Question

I have a logic question:

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

what would be the sum of products for that using k-map (please note that this is big-m and you have to find the answer in the sum of products)

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

Note: this is a homework question, i don’t want the answer as much as i want to be able to solve this 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 little m and this is big 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, this questions is constructed like that on purpose!

They asked you for worst case imaginable.

The don’t-cares do not help AT ALL and the ones aren’t next to each other.

When you have the (at most 4×4 because you can visualize that) K-map drawn out, do not bother to cover zeroes instead of ones hoping that it will be simpler.

When in k-map, it should be all there in front of you.

This was a trick question. For extra points you can reason why the circuit is not simplifiable, perhaps look it up in the literature. Also, there is a great deal of symmetry here, so perhaps you can get creative when you draw out the corresponding circuit. If you do it right, the picture should look very nice.

EDIT:

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

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

It should convince you that your function is not simplifiable.