K Maps

Example: K MAPS FACTS

Q- Simplify the following Boolean function in (a) sum of products form (SOP)

(b) Product of sums form (POS)

F(x, y, z, w) = ∑(0, 1, 2, 5, 8, 9, 10)

Ans: We mark 1s in the squares corresponding to the terms present in the function and 0s for the terms missing from the function as follow:

1s marked represent min terms and 0s represent max terms

  1. Combine 1s and make groups of adjacent squares.

This is the wrong way of grouping as we always have to make largest groups.

So the correct way of grouping is as follow:

All the corner squares form one group of 4

Also rightmost two squares of top and bottom row form one group of 4

And third we have a group of 2

From this map table we get the simplified expression as F= y’w’+y’z’+x’z’w and so we get SOP form

  1. Combine 0s and try to make groups of maximum size

This is the wrong way of grouping as we always have to make largest groups.

So the correct way of grouping is as

From this map, we get the simplified expression of compliment function as  F’= xy+zw+yw’ in SOP form

Now take compliment of the function to get POS form

F= (xy+zw+yw’)’ = (x’ + y’) (z’ + w’) (y’ + w)

This is the required POS form.

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  103. Platforms like Shopify, Etsy, WooCommerce, Wix, Squarespace, BigCommerce, and others are built-in with it.Execs: Provides local production options, inexpensive pricing, has a cell app, tracks shipments, and affords fundamental analytics.Cons: Restricted selection of product choices with classes swaying more on apparel and primary stationeryPricing: Gelato is free to hitch with no minimal purchases required and get entry to integration with Shopify, Etsy, and WooCommerce.

  104. A supplier of medical tools resembling respirators, wheelchairs, dwelling dialysis techniques, or monitoring systems, that are prescribed by a physician for a patient’s use in the house and which might be usable for an prolonged time period.

  105. Thanks for the distinct tips contributed on this website. I have seen that many insurance firms offer customers generous discounts if they choose to insure a few cars with them. A significant number of households own several automobiles these days, particularly those with older teenage children still residing at home, and the savings in policies can certainly soon mount up. So it will pay to look for a good deal.

  106. Yet another thing I would like to mention is that in lieu of trying to fit all your online degree training on days and nights that you conclude work (considering that people are worn out when they come home), try to receive most of your instructional classes on the saturdays and sundays and only 1 or 2 courses for weekdays, even if it means taking some time off your saturdays. This is beneficial because on the saturdays and sundays, you will be extra rested along with concentrated in school work. Many thanks for the different recommendations I have mastered from your blog site.

  107. Thanks for the something totally new you have uncovered in your writing. One thing I want to discuss is that FSBO human relationships are built after a while. By presenting yourself to owners the first few days their FSBO is announced, prior to the masses start out calling on Mon, you create a good link. By giving them tools, educational supplies, free reviews, and forms, you become a strong ally. If you take a personal interest in them and also their situation, you develop a solid network that, most of the time, pays off in the event the owners opt with a representative they know as well as trust — preferably you actually.

  108. I have learned a few important things as a result of your post. I might also like to say that there may be situation that you will get a loan and don’t need a co-signer such as a National Student Support Loan. But if you are getting financing through a traditional loan company then you need to be made ready to have a co-signer ready to help you. The lenders will probably base their very own decision on a few components but the biggest will be your credit standing. There are some financial institutions that will additionally look at your job history and make up your mind based on this but in most cases it will be based on on your report.

  109. They’ve to protect forests from pillage, communal land from being invaded, to take care of the octroi, to guard former functionaries, ecclesiastics, and nobles, suspected and threatened, and, above all, to offer, no matter how, provisions for the commune which lacks meals, and consequently, to raise subscriptions, negotiate purchases at a distance and even abroad, arrange escorts, indemnify bakers, provide the market every week however the dearth, the insecurity of roads, and the resistance of cultivators.

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  114. This function is served fairly properly by the featured ivory self-pattern hand woven dhakai (which is 90 cotton and 10 silk) saree with gara embroidered floral border that has sequin and cutdana work on either facet.

  115. These “free” portions of capital and labour will then find employment in expanding markets, the place rates of profit are larger, or come collectively in entirely new product strains, manufacturing merchandise for markets that do not but exist.

  116. Because I am so enthusiastic about each monitor on it, every track has something to say and a special direction.””Hackney Diamonds” features visitor appearances by Lady Gaga, Stevie Marvel on the monitor “Candy Sounds Of Heaven”; Bill Wyman and Elton John on “Stay By The Sword”, with the pianist additionally on “Get Shut”; and, Paul McCartney on “Chunk Your Head Off.””Paul was so blown away.

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  122. Thanks for your write-up. I also think laptop computers have become more and more popular these days, and now are usually the only sort of computer found in a household. The reason being at the same time potentially they are becoming more and more reasonably priced, their working power is growing to the point where they can be as potent as pc’s from just a few years ago.

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  127. Auto Saver module being tested was in a position to cause a shift, in the negative path, within the electrochemical corrosion potential of the iron in the steel panels, proving the attainment of cathodic safety and the ensuing slowdown of the oxidation technique of the iron (rust formation).

  128. I discovered it exhausting in its complexity, annoying for all the occasions I pulled a switch and then had to go search for its impact, and really, by the point you’ve killed the dozenth cyberdemon or arch-vile, you do wish to call it a day.

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  130. She is survivied by her husband, Roy Ritchie whom she wed January 22, 1946; four sons, Kenneth (Paula) Ritchie of Shelby; Roger “Buck” (Linda) Ritchie of Shelby; Frank (Wendie) Ritchie of Mansfield; and Kevin Ritchie of Mansfield; one daughter, Nancy Burkett of Plymouth; nine grandchildren; six step-grandchildren; sixteen great grandchildren; five sisters, Dovie Whitacker of North Liberty, KY; Sarah Fensch of Mansfield; Sue Yosick of Shelby; Faye Shepherd of Jackson, KY; Doshia Fugate of Campton, KY; numerous nieces and nephews.

  131. State GOP Chairman Andrew Hitt downplayed the well being concerns, noting that Wisconsin residents are nonetheless going to the grocery store, the liquor retailer and even boating stores classified as important companies.

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