Questions tagged [karnaugh-map]
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23 questions
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A confusion about Karnaugh Map
Consider the following four variable Boolean function:
$$F(A,B,C,D)=\sum(0,2,3,5,7,8,9,10,11,13,15)$$
If I show you the map, then what I get is:
I have marked the Essential Prime Implicants with a ...
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Karnaugh map minimization confusion
I'm given a Karnaugh diagram like below. And the correct way to circle the elements. I learned that when two elements are at the edges of a diagram they wrap around. So my question is why do we not do ...
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Determining linear boolean functions from a Karnaugh map
I'm currently working with Karnaugh maps and I'm not completely really sure how boolean linear functions can be determined by looking at the K-map.
As I understand it (by looking at the Wikipedia ...
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Prove or disprove that the Quine-McCluskey method generates the circuit with the minimum inputs and minimum gates?
Recently, when I self-learnt Discrete Mathematics and Its Applications 8th by Kenneth Rosen, it says in 12.4 Minimization of Circuits which uses the Karnaugh Map or the Quine-McCluskey method:
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How to prove a minimum number of queries needed to determine a piece of information
You have 27 coins, 1 of which is a different weight. Using a balance scale with 2 pans, how can you determine which coin is different in only 4 weighings?
Generalize this to N coins.
Hint
Solution
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Can anyone solve this? Is the answer 4 or 7. I'm confused
I'm trying to solve this but I'm confused with different answers. I'm getting 4 but the answer written is 7. Please guide me.
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K-Map Reduction Grouping Question
I have a simple question regarding reduction using K-Maps.
My professor gave this example:
While I somewhat understand that we can only group quantities of base 2 numbers, why did my professor group ...
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What is the intuitive logic behind the working of the Variable Entered K-Map (VEM)?
In this site here they have just said how to minimize a function using VEM. But no intuitive logic behind the same has been stated, making it too mechanical. And I am very bad at memorizing things, so ...
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Karnaugh Map: does maximal overlap always produce simplest boolean expression?
Suppose I have a 4x4 Karnaugh map with a few cells that are don't cares, and there are two ways of producing 3 groups of 4 cells. One of these ways overlaps groupings more that the other. Is one way ...
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Why do Karnaugh maps work?
The question is quite straightforward: Why do Karnaugh maps work? What was the reasoning that led Maurice Karnaugh to come up with these maps? At first glance, it doesn't seem a natural approach, ...
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Boolean function minimization
Does there exist a Boolean function for which no sum-of-products expression that minimizes the number of products also simultaneously minimizes the number of literals (counting repetitions)? ...
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Minimizing a multiple output circuit with K-maps - and without
I'm currently working on learning to minimize a circuit which has multiple outputs using K-maps. My universities script seems rather unhelpful to me which left me in a spot where I have a very rough ...
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Number of literals in the given boolean expression
Count the number of literals in the following expression :
F = AB' + BC' + CD' + DE'
According to me, the answer should be 8. But my solution suggests that the answer should be 6. Can anyone help me ...
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Someone explain the Venn diagram for the logic equation (A+B)(B+C)
I posted a similar question here, however I have another question regarding Venn diagrams and logic circuits...
In this problem:
$$(A+B)(B+C)$$
Wouldn't the Venn diagram look something like this?
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Is this possible to solve boolean satisfiablility by using karnaugh maps to simplify the whole given boolean formula by simplifying subformulas?
Building karnaugh map for the whole given boolean formula always costs Θ(2n) both time and space complexities, where $n$ is the number of boolean variables in the given boolean formula.
It is ...
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How do i simplify this SOP expression?
Hi i have derived the following SoP (Sum of Products) expression , by analyzing the truth table of a 3 bit , binary to gray code converter. I ask for verification, because i feel as though this answer ...
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Boolean expression logic law confusion
I've been trying to attempt a particular question that I need to translate truth table into boolean expression but I'm completely stuck on one point now.
First, I worked it out by using Sums of ...
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Simplifying Boolean Expression
I am designing a 4-bit comparator with a look ahead unit using a bit slice approach. I have to break the propagation of the Logical expressions for (A<B)i and <...
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Which formula corresponds to this K-Map?
I have a K-Map and I need to figure out which expression isn't equivalent to the provided K-Map.
$f(w,x,y,z) = \sum(3,7,9,11,13,15) + \Phi(4,5,6)$
We know that both options (a) and (b) are ...
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Is Karnaugh Map possible for Maxterms?
I read about Minterms i.e. sums of products, simplification using
Karnaugh Graph. Can this graph be used for Maxterms, i.e. products
of sums, as well? If yes, then how?
If not, then is there some ...
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Karnaugh map simplification
I'm working through an example that looks like a fairly simple Karnaugh map and simplification, but I feel stupid that I can't seem to understand the correct answer.
This is the map:
My groupings:
...
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Do Karnaugh maps yield the simplest solution possible?
I'm learning to use a Karnaugh map, but I'm not sure if I obtained the simplest expression possible. Have a look at this example:
Truth table (inputs are A B C; output is F):
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Karnaugh map with don't care: increasing the number of groups instead of simplifying
AB
00 01 11 10
00 | x | 1 | 0 | 1 |
CD 01 | 0 | 1 | x | 0 |
11 | 1 | x | x | 0 |
10 | x | 0 | 0 | x |
The answer to the ...
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