I put this into a k-map and it has 5 terms is somthing wrong?

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In summary: A'B'CD'In summary, the K-map has four terms, each of three variables. The first term is A'B'CD', the second term is ACD'AB'CD', and the third term is B'CD'A'BC'.
  • #1
mr_coffee
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Okay i have 4 inputs, A,B,C,D, and when i put it into a K-map i got 5 terms, its a prime number circuit. It will output 1 if the number is prime, example...
2,3,5,7,11,13. So 1101 == 13 would output a 1.
A = 1, B = 1, C = 0, D = 1; Output = 1
From suming up the min terms on my truth table i got the following boolean expression:
Note: 'A means A complemented

'A'BC'D + 'A'BCD + 'AB'CD + 'ABCD + A'BCD + AB'CD

I put it into a K-map and got the following:
'A'BC'D + 'ACD + 'ABD + 'BCD + B'CD

Does that look right to you? I already wasted an hour implemented the wrong diagram because i screwed up the k-map and i want to make sure i didn't screw it up again. Thanks.
 
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  • #3
Thanks for the responce...but ]shouldn't u loop some more? Here is what I got...but it still isn't right because when i create a circuit out of it using MAX PLUS II, it says A is not needed! which makes no sense to me...
Here is my k-map...
http://img137.imageshack.us/img137/5189/lastscan6nq.jpg
 
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  • #4
Ah yes. I see where I forgot to loop.
I think you make some mistakes in the k-map
Code:
'A'BC'D + 'ACD + 'ABD + 'BCD + B'CD
Thats what you have. I'm look at the k-map and I can't see 'A'BC'D in the k-map. I see A'BCD. Why is it that you put the upper right most 1 by itself. Just looping it with the 1 to the left of it is good enough. Looking at the last row I see that you have 'BCD. How did you end up with that?
Here is what I got
Code:
'A'BC + 'ACD + 'ABD + B'CD + A'BCD
I'm also taking this course right now, I know how confusing this topic can get.
 
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  • #5
That is wrong, but thanks! I figured it out finally!
 
  • #6
For whatever it is worth, there are four terms, each of three variables. In other words, each loop encompasses two cells.

I have a couple of suggestions (in real life - - - if your instructor does it the other way, you are stuck with it in class). First, try using the apostrophe after the variable to show a "negation", this is a bit more familiar to most of us. (It is unfortunate that most of our typing program packages don't provide for an "overline".) Second, make "A" your low-order variable. Then, A'B'CD' would be "0100". This makes it a little easier to put it into an ordered K-Map (I keep preaching the use of ordered maps - - - but most still don't bother.) Third, try to learn and use the ordered K-Map somewhere down the line. It makes the operation far more automatic and gives more capability.

KM
 

1. What is a K-map and how does it work?

A K-map, also known as a Karnaugh map, is a graphical representation of a truth table used for simplifying boolean expressions. It is used in digital logic design to minimize the number of logic gates needed to implement a boolean function. The K-map is divided into squares, each representing a possible input combination, and the output values are plotted within these squares. This allows for easy identification of patterns and simplification of the expression.

2. What are the 5 terms in a K-map and how are they determined?

The 5 terms in a K-map refer to the number of variables in the boolean expression. These are represented by the number of squares in the K-map, which is determined by the number of inputs in the truth table. For example, a K-map with 2 inputs will have 4 squares, while a K-map with 3 inputs will have 8 squares. The terms are labeled as A, B, C, D, and E in a 5-term K-map.

3. How do I know if something is wrong when I put it into a K-map and it has 5 terms?

If your boolean expression has 5 terms and you are using a 5-term K-map, then there is nothing wrong. However, it is important to double check your truth table and make sure all the input combinations and output values are correct. If there are any errors in the truth table, it will affect the simplification process and may result in incorrect results on the K-map.

4. Can I use a K-map for expressions with more than 5 terms?

Yes, K-maps can be used for boolean expressions with more than 5 terms. However, for expressions with more than 5 variables, multiple K-maps may be needed. This is because a 5-term K-map can only represent 32 possible input combinations, and any additional variables will require more squares and therefore, more K-maps.

5. How do I simplify an expression using a K-map with 5 terms?

To simplify an expression using a 5-term K-map, follow these steps:

  • 1. Create a truth table with all possible input combinations and the corresponding output values.
  • 2. Group the squares on the K-map that have a 1 output value. The groups should be as large as possible and can overlap.
  • 3. Identify the pattern in each group and write the simplified expression using the variables in the pattern.
  • 4. Combine the simplified expressions from each group to get the final simplified expression.

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