# problem with dont cares in a kmap

Discussion in 'Homework Help' started by inkosi, Sep 19, 2014.

1. ### inkosi Thread Starter Member

Dec 10, 2013
35
0
Hello friends,

I need some help with this question I got. It says design a logic circuit that responds with 1 when even numbers (from 0-8 so 0, 2, 4, 6, 8) appear at the inputs. So I made this 4 variable kmap

However I am not sure if I used "don't cares" correctly. My simplified expression is just D'. From looking at my truth table this looks correct but someone told me my answer was wrong. Is it? If so what exactly is wrong?

2. ### MrChips Moderator

Oct 2, 2009
12,652
3,461

Check your answer against the binary values. When is the LSB zero? When D = 0.

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3. ### inkosi Thread Starter Member

Dec 10, 2013
35
0
Thanks. I thought my answer was right since it did match with the truth table I made. I have one last question:

For the truth table like this, we would need to make a loop of 8 around the 2nd and 3rd column right? Just want to clear a doubt I'm having with these "don't cares".

4. ### MrChips Moderator

Oct 2, 2009
12,652
3,461
The x to mark a "don't care" logical outcome means exactly that, the result doesn't care because that binary state will never be reached.

Use the x to your advantage. Threat it as a logic 1 if it helps you to reduce the boolean expression otherwise don't use it.

Now, with the drawing as you have modified and shown, what is the simplest boolean expression you can write?

5. ### inkosi Thread Starter Member

Dec 10, 2013
35
0
X = D is my simplified one. It makes sense to me as well.. since the output is 1 when D = 1 according to the truth table. Is that right?

6. ### dalam Member

Aug 9, 2014
58
6
I think that X=D is incorrect. I got X=AD+BD.

You can also get CD+BD depending on your choice of loop.

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