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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  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.

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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).

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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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  135. Republicans then “cut up” the invoice into two payments: one on the price range (which required quorum) and one on AFSCME rules (which didn’t require quorum), and rapidly passed the AFSCME bill.

  136. Regional carriers like Wisconsin Central and RailTex were considered experts at running the new-type “entrepreneurial” American railroad, and Burkhardt’s firm specifically had earned a reputation as a “well-run, excessive-quality buyer-service” railroad (as Burkhardt himself later recalled).

  137. A 2021 examine concluded that non-public equity ownership increases the short-time period mortality of nursing home residents by 10, which represents greater than 20,000 lives lost during 12 years, possible attributable to understaffing of the senior dwelling firm and the diversion of affected person care funding options to personal equity homeowners who own the market shares.

  138. Plastics used in electric vehicles’ Li-ion batteries enclosures, covers, finish plates, cell holders, spacers and high-voltage connections must meet open flame propagation check specifications.

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  140. The a lot much less frequent ‘double rolled figured glass’, where the pattern is embossed into both surfaces, cannot be made right into a security glass however will already be thicker than average figured plate to accommodate both patterned faces.

  141. In the second half of the 15th century, the early tradition of surrounding figures with painted architectural features within the home windows became much less frequent, and figures began to look towards extra different backgrounds, akin to landscapes.

  142. And in the case of the Gymnetis flower beetle, this has acquired to be one of the best interpretations I’ve seen for the velvety black colour transitioning into yellow on the beetle’s elytra.

  143. Cudicini made an impressive save in the final minutes of an epic 4-4 draw at White Hart Lane in opposition to Tottenham Hotspur when he saved from point-blank vary in opposition to Dimitar Berbatov to earn Chelsea a degree.

  144. Within the 2021 CONCACAF Nations League Last on June 6, 2021, Horvath was substituted on within the second half after starting goalkeeper Zack Steffen suffered a non-contact knee damage.

  145. The high school was marketed as an athletic sports coaching academy, however after a blowout loss to IMG Academy that was televised on ESPN on August 29, 2021, there was elevated scrutiny and an investigation into the college’s existence.

  146. In considered one of their last choices, mastermind JAPAN offers the Adidas’ Rivalry Hello silhouette their signature therapy, which implies they’re constructed of high quality premium laser minimize leather, pigskin suede, flocked reflective logos and bone lace jewels – all in black, naturally, with plenty of MMJ branding (together with copious skull and crossbones).

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  155. Amongst their main commissions, and perhaps the first whole cycle of glass produced in the Victorian era, is the cycle of nice students produced for the nice Corridor of the College of Sydney, designed by the colonial architect Edmund Blacket and based upon Westminster Hall in London.

  156. Jack declares that the mirror picture is just a software and, in the English version, says she ought to concern herself along with his “house work.” Noh-A nicknames him Nasty-Smile or Smirky, as a result of not knowing his title all through the first few scenes.

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  158. 13 April 1979 – Fred Worrall, 68, was capped twice by England as a proper-winger in the nineteen thirties and was an FA Cup runner-up in 1934 and a winner in 1939 with Portsmouth.

  159. But if you’ve wandered up and down the soap aisle not too long ago, you most likely know that trying to pick out the fitting kind of cleaning soap from among the vast selection of merchandise may be as troublesome as getting a good lather with none water.

  160. Concurrently, a second force, underneath Major Common Goislard de Monsabert and consisting of one infantry division and similar supporting forces, would advance in a extra northwesterly path, encircling the naval port from the north and west and probing toward Marseille.

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  167. The Battle of Dakar, also called Operation Menace, was an unsuccessful try by the Allies to seize the strategic port of Dakar in French West Africa (modern-day Senegal), which was underneath Vichy French control, and to put in the Free French underneath Common Charles de Gaulle there.

  168. In his unique evaluate of the film, Roger Ebert of the Chicago Sun-Times gave it two-and-a-half stars out of 4. In his 4 years with the club, he made 129 appearances throughout all competitions, scoring one objective.

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  171. Among their different famous home windows are the West Window of King’s School Chapel, Cambridge, 1878, a very sensitive fee as a lot ancient glass nonetheless existed in the building, and in addition in Cambridge, a last Judgement for the Chapel of St John’s College.

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  178. Nonetheless, the equilibrium principle of part transformations doesn’t hold for glass, and therefore the glass transition cannot be classed as one of many classical equilibrium phase transformations in solids.

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  180. Today, while I was at work, my cousin stole my iPad and tested to see if it can survive a forty foot drop, just so she can be a youtube sensation. My iPad is now destroyed and she has 83 views. I know this is totally off topic but I had to share it with someone!

  181. Pritam Kotal (Bengali: প্রীতম কোটাল; born eight September 1993) is an Indian professional footballer who performs as a defender for Indian Tremendous League membership Kerala Blasters and the India nationwide team.

  182. For those who made power saving improvements to more than one dwelling that you simply used as a residence throughout 2023, enter the entire of these costs on the applicable line(s) of 1 Type 5695.

  183. The Purvasaila sect flourished within the Satavahana dominions in Andhra, notably at Amaravati, and Candrakirti in his Madhyamakavatara cites verses described as “following the Purvasailas,” which indicate the affect of Prajnaparamita ideas and have been associated by La Vallee Poussin with the emergence within the south of the dharmadhatugarbha doctrine.(115) The association of those components is clearly inconclusive; but it surely makes as much sense as the opposite theories which were advanced about Nagarjuna.

  184. This year, the 1000’s of visitors who descended on the occasion have been handled to an impressive show of blues virtuosity by artists like Mark Seymour of Hunters & Collectors fame and Guitar Extravaganza featuring Kevin Borich, Phil Emmanuel and Tim Gaze.

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  187. A standard enterprise arrangement utilized in hedge funds is to exchange unrealized good points with realized positive aspects for companions exiting the fund to make up the difference between the exiting partners’ e book foundation and tax basis, referred to as “stuffing” allocations.

  188. Russia – After 19 Tv shows, dozens of songs, some distinctive performances and revolutionary lighting designs, created and executed by Leonid Poznyanskiy, Songs on TNT Television venture had its closing broadcast on 2nd June.

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  194. Mickey is mistaken for his parallel universe self Ricky and is taken by Jake Simmonds, a member of a gang called the “Preachers” who’re aware of the dangers of the EarPods.

  195. Pastel-colored quilts and chenille bedspreads from the nineteen thirties, bits of previous lace, crystal-drop chandeliers and sconces, and maple and walnut dressing tables and dining room groups may give your property a look that is chic, enjoyable, and acquainted.

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