABC'+AB'D+AC'D] Rearrange and add another ABC' term
[A'(BD')+A(BC')+(BD')(BC')]+[(AC')B+(AD)B'+(AC')(AD)] Group concensus
A'BD'+ABC'+ABC'+AB'D Drop duplicate term
A'BD'+ABC'+AB'D

So how did I know how to rearrange the terms and add a duplicate term? The answer is that I used a Karnaugh map to see what the concensus terms were. Then it was easy to group them and apply the theorem. Of course, you don't have to show your Karnaugh map, do you? People will think you are a genius at seeing those consensus patterns if they don't know about K-maps. You can spend a lot of time trying to find the pattern without the K-map.

Ratch

Thanks for your reply.