6
votes
Accepted
Is this possible to solve boolean satisfiablility by using karnaugh maps to simplify the whole given boolean formula by simplifying subformulas?
"arbitrary chosen" in a NP problem where the followup results in a P algorithm typically means that the choice matters a lot and trying them all and backtracking over bad choices looking for the ...
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3
votes
Accepted
Why do Karnaugh maps work?
The key here is graycode. I think the easiest way to see why Karnaugh maps work is to go through an example:
Consider the following truth table:
$\hskip2in$
We can easily find the logical formula ...
- 181
3
votes
Accepted
3
votes
Do Karnaugh maps yield the simplest solution possible?
Karnaugh maps do not always give the simplest expression possible, but they do always give the simplest "Sum of Products" expression possible (https://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/...
- 1,328
2
votes
Number of literals in the given boolean expression
Does your material use the (strange) convention of notating $\neg A$ as $A'$?
If so, there are 6 literals (5 without the LHS). If $A'$ is distinct from $A$, there are 9 (8 without LHS) and the ...
- 12.6k
2
votes
Accepted
Someone explain the Venn diagram for the logic equation (A+B)(B+C)
The misunderstanding here is the same as in your previous question. If $B$ is true, the formula is true whatever the values of $A$ and $C$ are. This means that the whole of the $B$ circle ...
- 81.4k
2
votes
How do i simplify this SOP expression?
You can verify that the two expressions are equivalent by using some logical equivalences. Below I'm using 1 to represent true.
$$\begin{align}
a'bc'+a'bc + ab'c'+ab'c &= (a'bc'+a'bc) + (ab'c'+ab'...
- 14.8k
1
vote
Can anyone solve this? Is the answer 4 or 7. I'm confused
It's 4 because you're allowed to "wrap around" from the top edge to the bottom edge or from the right edge to the left edge (those moves still represent 1-bit changes because the Gray code ...
- 319
1
vote
Accepted
Minimizing a multiple output circuit with K-maps - and without
Good job on $f_a = \overline acd \lor bc \lor bd$.
With $f_b$, I'd denote it as $b\overline d\lor b\overline cd$ - you missed overlap with $\overline d$: $f_b = b\overline c \lor b\overline d$.
I'd ...
- 965
1
vote
How do i simplify this SOP expression?
K-map Simplification leads to the expression which you have arrived at . For checking the same you can create a truth table for your simplified expression and match the outputs with those of the ...
1
vote
Accepted
Which formula corresponds to this K-Map?
First, you need to describe all three of your options using a minimum amount of literals.
To achieve this you will need to do the following (use basic boolean algebra laws):
Using the Distributive ...
- 100
1
vote
Karnaugh map simplification
First, when you are trying to group, you must use the biggest possible group. A group's size has to be a power of 2 (1, 2, 4, 8...).
In this case you need to make 2 groups:
cells 4, 5, 12, 13: $A'D$
...
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