Karnaugh Map (K-map) : 4-Variable K- map Explained (with Solved Examples)
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- Опубликовано: 30 июл 2024
- In this video, the 4 Variable K-map is explained and the minimization of the 4 variable Boolean functions using the K-map is explained with different examples.
The following topics are covered in the video:
0:00 Introduction
0:26 Construction of 4-variable K-map
4:31 Mapping the 4 variable Boolean Function in K-map
6:00 Minimization of 4-variable Boolean Function using K-map
10:25 Example 1
11:28 Example 2
13:11 Example 3
14:41 Example 4
16:08 Example 5
18:15 Example 6
Karnaugh Map (K-map)
The Karnaugh Map is a technique for simplifying the Boolean function.
4- Variable K-map:
The 4-Variable K-map consists of 4x4 cells. Each cell of the map represents a particular minterm.
During the mapping of the function in the K-map, the minterms which are present in the function are represented as '1' in the map. (when the function is given in SOP form)
The cells in the K-map are arranged such that, the two adjacent cells of the map differ by only 1 bit.
Boolean Function Minimization using K-map (Rules):
1) Make the group of adjacent '1's in the map to minimize the function.
2) The group of '1's should be in the power of 2. (i.e the group size should be 2, 4, 8, etc).
3) The shape of the group can be either square or rectangle.
4) During the minimization and grouping, just ensure that all the 1's in the map get covered.
5) During Minimization, the overlapping of the group is allowed.
In this video, the minimization of 4-variable functions using the K-map is explained with different examples.
This video will be helpful to all the students of science and engineering in understanding the 4 variable Karnaugh Map (K-map) and how to minimize 4-variable Boolean expressions using K-map.
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#Kmap
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Наука
![Example: Solve a Product of Sum (POS) expression using KMAP [3 & 4 variable]](http://i.ytimg.com/vi/YxGvrurqSOE/mqdefault.jpg)
Timestamps:
0:00 Introduction
0:26 Construction of 4-variable K-map
4:31 Mapping the 4 variable Boolean Function in K-map
6:00 Minimization of 4-variable Boolean Function using K-map
10:25 Example 1
11:28 Example 2
13:11 Example 3
14:41 Example 4
16:08 Example 5
18:15 Example 6
Never thought electronics is that easy..
You just need right teacher you can learn anything you want ☺️☺️
GOD this one video covered so much. Really informative and way to explain it! love it
Have a midterm tomorrow and this was a lifesaver. Thank you so much!
I'm doing CS here in Zambia and you videos are really helpful good job
Sir, your K-map explanation is very clear. Thanks
This is life-saving. Thank you.
🙌 Thank you for the wonderful lecture!
Thank you so much for this.
Best explanation.
God bless you.
Yesss.. This is what I was waiting for
better than neso academy
Very good explanation, Sir.
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Most helpful 👍🏻
Thank you sir very well explained❤
Excellent classes sir
THANK YOU SO MUCH!!
Thanks a lot for this
Excellent 👍
Thank you! amazing
great work
Perfect txt explaining everrr
Just SUPERB
I have my unit test on DPSD tomorrow and I am watching it now
Thanks a lot
Do we need to minimize it further ?
thank you sir
thank yu may lord give yu more
Beautifuly explained thank you.
Nice
Best Video
good video
RESITOR THANK YOU FOR YOUR EXPLANATION I CAN'T USED OLD RESISTOR THE SAME VALUE DIGITAL SUFACE RESISTOR
Yes..... totally agreed..
☠️
goodjob
What if they are in column and can't be paired 8... Do we seperate it to 2:2
you can make the group of 2. For more info, you can check this video, where couple of questions related to K-map have been solved.
ruclips.net/video/cTRDJrq5ySM/видео.html
Are you from kolhapur ?
Literally my next exam is electronics on Monday
hello styrish
@@870affan8 hi bro.. All the best for tomorrow's electronics exam 🤘❤️
i think at 14:33 another 4 1's can be done instead of 2 1's.
After making two groups of 4 1s, only two mimterms m13 and m9 are remaining. And it can be covered by making the group of 2 1s. If there is one more mimterms m11, then we would have made a group of 4 1s.
I hope, it will clear your doubt.
👏👏👏👏👏
why in the example 3 you haven't taken the group of 4 with5,7,13,15 ?
You can if you want. But here the idea is to cover all the minterms (with '1') by making minimum number of groups. Here, just by making three groups {(4,5,6,7) (13,9) and (14,15)}, we are able to cover all the 1s in the K-map. If you make a group of 4 1s with (5,7,13, and 15) then to cover remaining 1s, you need to make another three groups. So, that is why, here (5,7,13 and 15) are not grouped, and instead 4,5,6 and 7 is grouped. I hope, it will clear your doubt.
What if there is only one variable group formed do we ignore it???????
No, all the minterms for which output is 1 needs to be covered. If that 1 ( minterm) cannot be grouped with any other minterm then you just need to make a group of only that 1.
12:27 why didn't you made pair of 13 and 5
Here the goal is to cover all the 1s in the k-map by making the minimum groups. Of course, you can make the group of 5 and 13, but If you make the group of 5 and 13, then to cover 9, you need to make another group with 13. So, group (5, 13) is redundant over here, More technically if I say, then these three groups (shown in the video) are essential prime implicants. The essential prime implicants will always be the part of the final minimized expression. The (5, 13) is prime implicant.
For more info, you can check this video : ruclips.net/video/fmAwCosFSRs/видео.htmlsi=3XL4fZlaaXm40y4l
Bro at 8:18 cant 8 9 be included in Grouping
8 and 9 can be grouped but to cover the minterm 1, one needs to make the group of 1 and 9. Similarly, to cover 10, one needs to make group of 1 and 10. So, yes we can make the group of 8 and 9, but during the minimization or for finding the minimal expression, that group will be redundant. Because just by making these two groups, we are able to cover all the 1s in the K-map.
In the next video, I am going to cover it in detail. (The concept of Prime implicant and the essential prime implicant)
After that, I think your all doubts related to K-map will get clear.
My tomorrow's exam is about digital electronics 😲👍
Waiting for prime implicant and essential prime implicant 🙋🙋🙋
Thanks a lot
Does that mean you have to group
the ones without anyone remaining
No reply yet😢
Yes, all the 1s needs to be covered in the k-map.
Thanks again
God richly bless u
Please l need the laws of boolean algebra and l also want to know if a boolean expression must be simplified to the lowest level
Tomorrow am getting everything.......
my question is that at11:59 can we not make the group of two 1s that are in box no 5 and 13 and in 6 and 4
You can make those groups. But those are redundant groups. Because to cover 9 and 14, you need to make another groups. Just by making these three groups, we are able to cover all the 1s in the K-map. (basically the two groups you were talking are the non-essential prime implicants)
For more info, please check this video. Your doubts will get clear.
ruclips.net/video/fmAwCosFSRs/видео.html
can i make a pair of two with elements in block 10 and 0
No, you cannot group them. You can make the group of four 1s in the corner, but you cannot group the two 1s which are in the opposite corner. You can combine these groups of 1s. (0,2) (0,8) (8,10) (2,10). But you cannot make the group of (0,10) and (2,8)
Thank you@@ALLABOUTELECTRONICS
can you teach how to make state diagram, state table and kmap when given 8bit input?
I will cover the state diagram very soon.
6:40 I didn’t understood like how do you that it will come BD ?
On the vertical side of the map, we have two variables A and B. And on the horizontal side we have C and D. Now, in this group if you see, on the vertical side the variable B is not changing. ( 01 and 11, the second variable B value is 1). Likewise, on the horizontal side, the variable D is not changing. ( 01 and 11, the second digit is representing variable D, and its value is 1). Therefore, we can say that this group of 4 represents B.D. I hope, it will clear your doubt.
@@ALLABOUTELECTRONICS ok yes it cleared my doubts thank you and fabulous explanation 👍🏻👍🏻👍🏻
17:05 why you have not made second group as group of 8 ?
we can represent this only by D since it is not changing
Which group ? I can only see 1 group of 8. That is C'. The other groups are groups of 4. The group should be in the power of 2. And it has to be symmetrical. It can be either square or rectangle. As per that, there are only three groups.
@@ALLABOUTELECTRONICS oh, I mistakenly assumed that second group can have 8 elements but I am now clear that it will be actually group of six which is not possible as you told.Thanks and sorry.
Today is digital lab exam 😌
Tommrrow is my exams 😉
Bro don't care condition example you didn't include 🤐
It will be covered seperately. ( In the seperate video)
@@ALLABOUTELECTRONICS okay 😉❤️
You made mistake in example 4
As far as I can see, there seems no mistake in example 4. But still, if you feel there is a mistake, please mention the timestamp where you feel, there is a mistake.
Whyareyoutalkinglike - thiisss
Lol😂
Like what
You should thank him for his efforts rather than this.
There is an Arabic proverb that says : "They did not find any flaw in the gold, and they said its sparkle blinds the eyes."
Is your keyboard doesn't have spacecap
vik
k map
Well explained, thanks to you man!🎉