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?

 

You have used "don't care" correctly. Your answer is correct.

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

 

You have used "don't care" correctly. Your answer is correct.

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

Thanks. I thought my answer was right since it did match with the truth table I made. I have one last question:

(I added the 1 in)

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".

 

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?

 

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?

 

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?

I think that X=D is incorrect. I got X=AD+BD.

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