Help with truth table and K-Maps [closed]

Question

I am currently working on a traffic light system, the state transition table developed for the project reads as follows:

I have additionally used Neeman's Digital software to create a table (and K-Maps) for the output F2, F1, and F0.

As I was trying to repeat the process for D2, D1 and D0, with a table that has the following appearance. I would like to clarify that the Input I is being represented by E in the table.

Which returns the following expressions for the output expressions:

I have also tried replacing the x with 0 and get the following output expressions:

Both these aproaches revealed insufficient, because only F0 (the GREEN light) gets lit up, even when Input is true. I would therefore like help resolving this issue.
Thank you very much.

Answer 1

to start

I believe you have correctly drawn out a viable table with everything you need. I can't argue with it. But it appears you need help with k-maps. So let's get going on that.

(In the following, I'm using a tool called Neemann's Digital.)

RED k-map

The k-map for the RED LIGHT is probably easier to see and make from your table:

\$\quad\quad\quad\quad\quad\$

Here's what the above might look like as a start for your circuit:

GREEN k-map

The k-map for the GREEN LIGHT is only slightly harder to see by eye:

\$\quad\quad\quad\quad\$

But you know that it must only the case for \$\overline{S_2}\: \overline{S_1}\: \overline{S_0}\$, too, because of how you designed things. So it's not difficult to work out the above k-map from that knowledge.

Here's the newly modified circuit to include that light:

RED k-map you produced

But let's stop for a moment and look at what you actually produced for your RED table (newly updated in your question -- thanks):

It's not correct. I'm not sure how you created your table on the left side there. But you missed a lot. Do you see how it is really just \$S_2+S_1 S_0\$?

(This is just doing it by eye. But it's also not hard to see.)

automated tool

Perhaps you would like to use an automated tool for this work, instead?

Let's take a moment's break and grab up a copy of Neemann's Digital.

Then you may access the following service it offers:

This will pop up a starter dialog for you that looks like this:

Right-click on the titles to change them (note that using an underscore in the name causes the following text to appear as a subscript):

Then add another input variable:

Unfortunately, this adds it to the end of the current list (and gives it a default name, which you need to rename as well.) So move it to the front:

Now rename the output column Y to RED and add more output columns:

Your table might now look like this:

At this point, start marking the values in the output columns. For example, this is what it looks like when modifying the GREEN column to make it a 1:

When done, you should have the following table completed:

Then select the k-map option:

Then you can work through that to find:

This is a little more nuanced than what I produced above, as it includes the don't care states for state 7.

If you now use the following table service:

It will generate the logic for the above in a separate instance of Digital:

On the left side above is what Digital generated, directly, using AND/OR logic.

Clearly, also, the inputs will instead be coming from the D FFs you already know you need to set up. So on the right side I've added those, by hand.

summary

At this point, I think I've carried you far enough along. You should be able to generate your own table for creating the inputs needed for the D FFs. If you followed the above process, all you need to do is now add three more output columns to represent the next state in your table. Then correctly fill them out. (If you want, you can reorder the output columns, too.)

I also would suggest that you play with some of the other options you have available in Digital, too. I've only touched upon a few of your choices. For example, Digital will generate CUPL or JEDEC code that can be used to program a GAL16V8! Explore.