The sum of the works for this using the k-card

Question

I have a logical question:

If I have: f (A, B, C, D) = M (4,7,8,11). D (1,2,13,14)

what will be the sum of products for this, using a k-card (note that this is big-m, and you should find the answer in the sum of products)

I drew a k-map, the problem is that I cannot find a way to cover zeros without specifying 4 members each with 4 boolean members (A, B, C and D) without using D terms, is that right?

Note: this is a question about homework, I don’t want an answer as badly as I want to solve it myself.

+---+---+---+---+ 00 | 1 | 0 | 1 | 0 | +---+---+---+---+ 01 | x | 1 | x | 1 | +---+---+---+---+ 11 | 1 | 0 | 1 | 0 | +---+---+---+---+ 10 | x | 1 | x | 1 | +---+---+---+---+ 00 01 11 10 

I edited the map because it was made for small m, and this is large m

Answer 1

It looks like this:

 \ AB 00 01 11 10 CD +---+---+---+---+ 00 | 0 | 1 | 0 | 1 | +---+---+---+---+ 01 | x | 0 | x | 0 | +---+---+---+---+ 11 | 0 | 1 | 0 | 1 | +---+---+---+---+ 10 | x | 0 | x | 0 | +---+---+---+---+ Simplest answer = OR(AND(*,*,*,*), AND(*,*,*,*), AND(*,*,*,*), AND(*,*,*,*)) where You can use A, B, C, D, NOT(A), NOT(B), NOT(C), NOT(D) instead of * =================================================================== 

Haha, these questions are built so purposefully!

They asked you to present the worst case.

Not all worries help ALL, and they are not next to each other.

When you have (no more than 4x4, because you can visualize it), the K-card is stretched out, do not worry to cover the zeros instead of those who hope that it will be easier.

When in k-map everything should be ahead of you.

It was a trick. For extra points, you can explain why the scheme is not simplified, perhaps look at it in the literature. In addition, there is a lot of symmetry here, so perhaps you can become creative when you cross out the corresponding scheme. If you do everything right, the image should look very beautiful.

EDIT:

You can install this software for Linux and play with it:

http://sourceforge.net/projects/gkmap/

This should convince you that your function is not simplified.