Prashant-Vinod Mookhey

In this article, we will take a look at the Introduction to K-Map (Karnaugh Map) according to the GATE Syllabus for CSE (Computer Science Engineering). Read ahead to learn more.

Table of Contents

In numerous digital circuits and other practical problems, finding expressions that have minimum variables becomes a prerequisite. In such cases, minimisation of Boolean expressions is possible that have 3, 4 variables. It can be done using the Karnaugh map without using any theorems of Boolean algebra. The K-map can easily take two forms, namely, Sum of Product or SOP and Product of Sum or POS, according to what we need in the problem. K-map is a representation that is table-like, but it gives more data than the TRUTH TABLE. Fill a grid of K-map with 1s and 0s, then solve it by creating various groups.

Here are the steps that are used to solve an expression using the K-map method:

1. Select a K-map according to the total number of variables.

2. Identify maxterms or minterms as given in the problem.

3. For SOP, put the 1’s in the blocks of the K-map with respect to the minterms (elsewhere 0’s).

4. For POS, putting 0’s in the blocks of the K-map with respect to the maxterms (elsewhere 1’s).

5. Making rectangular groups that contain the total terms in the power of two, such as 2,4,8 ..(except 1) and trying to cover as many numbers of elements as we can in a single group.

6. From the groups that have been created in step 5, find the product terms and then sum them up for the SOP form.

Z = ∑P, Q, R (1, 3, 6, 7)

From the red group, the product term would be —

P’R

From the green group, the product term would be —

PQ

If we sum these product terms, then we will get this final expression (P’R + PQ)

F (A, B, C, D) = ∑(0, 2, 5, 7, 8, 10, 13, 15)

From the red group, the product term would be —

BD

From the lilac group, the product term would be —

B’D’

If we sum these product terms, then we will get this final expression (BD + B’D’)

F (P, Q, R) = π(0,3,6,7)

From the lilac group, the terms would be

P Q

If we take the complement of these two

P’ Q’

And then sum up them

(P’ + Q’)

From the blue group, the terms would be

B R

When we take the complement of these terms

B’ R’

And then sum them up

(B’ + R’)

From the red group, the terms would be

P’ Q’ R’

If we take the complement of the two terms

P Q R

And then sum them up

(P + Q + R)

If we take the product of these three terms, then we will get this final expression –

(P’ + Q’) (P’ + R’) (P + Q + R)

F (P, Q, R, S) = π (3, 5, 7, 8, 10, 11, 12, 13)

From the blue group, the terms would be

R’ S Q

We take their complement and then sum them

(R + S’+ Q’)

From the purple group, the terms would be

R S P’

We take their complement and then sum them

(R’ + S’+ P) S

From the red group, the terms would be

P R’ S’

We take their complement and then sum them

(P’ + R + S)

From the lilac group, the terms would be

P Q’ R

We take their complement and then sum them

(P’ + Q + R’)

Finally, we will express these in the form of the product –

(R + S’+ Q’).(R’ + S’+A).(P’+ R + S).(P’+ Q + R’)

Pitfall – Always remember that POS ≠ (SOP)’

*Here, the correct form would be (POS of F) = (SOP of F’)’

1. There are a total of ______ cells in a K-map with 4-variable.

a) 8

b) 18

c) 16

d) 12

Answer – (c) 16

2. The don’t care condition could be used in order to simplify the Boolean expressions in the ___________.

a) Latches

b) K-maps

c) Terms

d) Registers

Answer – (b) K-maps

3. Logic gates can be widely used in the _______________ design and are therefore available in the IC form.

a) Digital

b) Sampling

c) Systems

d) Analog

Answer – (a) Digital

4. Entries are also called the _______________ mapping.

a) Boolean

b) K

c) Straight

d) Diagonal

Answer – (d) Diagonal

5. Every product term of the group, a’.b.c’ and a.c, represents the ____________ in that particular group:

a) Sum of Maxterms

b) Sum of Minterms

c) POS

d) Input

Answer – (b) Sum of Minterms

No, you cannot delete Archive Utility from Mac computers. Archive Utility is a built-in app that comes with the Mac operating system and it is responsible for unpacking compressed zip files and archives.

It is also responsible for compressing files into zip files when requested. In order to delete Archive Utility, you would have to delete the entire operating system, which is not recommended.

To remove Archive Manager from your system, you’ll need to manually uninstall it. First, open the Control Panel and select “Uninstall a Program”. Find Archive Manager in the list and click the uninstall button.

You may be prompted to remove any configuration files left behind. If so, click ‘Yes’ to delete them. Once the uninstaller has finished, Archive Manager should be fully removed from your system. Some versions of Archive Manager may also include an uninstaller at the application level.

If so, you may find a shortcut in your Start menu or you can use Windows Search to locate it. If you do find the uninstaller, then you can use it instead of the Control Panel for a more tailored uninstall.

Archive Manager Ubuntu is a GUI-based file archiving application included with the Ubuntu operating system. The application, which is also known as “File Roller,” provides users with an easy way to compress and extract files of various types, including ZIP, TAR, and GZip.

It also supports the extraction of several other file types, such as RAR, XAR, and 7-Zip. Archive Manager Ubuntu is a user-friendly tool that can be used to quickly and easily compress and extract files without any advanced knowledge of archiving or compression.

It also includes support for password-protected archives, which can add an additional layer of security to a file or a set of files. The application can also be used to navigate through archives and view file properties, such as size, type, and date and time of creation.

Yes, Windows does have an Archive Manager. It is a built-in feature of the Windows operating system that allows users to manage, compress, and extract files and folders in various formats. In addition, users can also create and add comments to their files and folders, as well as manage their storage space.

The Archive Manager works with several file formats such as ZIP, RAR, and 7z, allowing users to easily access files and folders from multiple sources. Additionally, the Archive Manager’s intuitive user interface makes it easy for users to quickly access the files and folders they need.

To access the Archive Manager, users simply have to open the File Explorer, right-click on a file or folder, and select “Compress (or Extract)”. With these features, Windows users can easily manage their files and folders without needing to install an additional application.

The actual salary of an archive manager may vary depending on where the job is located. According to Salary. com, the average base salary for an archive manager in the United States is $59,478 annually.

However, salary can range from $47,541 to $77,077. Of those surveyed, most reported an annual salary of $59,978.

Meanwhile employers may also offer other financial benefits such as bonuses, occupational incentives, and additional rewards. It is important that you do your research in terms of the company you will be working for and what kind of salary package you can expect.

Also, remember that salaries are always negotiable, so do not be afraid to make your case.

In addition to salary and other benefits, archive managers will likely be given the opportunity to travel, attend conferences, and make professional connections while on the job. This can be a great way to increase your network and expertise in your chosen field.

Overall, an archive manager can expect to make an average base salary of $59,478 annually, but this may vary drastically depending on the job and location. Nevertheless, it is an important job that is essential to the operations of many organizations.

With good negotiation skills, employers may be open to increasing salaries for those willing to give their best work.

Yes, Mac systems come with an Unzipper installed by default. The Unzipper is known as Archive Utility and is located in the Utilities folder inside of the Applications folder. You can access this Unzipper by opening the Finder window and going to the Go menu, then selecting Applications and opening the Utilities folder.

The Unzipper has a simple user interface, you just need to drag-and-drop a ZIP file into the window and choose what to do with the content – “View Contents”, “Extract” or “Cancel”. Additionally, you can use third-party apps to open ZIP files on Mac systems, such as The Unarchiver.

This app is available for free in the Mac App Store and offers more features than Archive Utility.

The Unzipper for Mac is a file decompression utility specially designed for Mac devices. It’s a powerful tool for extracting data from archived files and works with a wide range of file formats, including. Zip,.

Rar,. 7z,. Tar,. Gz and. Cab. The Unzipper for Mac is incredibly intuitive, making it easy to extract files and folders quickly and easily. It offers an efficient drag-and-drop feature that allows you to simply select the file or folder to be unzipped and drop it onto the Unzipper window.

Furthermore, it’s a highly secure application, providing encryption and password-protection for sensitive files. It also includes an Advanced Mode to customise your Unzip settings. Ultimately, the Unzipper for Mac is a versatile and very user-friendly compression and decompression utility.

It’s a must-have tool for any Mac user, as it simplifies and speeds up the process of extracting data from zipped files.

It is possible that you are unable to open a zip file on your Mac for one of several reasons.

1. You may be trying to open a corrupted or password-protected ZIP file. If this is the case, the file may not open on any device because the original file is damaged.

2. Your Mac may not have the necessary software installed to open the ZIP file. You can download an application, such as The Unarchiver, that can open various archive file types.

3. It is possible you don’t have the latest version of macOS installed. If this is the case, you may not have access to the Archive Utility, which is the tool used to open ZIP files. To download the latest version of macOS, visit the Apple website.

4. You may have a poor internet connection. If the ZIP file was sent to you via email or a website, then a slow or unreliable connection may prevent the file from downloading properly.

If none of the above apply to you, then you may need to contact the sender of the ZIP file to determine why it is not opening on your Mac.

Unarching files on a Mac is fairly simple:

1. Download the appropriate unarchiving program. Several programs are available for free, such as UnRarX and The Unarchiver.

2. Open the unarchiving program.

3. Click the “Open” icon and select the file you’d like to unrar.

4. Click the “Extract” icon and choose the destination folder where you’d like the files to be extracted to.

5. Once the files have been extracted, the unarchiving program will finish the process. You should now see the files in the destination folder.

6. If you’d like to delete the original rar file, select the file and press Command+Delete to move it to the Trash.

On a Mac, you can double-click to open something or select an option. To do a double-click, press the mouse or trackpad button two times quickly without much movement in between clicks. Depending on what you are trying to do and the speed of your mouse or trackpad’s response time, you may find yourself double-clicking three or more times, but that doesn’t matter as long as you press the click button consecutively and quickly.

Keep in mind that some tabs and boxes may require that you double-click and hold after the second click and drag in order to select an option. This enables you to drag an object or highlight a specific portion of text.

Double-clicking is an easy and useful way to open folders and files or to choose an option when you’re working with your Mac.

Archive on a Mac is the process of keeping a backup of important files and folders in a way that they can be accessed and recovered down the line if necessary. When archiving a file on a Mac, the file is typically compressed and encrypted so it can be stored away for safekeeping.

The archived data is often stored in a dedicated folder or connected backup drive so it can easily be located in the future. Archiving is typically done on an as-needed basis so files can be stored away securely and safely in the event of a computer crash or data loss.

Archive files are usually stored in a location that is separate from other files on your device. Depending on the type of file and the operating system you use, you can usually find the archived files in either a specific folder or a different drive.

If you use Windows, the archive files are likely located in the C:\ drive. You can try looking in an Archive folder located in the root directory of the same drive. Additionally, you can search for an “Archive” or “Archives” folder in the main directory or in other folders that are part of the C:\ drive.

If you use macOS, the archived files will likely be found in the user Library Folder, or “~/Library/Archives”. You can also search your device for “. archives” to see if it may have been stored in a different location.

Finally, if you usen another type of operating system like Linux, you should try searching for “/etc/archives”.

No matter what type of file/operating system you are using, you can also try searching for the archived files using a search engine, as archived files can sometimes be misplaced or even deleted.

It is always a good idea to make sure that your archived files are stored in the correct folder or drive, as this will will help keep them secure and ensure that they are easy to locate in the future.

Archiving a file on a Mac is a way to save and store a document or folder that may contain multiple files. It is similar to compressing a file, but instead of the data being converted into a smaller size, the data is copied and stored in archive file format.

These are markers or guides to be aligned with particular points on the wheel. The alignment matters for the balancing of the wheel: If these dots on the tires are properly aligned with certain points on the wheel, minimal weights will be used for balancing.