Problem Detail:
AB 00 01 11 10 00 | x | 1 | 0 | 1 | CD 01 | 0 | 1 | x | 0 | 11 | 1 | x | x | 0 | 10 | x | 0 | 0 | x |
The answer to the above Karnaugh map is $F(ABCD) = B D + bar B bar D + bar A bar C bar D + bar A C D$ according to my book and the K-map solvers online. But what I don’t get is that I can further reduce the terms in this answer: $F(ABCD) = bar B bar D + bar A CD + bar A B bar C$ also covers all the min terms in lesser groups. The answer in my book just has a bigger group covering additional don’t cares. Since they are optional shouldn’t my answer be correct?
Asked By : imhobo
Answered By : ZeroUltimax
Your answer is correct. It is also more reduced. The reason your book and the solver give you a bigger equation is because they use a greedy algorithm that attempts to match bigger groups (groups with less variable in them). This will have an optimal behavior if the map has no “don’t cares” [reference needed]. To have optimal behavior with “don’t care”, you have to consider that an X can be either a 1 or a 0. That means that for each X, you have two versions of you map. So, if you have $N$ “don’t cares”, you will have to reduce the $2^N$ versions of the map and choose the smallest reduced operation from the results. Extra If you have lots of those maps to reduce, i suggest you use Logic Friday or a similar equation reducer.
Best Answer from StackOverflow
Question Source : http://cs.stackexchange.com/questions/29164
