HRM cast study Essay Example | Topics and Well Written Essays - 500 words

HRM cast study - Essay Example One of the aspects that will hinder the successful delivery of Ralph’s strategy is his father’s influence on management of the business. As seen from his management of the company, William always likes his ideas implemented. From the information provided, Ralph fears that his father might object the strategy. Putting into consideration the powerful position he holds, that of the chair to the company, William’s objection of the strategy will be effective on the level of its success. Another area that might hinder the delivery of this strategy is the role of the staff in the formulation of the strategy. A successful strategy should be drawn from the many decisions made by staff members over a period of time (Epstein 2004, p.24). Once compiled, this strategy will reflect the views of the staff. Considering that it is the same staffs that will be expected to implement it, the level of success of such a strategy will be expected to be high should they be involved in strategy formulation. This is not the case, however, with the strategy adopted by Random Alloys. The managing director, without incorporating all staff members, formulated the strategy. As indicated by the members of staff in their remarks in the questionnaires, there is a feeling among staff members that they are not included in any changes made in the company. The staff are only included when the changes are happening. Lack of a clear flow of information within the company can also hinder the level of success of its delivery (Alston & Bryson 2013, p.145). Currently, Random Alloys lacks a defined formula through which information is communicated to members of staff. This leaves staff members looking for information they need from only those they know in the various offices. Lack of clarity on who gathers and provides information within the company will translate to misunderstandings during the implementation of the

Native American Paper Essay Example for Free

Native American Paper Essay In the pre-Columbian era when the Europeans had not yet discovered the â€Å"New World† there lived many distinct but also similar tribes that ruled all across. Many tribes existed during this era of prosperity for the Native Americans. A few of the main tribes of it are the Cherokee, Iroquois, Navajo, and Sioux who were all special in their own way. Firstly, the Cherokee were made up of seven clans with which each had a different purpose and job. The names and jobs of all the tribes in English are Long Hair which sends the Peace Chief, Blue who is the oldest; Wolf to protect clans, Wild Potato is the keeper of the land (gatherers), Deer is the fastest runners and hunters, Bird sends messengers, and lastly Paint are the medicine people. The belief system for the Cherokee was that good is rewarded and evil is punished. One main object they used was river cane making and using it for multiple purposes. The Trail of Tears was an important part of the Cherokee past since they used it to move to a different territory. (Information for the Cherokee Paragraph: Secondly, the Iroquois were consisted up of a small amount of tribes such as Cayuga, Mohawk, Oneida, Onondaga, Seneca, and Tuscarora. The main Iroquois considered themselves to be a superior people which lowered their numbers as time went by. One more reason the numbers went down was because they joined the British during the Revolutionary War. The belief of the Iroquois was that they should not kill each other and a sense of internal unity. The way the Iroquois survived was through a political system. (Information for the Iroquois Paragraph:? http://www. tolatsga. org/iro. html).

Supervision Model for Psychological Assessments

Supervision Model for Psychological Assessments Smith and Harty (1987) were pioneers in providing a model of supervision for conducting psychological assessments. Their model put forth that the supervisor’s responsibility is to ensures that the beginning supervisee accurately score their protocols and help him/her respectively create and order hypotheses by clinical relevance and amount of certainty. Additionally, this model features the supervisor having expectations that the supervisee will individually generate hypotheses while the supervisor judges and double-checks his/her work. The final portion of Smith and Harty’s model entails the supervisor serving as a consultant to the supervisee once the supervisee is competent. Finkelstein and Tuckman (1997) build upon Smith and Harty’s model by adding onto what is typically already done by supervisors (i.e., modeling the behavior of their own mentors when they received supervision in the past). Specifically, Finkelstein and Tuckman outline a model of supervisee development from beginner to expert. The first step for supervisors to teach supervisees is entitled â€Å"Learning the Basics of Test Administration and Scoring.† In this step, the supervisor serves as a â€Å"tour guide† for information found in test manuals (e.g., testing conditions and general scoring rules), teaches â€Å"macro-level scoring† of each test (e.g., calculating IQs, percentiles, and age levels), and emphasizes the pros and cons for each tests and how it can best answer corresponding referral questions. The next step, entitled â€Å"Generating Primary Inferences†, involves extrapolating inferences from all aspects of the assessment process includin g tests, behavioral observations, and relevant history. During this step, the supervisor’s role is to explain the rationale for the generated hypotheses, address how experience aids competence in hypothesis development, and curtail idealization of the supervisor and devaluation of the supervisee’s own abilities. The third step in this model involves clustering related hypotheses. This step involves the supervisor helping the supervisee integrate multiple sources of data into digestible patterns and clusters that will ultimately be documented in an outline that serves to guide the formal report. The fourth step, entitled â€Å"From Outline to the Written Word,† involves the supervisor’s role in helping the supervisee convert the outline into a useful report (e.g., proofreading, suggesting revisions, and preparing supervisee to provide feedback). The fifth stage in this model, entitled â€Å"Internalizing Diagnostic Norms,† is designed for more advanced students who have mastered basic assessment skills and are in need of more â€Å"content knowledge.† Specifically, the supervisor’s role in this stage involves ensuring exposure to a wide variety of assessment questions and helping the supervisee recognize patterns and deviations in test results and specific patient populations. The sixth stage encourages autonomy and promotes consultation when there is less need for direct guidance. The authors state that supervisors need to be aware that this stage often involves a â€Å"dynamic tension† between autonomy and dependence for the supervisee. The sixth stage involves the supervisor encouraging complete autonomy for the supervisee, which typically occurs after one has obtained his/her license and will be generating reports independently. The final stage in this model involves the former supervisor help ing the former supervisee transition into becoming a supervisor for the next generation and serving as a consultant throughout this life-long process. Regarding the take home message for their model, Finkelsten and Tuckman proclaim that this interpersonal and intrapersonal process should produces supervisee that are able to master assessment by integrating â€Å"all the various and diverse introjects from past supervisors into a unique self (p. 95).† Yalof and Abraham (2009) summarize core supervisory considerations and promote an integrative approach to supervision that is aimed to strengthen psychological report writing and improve preinternship preparation for psychology graduate students. The first area these authors address is regarding assessment competency and citing the foundational skills in assessment education and training (e.g., psychometrics, theory) outlined in the 2002 Psychological Assessment Work Group (PAWG: Krishnamurthy et al., 2004). Next, the authors describe the various developmental stages that supervisees evolve from and outline several markers that are used to define â€Å"assessment† competency. From this point, Yalof and Abraham go into greater detail regarding multicultural supervision. Specifically, they encourage supervisors to help supervisees address differences in cultural background and determine if assessment measures are culturally sensitive (Allen, 2007) as well as discuss the importan ce of attending to personal and community histories (Hernà ¡ndez, 2008). Next, Yalof and Abraham advise supervisors to help supervisees consider ethical applications and acculturation in assessment. Furthermore, the authors cite the APA Ethical principles and standards (2002) as a good starting point for supervisees to develop their own ethical identity. Furthermore, the supervisor needs to address how the supervisee should best adapt different learning strategies that will promote greater integration within the practice of psychological assessment (Handelsman, Gottlieb, Knapp, 2008). Next, Yalof and Abraham spell out seven supervisory techniques that draw upon extant literature to promote growth in assessment supervisees. The first technique involves providing information related to ethical practice in assessment including risk management strategies (e.g., documentation, informed consent, consultation). The next technique involves emphasizing the skills that correspond with rapport building and diagnostic interviewing. The third technique suggests that supervisees be provided with extra practice activities (e.g., scoring protocols, reading sample reports, critiquing reports) that will further their respective competency. The fourth technique advises supervisees to conduct a literature review regarding the referral question to become more familiarized. The fifth technique promotes supplemental peer supervision as it promotes collegiality, socialization, and a collaborative learning environment for learners. The sixth technique suggests that the unconscious influen ces between the client, supervisee, and supervisor that occur throughout an assessment explicitly be explored. Finally, the supervisor needs to encourage and promote critical thinking skills corresponding to which ever developmental stage the supervisee is currently in. Yalof and Abraham recommend Johnson-Laird’s typology of thought (e.g., inductive thinking, associative thinking, creative thinking, and self-reflective thinking) to help guide supervision. The final portion of this article features a case illustration to demonstrate how supervisory probes encourage growth and development for the supervisee. The take home message for this article revolves around the supervisor’s ability to most effectively intervene in the supervisee’s cases. Specifically, Yalof and Abraham propose that the supervisor needs to thoughtfully and instructively probe the supervisee throughout the assessment process to maximize conceptual, critical, and creative thinking regarding the client. References Allen, J. (2007). A multicultural assessment supervision model to guide research and practice. Professional Psychology: Research and Practice, 38(3), 248-258. doi: 10.1037/0735-7028.38.3.248 American Psychological Association. (2002). Ethical standards and code of conduct. American Psychologist, 57, 1060-1073. Finkelstein, H., Tuckman, A. (1997). Supervision of psychological assessment: A developmental model. Professional Psychology: Research and Practice, 28(1), 92-95. doi: 10.1037/0735-7028.28.1.92 Handelsman, M. M., Gottlieb, M. C., Knapp, S. (2008). Training ethical psychologists: An acculturation model. In D. N. Bersoff D. N. Bersoff (Eds.), Ethical conflicts in psychology (4th ed.). (pp. 122-127). Washington, DC, US: American Psychological Association. Hernà ¡ndez, P. (2008). The cultural context model in clinical supervision. Training and Education in Professional Psychology, 2(1), 10-17. doi: 10.1037/1931-3918.2.1.10 Smith, W. H., Harty, M. K. (1987). Issues in the supervision of diagnostic testing. In R. H. Dana, W. T. May, R. H. Dana W. T. May (Eds.), Internship training in professional psychology. (pp. 410-418). Washington, DC, US: Hemisphere Publishing Corp. Yalof, J., Abraham, P. (2009). An integrative approach to assessment supervision. Bulletin of the Menninger Clinic, 73(3), 188-202. doi: 10.1521/bumc.2009.73.3.188

Staffing and Selection Essay -- essays research papers

  Ã‚  Ã‚  Ã‚  Ã‚  Bank of America is a corporation that employs over 175,000 associates that provide financial products, services, ideas, and solutions to customers in the United States. The Global Corporate and Investment Banking group (GCIB) has offices in 35 countries serving clients in more then 150 countries, with associates in all of the Americas, Europe, and Asia (Anonymous, 2004). Choosing the most qualified individual may seem like a daunting task. Bank of America’s policies and procedures for hiring associates provide a solid foundation for acquiring the best talent. With standard policies for interviewing, all individuals are subject to the same questioning. There is diversity within large number of associates the bank employs. Globalization in the business world is a necessity and corporations must increase the sensitivity levels when attempting to recruit new talent. When attempting to acquire new talent, Bank of America encompasses a wide range of staffing pra ctices and selection tools. In response to diversity and technology trends, Bank of America’s staffing practices are effective in meeting current and future employment needs of the organization.   Ã‚  Ã‚  Ã‚  Ã‚  Bank of America’s multicultural supplier and development program began in 1990. The program increased the amount of quality products and services the bank obtains directly from businesses owned by minorities, women, and veterans with disabilities. Helping diverse businesses grow through contracting opportunities and bank products allows Bank of America to grow at the same time. Within the bank, new computer-based diversity training Bank of America’s staffing department works closely with various state and local agencies to provide people with disabilities equal access to the company’s may employment opportunities. Dozens of agencies within the community that handle an applicant pool of individuals with disabilities receive a listings of open positions and job postings from Bank of America. The personnel department developed relationships with certain organizations that provide vocational services that cater to individuals with disabilities. Co mpanies like Bridges, Toolworks, and Easter seals all maintain a healthy relationship with Bank of America in order to develop ongoing relationships that assist in the hiring of individuals with disabilities. Departme... ...ng free of charge, executives and associates have incentive in wanting to be a part of Bank of America. Technology will change and Bank of America’s hiring process will change along with it. Planning for years to come, the bank devotes a lot of time and money into using and developing technology to acquire and retain the best possible talent.   Ã‚  Ã‚  Ã‚  Ã‚  In conclusion, Bank of America must follow certain business trends to stay ahead of competition. With diversity and technology, the bank devotes different departments in assuring the best talent joins the bank. Different types of research for future staffing practices assure that trends do not outdate Bank of America’s selection tools. Using different technological tools and diversity training makes the bank one of the leaders in recruitment. Strong relationships between staffing and personnel, as well as detailed selection tools, are examples of devotion to excellence. References Anonymous. Retrieved February 24, 2005 from Bank of America’s local intranet. Anonymous. (n.d.) Outreach and Recruitment Activities. Retrieved on February 24, 2005   Ã‚  Ã‚  Ã‚  Ã‚  from http://www.cablen.org/bestprac.htm

External Factor Analysis of Accounting Firm Essay

It is a part of the external analysis when conducting a strategic analysis or doing market research and gives a certain overview of the different macroenvironmental factors that the company has to take into consideration. Political factors, or how and to what degree a government intervenes in the economy. Specifically, political factors include areas such as tax policy, labour law, environmental law, trade restrictions, tariffs, and political stability. Political factors may also include goods and services which the government wants to provide or be provided (merit goods) and those that the government does not want to be provided (demerit goods or merit bads). Furthermore, governments have great influence on the health, education, and infrastructure of a nation. Economic factors  include economic growth, interest rates, exchange rates and the inflation rate. These factors have major impacts on how businesses operate and make decisions. For example, interest rates affect a firm’s cost of capital and therefore to what extent a business grows and expands. Exchange rates affect the costs of exporting goods and the supply and price of imported goods in an economy Social factors  include the cultural aspects and include health consciousness, population growth rate, age distribution, career attitudes and emphasis on safety. Trends in social factors affect the demand for a company’s products and how that company operates. For example, an ageing population may imply a smaller and less-willing workforce (thus increasing the cost of labor). Furthermore, companies may change various management strategies to adapt to these social trends (such as recruiting older workers). Technological factors  include ecological and environmental aspects, such as R&D activity, automation, technology incentives and the rate of technological change. They can determine barriers to entry, minimum efficient production level and influence outsourcing decisions. Furthermore, technological shifts can affect costs, quality, and lead to innovation. Environmental factors  include weather, climate, and climate change, which may especially affect industries such as tourism, farming, and insurance. Furthermore, growing awareness to climate change is affecting how companies operate and the products they offer–it is both creating new markets and diminishing or destroying existing ones. Legal factors  include discrimination law, consumer law, antitrust law, employment law, and health and safety law. These factors can affect how a company operates, its costs, and the demand for its products.

Turners Thesis essays

Turner's Thesis essays The wide open frontier a place of freedom and promise. Fredrick Jackson Turner states that the frontier changed almost every aspect of the pioneer making them distinctly American. Unfortunately, Turner's thesis as it is called is not true in all aspects. Many historians including Carl Degler who wrote the book "Out of Our Past" disagree with the cultural aspect of the thesis. Throughout his book he cites many pieces of evidence that prove Turner's thesis wrong. One of the pieces of evidence that he presents is the many frontier states constitutions. One of Turner's hypothesis that found wide acceptance among historians is that American democracy is a unique product of the struggle with the wilderness. The main way of proving this point has to been to point out the many democratic features of the western states constitutions.(i.e. universal manhood suffrage, and elected officials) Through this comes the argument that democracy actually spread from the west to the east. This is easily proven wrong however by comparing the western and eastern states constitutions. For example the first states over the Appalachian Mountains Tennessee and Kentucky both modeled their constitutions after the Pennsylvania constitution of 1790 a document which was more conservative than the 1776 laws of the state. Another example of this is the state constitutions of the Ohio-Mississippi region. At that time nicknamed the "Valley of Democracy" yet historia n John Barnhart found only eleven original clauses in Ohio's first constitution which had 106 clauses in total. Another piece of evidence that Degler states in his book is economic. As his book states that it takes a year and a half of an average urban workers pay to start a farm in the west or frontier. In essence this means that the poor urban man is going to become a poor frontiersman with no money to change economically or culturally. ...

Select and explain the most important turning points in Nelson Mandelas life Essay Example

Select and explain the most important turning points in Nelson Mandelas life Essay Example Select and explain the most important turning points in Nelson Mandelas life Essay Select and explain the most important turning points in Nelson Mandelas life Essay In my opinion there were 6 major turning points in Nelson Mandels life. I am going to explain what they are, why I chose them and the impact in which it had on his life. I am going to do this in the order of significance, starting form the least important and working my way up to the most important. On 10th may 1994, in the first multi-racial elections, Nelson Mandela became the first black president of South Africa in nearly three centuries. I classed this event as the least important of the 6 points because although it is important in the structure of his political life, it is not as important as some other events. This was the final turning point in Mandelas life because it was as if that, him becoming president was a tribute to his success and achievement for his people. He became president, 2 years after signing a constitution agreement with F. W de Klerk, which wiped out apartheid and introduced democracy. This was his goal for life and by then becoming president it was an added bonus to say thank you for giving up his life for his people. This also gave hard evidence that people admired him and thought of him as a hero. After moving to Johannesburg form Qunu in 1940 to study a law degree, Mandela soon realized the importance of skin colour. When he moved to Johannesburg he was treated badly by the whites, which put him out of his comfort zone of his hometown. He was treated inferior, made to live in shantytowns in the suburbs of the city and paid less than white people. This was a shock to Mandela and made him realise that he should do something about it because he didnt like him and his people being treated any different or inferior just because of their skin colour. In 1944 this then led to him joining the African National Congress (ANC). The event of him moving to Johannesburg and then joining the ANC was in my opinion the 5th most important turning point in Mandela life because if he had never gone to Johannesburg then he would never have experienced the inferity of black people. This means that it was most likely that he never would have joined the ANC and therefore never would have got into the role of a leading person in the conflict of apartheid. This furthermore means that he would have never gone into prison and we today, wouldnt even know who Nelson Mandela was. Accept this did happen. So this proves that this event had a large impact on his life and was a turning point in his political life because it changed his life forever. I think that the 4th most important turning point in Mandelas life happened in 1992 when he signed a constitutional agreement with the current white president, F. W. e Klerk which was designed to abolish apartheid and introduce democracy to South Africa. The wiping out of apartheid meant that black people did no longer have to carry around the hated pass books anymore, they were now allowed to use the same amenities as whites such as public toilets and they were no longer forced into a particular racial group. This was a turning point in Mandelas life because form the moment apartheid began, his goal and aim for life was to get the black population of South Africa free form it and treated equally. The acts that got him imprisoned for 27 years were all to appeal and protest against apartheid and now that it was over, it was as if a massive weight had been lifted form his shoulders. He had now reached his goal for life and whatever lay ahead would be a bonus. On 20th April 1964, Nelson Mandela was brought to court for his acts of terrorism. He was charged with sabotage with the penalty of either death or life in prison. He then got sentenced to life imprisonment on a prison on Robben Island, just off the coast of South Africa. In my opinion, Nelson Mandela being sentenced to life imprisonment was the 3rd most important turning point in his life. This is because although Nelson Mandela done a lot of other political events during his life, this was the event that stood out all over the world. Countries such as the UK supported Mandela and done all they could to get him released throughout the whole 27 years he spent in prison. This was to the extent that a free Mandela concert was held in London in 1988 and it was broadcast around the globe. I classed this event as third most important because it played a huge role in why Mandela is respected nowadays in that people respect the fact that he gave up his life and his family to do things for his people which he knew would send him to prison. The impact I think this had was that so many people were involved and it had affected a large number of people al over the globe, Nelson Mandelas prison sentence will go down in history for centuries to come. In my list of 6 main turning points in Nelson Mandelas life I classed the exhibition of Sharpeville as the 2nd most important. On March 21st, 1960 an ordinary protest was organised to happen at a local police station in Sharpeville. The protest was against the hated pass books and the plans was for a large group of people to all hand in their pass books and offer themselves up for arrest. The idea was that the police knew that they couldnt arrest so many people so they would consider the pass book law. Except this isnt what happened. The police fired at the crowds and killed 69 people and wounded 180, these were both including women and children. This event was to change the ANC and therefore Mandelas views forever. This was the event that sent the ANC to violence and from this point on, violent protests were organised by Mandela and other leading positions of the ANC. I think this is the 2nd most important turning point in Mandelas life because this was the day that marked the start of violence in the South African apartheid split. If this event were not to have happened then the ANC would most likely not turned to violence and therefore the terrorist attacks acted out by Mandela would not have occurred and therefore he would not have been imprisoned and the whole situation of Mandelas sentence would not have been necessary. Last but not least, in my opinion the most important turning point in Nelson Mandelas life is when he refused his release from prison in return for denouncing the arms struggle. This event happened in 1985. The reason that he was offered his release for denouncing the arms struggle was because it was getting out of hand and the South African government had no choice but to start negotiating with Mandela. I think that this point is the most important turning point in Nelson Mandelas life because he had already been in prison on Robben Island for 21 years and away from his family. Any normal person who ahs been in prison for that long would do anything to get out and see their family. But not Mandela. He stuck by his guns and refused his release in which made him stay in prison for a further 6 years before finally being set free and able to see his family. I think that this point is most important because it shows how dedicated he was to getting the result for his people, that he wanted and how much that ending apartheid meant to him. He sacrificed 27 years of his life and seeing his children grow up just to get freedom for his people. I think this proves that Nelson Mandela is quite a remarkable man and deserves all the credit he gets. I chose this point to go at the top because although it is a point that is not as public as Sharpeville for example, it has significance in showing how Mandela was determined and done literally everything in his power to succeed.

Oseberg - Viking Ship Burial in Norway

Oseberg - Viking Ship Burial in Norway Oseberg is the name of a Viking ship burial, located near present-day Tà ¸nsberg, Norway, about 60 miles (95 kilometers) south of Oslo, on the banks of the Oslo Fjord in Vestfold county. Oseberg is one of several ship burials in the region, but it is the richest and best preserved of such elite graves. Key Takeaways: Oseberg Ship Burial Oseberg is a Viking boat grave, the interment of two elite women inside a working ship. Created in 834 CE in eastern Norway south of Oslo, the ship and its contents were  remarkably well-preserved.  The ship was likely a royal barge built in 820 CE in western Norway.Completely excavated in 1904, archaeological research has been focused on the analysis and conservation of the recovered artifacts.   Viking Ship Description The Oseberg ship was a karvi, a clinker-constructed ship built almost entirely of oak, and measuring 70.5 feet (21.4 meters) long, 17 ft (5.1 m) wide, and 4.9 ft (1.58 m) deep, from the railing to keel. The hull was constructed of 12 board planks stacked horizontally on either side; the port and starboard upper board planks have 15 oar holes, meaning the ship would have been propelled by a total of 30 oars- the oars were included in the burial. Oseberg was an elaborately decorated ship, with several ornate carvings covering its hull, and it was decidedly not built for strength as a warship might have been. Analysis of the wooden parts of the ship suggested to archaeologists that the ship was originally a royal barge, built in Western Norway about 820 CE and used for short voyages along the coastlines. It wasnt terribly seaworthy, but it was overhauled immediately before the burial. The oars and yardarm were new and not the right size for the ship, and the anchor was too small. Tools found aboard the ship included two small axes, kitchen equipment including a quern for grinding grain located near a butchered ox. The handles on both were well-preserved, with a characteristic herringbone pattern known as spretteteljing in evidence. A small wooden chest was also identified: although it was empty, it is assumed to have been a tool chest. Animals represented in the faunal assemblage included two oxen, four dogs, and 13 horses; there were also sledges, wagons, and a vertical loom. Burial Chamber Gabriel Gustafson excavation: News photo of the Oseberg Viking Ship Burial, 1904. Hulton Archive / Getty Images In the middle of the barge was a timber-built box with a tent-like cover of roughly hewn oak planks and posts. The chamber had been plundered in the 10th century CE- apparently part of ritual disturbances of many mounds during the reign of Harald Bluetooth (911–986 CE), who had ordered the destruction of mounds as part of his Christianization of the Scandinavian people. Despite Harolds efforts, the chamber still included the fragmented skeletal remains of two women, one aged in her 80s and the other in her early fifties. When it was excavated in 1904, the interior of the chamber still contained the remains of several textiles. Some of the textiles may have been bedding, or wall hangings, or both. There were the remains of the womens clothing discovered as well: over 150 fragments of silk were found woven into the garments of the women. Twelve of the fragments were silk embroidery, the earliest found to date in Scandinavia. Some of the silk had been treated with madder and kermes dyes. Some historians (such as Anne-Stine Ingstad, associated with the discovery of Leif Ericssons Lanse aux Meadows camp in Canada) have suggested the elderly woman was Queen Asa, mentioned in the Viking poem Ynglingatal; the younger woman is sometimes referred to as a hofgyà °ja or priestess. The name of Oseberg- the burial is named after the nearby town- might be interpreted as Asas berg; and the word berg is related to the Old High German/Old Anglo-Saxon terms for hill or grave mound. No archaeological evidence has been found to support this hypothesis. Dating the Oseberg Ship Detail of the Oseberg Cart from the Oseberg ship burial, 9th century. Print Collector / Hulton Archive / Getty Images Dendrochronological analysis of the grave chamber timbers gave a precise date of the construction as 834 CE. Radiocarbon dating of the skeletons returned a date of 1220–1230 BP, consistent with the tree ring dates. DNA could only be retrieved from the younger woman, and it suggests she may have originated from the Black Sea region. Stable isotope analysis suggests the two had a primarily terrestrial diet, with relatively small amounts of fish compared to typical Viking fare. Excavation Prior to excavation, the large mound built over the top by the Vikings had been known as Revehaugen or Fox Hill: after the nearby Gokstad ship was discovered in 1880, Fox Hill was presumed to also hold a ship, and clandestine attempts to uncover parts of the mound began. Much of the soil was removed and used for fill before 1902 when the first official survey of what was left of the mound was conducted. Oseberg was excavated by Swedish archaeologist Gabriel Gustafson (1853–1915) in 1904 and eventually written up by A.W. Brogger and Haakon Shetelig. The remarkable preservation of the contents was the result of the weight of the huge mound built above it, which pressed the ship and its contents down below the water table. The ship has been restored and it and its contents have been on display at the Viking Ship House at the University of Oslo since 1926. But over the last 20 years, scholars have noted that the wooden artifacts have become increasingly brittle. Conservation When Oseberg was discovered over a hundred years ago, scholars used typical preservation techniques of the day: all the wooden artifacts were treated to various mixtures of linseed oil, creosote, and/or potassium aluminum sulfate (alum), then coated in lacquer. At the time, the alum acted as a stabilizer, crystallizing the woods structure: but infrared analysis has shown that the alum has caused the complete breakdown of the cellulose, and the modification of lignin. Some of the objects are only held together by the thin layer of lacquer. The Helmholtz Association of German Research Centres have been addressing the issue, and conservationists at the National Museum of Denmark have been working on developing a comprehensive approach to the preservation of waterlogged wooden objects. Although the answers are as yet unclear, some potential exists for the creation of an artificial wood to replace that lost. Selected Sources Bill, Jan. Ambiguous Mobility in the Viking Age Ship Burial from Oseberg. Materialities of Passing: Explorations in Transformation, Transition and Transience. Eds. Bjerregaard, Peter, Anders Emil Rasmussen and Tim Flohr Sà ¸rensen. Vol. 3. Studies in Death, Materiality and the Origin of Time. New York: Routledge, 2016. 207–253. Print. of Power Politics? Antiquity 86.333 (2012): 808–24. Print.Draganits, E., et al. The Late Nordic Iron Age and Viking Age Royal Burial Site of Borre in Norway: ALS- and GPR-Based Landscape Reconstruction and Harbour Location at an Uplifting Coastal Area. Quaternary International 367 (2015): 96–110. Print.McQueen, Caitlin M. A., et al. New Insights into the Degradation Processes and Influence of the Conservation Treatment in Alum-Treated Wood from the Oseberg Collection. Microchemical Journal 132 (2017): 119–29. Print. Nordeide, Sà ¦bjà ¸rg Walaker. Death in Abundance Quickly! The Duration of the Oseberg Burial. Acta Archaeologica 82.1 (2011): 7–11. Print.Vederler, Marianne. Silk for the Vikings. Ancient Textiles Series 15. Oxford: Oxford Books, 2014.

Tools for E-Businesses Research Paper Example | Topics and Well Written Essays - 1250 words

Tools for E-Businesses - Research Paper Example Since the first website appeared online, organizations, companies and institutions have gone on a rush. It is not enough to be on-line with a domain name and a simple website. A useful and well-designed website is an important factor to consider. Website statics are a major concern for the management who want to realize a return on investment for their money1. Despite the overrated chants for this new-age business concept that has suddenly become the goal of many commercial organizations, not much has changed in the traditional way of handling various business processes. E-business maintains the same principles of business operation as traditional commerce: people, both sellers and buyers, come together to exchange commodities and services over a network of computers. Ordering, buying, bidding, selling, customer services, inquiries and virtually all the business processes still uphold the underlying principles of commerce. E-commerce is a subset of the overall e-business strategy. It chiefly seeks to improve the buy-sell transaction activities in a business; as a result it increases the revenue. In a way e-commerce covers a range of on-line business activities for services and products, both businesses to customer and business to business on the Internet as a platform. E-commerce breaks the process of online business into showing the scope activities and information that is provided to the customer to conduct business and online shopping. Multiple and different functions go into the requirements of e-businesses. For instance, there are some basic functional necessities that cover the sort of specialized that perform the functions that run on the e-business mode. There are also other functions that cover the software and hardware requirements to carry out the same services. An analysis of how e-businesses verity credit, process an order and how they fulfill the order as well as how they verity shipments and all or any post sales process needs to be considered wh ile assessing the performance of an e-business. Functionality, both technical and non-technical, is fundamental for an e-business2. Technical functionality refers to the information processing capability of the e-business systems. It points to the server requirements, Internet speed requirement etc. These functional requirements are the foundations and platforms of the e-businesses. The nature that makes business processes virtual in e-business is supported by these systems. Many stakeholders control the entire system and as such an e-businesses smooth operation especially when operating online is controlled by many other people or organizations. Additionally, e-businesses need other functionality such as security, scalability and reliability to be in place. This may make or break a venture and essentially are what keeps any e-business venture in operation. Without security, performing reliable business functions will not be with trust on the end of the consumer. Consumer trust is v ital just like with a traditional store. Building consumer confidence in your system is in this case a good sign of growing business. Order processing needs the transaction processing and database information mining. Speed and efficiency are factors that are considered in evaluating the usability of a system supporting e-business. Payment methods include credit cards, electronic checking and digital cash.

International Business Essay Example | Topics and Well Written Essays - 500 words - 14

International Business - Essay Example Patricia focused too much on securing an international connection instead of gaining knowledge about the product which resulted in the immediate sense of failure once business meeting underwent. The initial approach of requesting information from home offices located internationally and conducting research via email is something which is commonly followed by businesses however such inquiries are usually improper and may result in irrelevant inquiries. It is, therefore, better to visit local trade offices of foreign consulates residing in the home country and seek information from them regarding businesses operating in their country. Another way of gathering information about potential targets is by accessing trade websites which provide useful information including the credibility of potential businesses. However, selection of targeted businesses should be made against the criteria based on the assessment of product or service offerings. Before conducting meeting it is important that mutual understanding is achieved between parties so that situations of despair are not faced. Biggest mistakes that business typically makes must be learned and avoided however it requires a thorough research and well-directed efforts if there is no prior experience.  Regarding Patricia business trip to Japan few major weaknesses could be identified regarding her overall understanding of the potential market and interaction with the possible business partner. Most importantly she seemed unprepared for the business trip which was made all of a sudden without any written understanding of each other’s business and products to be offered. Any such international business trip should be backed with the establishment of the business objective and an intensive study of the market which is targeted. The study of the potential market does include the survey of the market which is served by the machinery offered.

Discuss the origin and current situation of the Taiwan issue and the Essay

Discuss the origin and current situation of the Taiwan issue and the possible resolutions for Chinese government handling the Ta - Essay Example The United States 7th Fleet was tasked with patrolling the Taiwan Strait to stop a raid of Taiwan. Americans offered military and economic aid, and, in 1954, a joint security agreement was reached with the China’s Republic as part of America’s Cold War strategy of suppression of the Beijing government. However, military and financial aid was restricted to what Taiwan required to defend and finance itself against the People’s Republic of China, but not to hold up Chiang Kai-shek’s vision of â€Å"going back to the mainland.† The regime created, in 1949, on Taiwan, had provincial and national levels (Cole 4). The state level, with selected, as well as appointed officials from the mainland, represented itself as the Republic of China in global forums and apparently arranged for a go back to rule the entire mainland. Part 2: the current situation 2. Controversy of sovereignty over Taiwan i) Position of the People's Republic of China (PRC) The position o f PRC is that the Republic of China (ROC) stopped being a lawful regime after the founding of PRC on October 1st, 1949 and that they are the successor of ROC as the only lawful regime of China with the right to manage Taiwan with regards to the â€Å"succession of states† theory (Bush and O'Hanlon 23). The stand of PRC is that they and ROC are two diverse groups in the Chinese Civil War that never lawfully subsided. Hence, PRC argues that the two groups belong to one sovereign nation, China. Because Taiwan’s independence belongs to China, then PRC’s regime, along with its supporters, deem that the secession of the island should be settled upon by the 1.3 billion citizens of China rather than just the 23 million citizen of ROC who, at the moment, live in Taiwan (Bush and O'Hanlon 23). In addition, PRC states that the UN’s Resolution by its General Assembly recognizes that PRC controls China’s entire terrain including Taiwan. UN further classifies th is matter through acknowledging PRC as they only legal representatives of China. Therefore, PRC considers that it is within its lawful capacity to prolong its jurisdiction of Taiwan through any means possible (Bush and O'Hanlon 24). Furthermore, the stand of the People’s Republic of China is that ROC does not fulfill the fourth principle of the Montevideo Convention. PRC argued that the Montevideo Convention was agreed upon by only 19 states at the 17th Global Conference of American States (Bush and O'Hanlon 24). Therefore, the authority of the United Nations and the United States should supersede the Montevideo Convention. ii) Position of the Republic of China (ROC) ROC, on the other hand, claims that it maintains all the traits of a nation and that it was succeeded or replaced by PRC since it is still in existence even after PRC’s establishment. In line with the Montevideo Convention (1933), the mainly consulted source for the meaning of statehood, a nation should po ssess a defined territory, a permanent population, a regime, as well as a capacity to start relations with other nations (Bush 33). ROC affirms to meet all these principles since it has a government practicing successful jurisdiction over clear territories

Law of Evidence. write of silence Essay Example | Topics and Well Written Essays - 1250 words

Law of Evidence. write of silence - Essay Example However, as observed in R v Beckles, such inferences cannot be used to establish guilt. The House of Lords in R v Webber of 2004 that pursuant to Section 34 facts may include any fact that is an issue at the trial and tendered by the defendant in his or her defence. Moreover, facts will include any explanation or fact that the defendant would have logically raised at an earlier stage of the criminal proceedings. According to the ruling in R v Ali, the only recourse a defendant may have is to either deny culpability at the police station or to prepare a statement setting out his or her defence so as to preserve the right to raise the defence at trial. The right to a fair trial guaranteed by Article 6 of the ECHR demands however, that prosecutors bear the burden of proof. It was ruled in R v Condron that directions to the jury must be given with caution emphasizing the right to silence. The Judicial Studies Board established 6 points intended to ensure that adverse inferences contained in section 34 do not contradict Article 6. The 6 points correspond with the 6 requirements for adverse inferences as laid doing in R v Argent and are: There must be proceedings. Failure to mention a fact must predate the charge or when being charged. The omission must have occurred while being questioned under caution. The questions must have related to determining who committed the offence. The omitted fact must be one subsequently used in defence at the trial. The omitted fact must be one that accused was logically expected to mention. The courts have tried to set limits to what amounts as a new fact and to preserve the defendant’s right to remain silent. For example in R v McGarry, the defendant was charged with causing grievous bodily harm. In a written statement taken by the police, the defendant claimed that he acted in self-defence and did not answer police questions. At his trial, the defendant testified to facts substantiating and building on his claim of self-defen ce. The trial judge said that he was not inviting the jury to draw an adverse inference since D had not raised a new fact but did state that it was up to the jury to determine whether or not they wished to draw an adverse inference. The defendant was convicted and appealed. The appeal was allowed because the trial judge had a duty to direct the jury that they were not at liberty to hold the defendant’s failure to answer police questions since he did not rely on a new fact. R v B (MT) partially deals with circumstances in which a defendant may not be aware that a new fact may provide him or her with a defence. In this case the defendant was accused of sexual raping his stepdaughter, a minor and another girl under the age of 16. When questioned by the police, the defendant could not identify a motive for the girls to lie. However, at trial, his stepdaughter testified that she resented the defendant and did not want him to live with her mother. The defendant used this informatio n in his defence. The trial judge directed the jury that they could draw an adverse inference from this if they felt that it was reasonable for the defendant to raise the issue of motive while being questioned by police. The defendant was convicted and upon appeal, the Court of Appeal allowed the appeal on the grounds that the fact relied on was not a fact that the defendant could have known when questioned by the police. Likewise in Murray v UK before the European Court of Human Rights it was held

Health and Safety Essay Example | Topics and Well Written Essays - 500 words

Health and Safety - Essay Example Another recommendation was the Deregulation Unit was required to work on guide by the end of 1993 on formulation and implementation of EC law in the UK. Member states indeed have a delay experience on the state of implementation of EU law in transposition of directive as shown by statistics. There is usually an incomplete or incorrect transposition as indicated by statistics of infringement proceedings. In 2002-2005, there has been transposition and application of directive cases up to 78 per cent of them initiated by the European Union against Member States. This indicates very clearly that a problem is experienced by Member States in determining the national method of implementation to give effect to directives. (Hall, Smith and Tsukalis, 2001) Better Regulation Task Force has always urged the UK government on the need for a better and regulatory impact assessment since the problem of "gold plating" is still continuing. The European Commission impact assessments that are supposed to be attached to their legislative proposals are not comprehensive. In addition to the financial impact of the business, it is recommended that their scope is supposed to be extended to require social and environmental impact assessment.

Understanding The Business Environment Term Paper

Understanding The Business Environment - Term Paper Example The capital comes from the treasury or the local rates. The public limited aim at providing services to the nation, and in case of profit generation, it has handed hack to the government or the local authority. The government appoints a minister to take responsibility. The minister then appoints a chairperson and the board of directors who respond to daily activities in running the industry. The chairperson and board of directors then give an annual report to the minister who presents it to the parliament for public debate. The information then published for public. The private limited companies are businesses owned by private people. The owners do control and management. They are the directors and managers. The private people raise capital, and their aim is to generate profit. The profit or losses made equally distributed according to the number of shares one own in the company. The voluntary group is an organization consisting of people who offer unpaid services to the organization . Its resources (cash, labor and services) obtained through voluntary means. The co-operatives form when a group works together to accomplish a common need. They are significant status in the tax law in most countries. The co-operatives assist members with their primary business e.g. selling of milk or other farm products. Type of organization Examples- Name of organization and why it exist What sector does this organization operate within Public limited company CDC – A centre for Disease Control ministry of Public health Private limited company Fly Emirates Transport industry Voluntary DISABLED AMERICAN VETERANS AUXILLARY- facilitate medical treatment of veterans Medical industry Co-operatives BONGARDS’ CREAMERIES CO-OPERATIVE Milk processing industry US CDC; CENTRE FOR DISEASE CONTROL CDC is a division of the public health systems and workforce development based in Atlanta, Georgia USA. Its strategy is to work with partners with the aim of strengthening public health systems and the public health workforce. It applies public health sciences and practices to demonstrate health impact. Vision, mission and goals Its vision is to enable countries worldwide have efficient and equitable public health systems to protect communities. It also visualizes the enablement of persons to live productive and healthy lives. It has a mission of working with Ministries of Health (MOH), and various health partners to strengthen public health systems. They collaborate to develop the workforce using innovative programs and science. The aim at building sustainable capacity maintaining strong public health systems and responding to the changing and increasing health challenges. They have a mission of coming together with public health partners to diversify global health problems, practices experiences and resources. (Allison, M & Kaye J 2001) Their main goal is to use system development programs to help the Ministry Of Health worldwide build strong, effective and sust ainable programs. The system development programs include; FETP, Field Epidemiology Training Programs, Field Epidemiology, Laboratory and Training Programs (FELTP), Global Public Health information program (GPHIP),Sustainable Management Development Program (SMDP) and the Integrated Disease Surveillance and Response (IDSR). They thus help the MOH to improve public health systems locally, regionally and nationally. The internal and external stakeholders of the CDC Stakeholders include persons or organizations invested in a program. They are interest in the results and evaluation of the program where their interests and requirements considered and budgeted for in the planning process. These

Law of Evidence. write of silence Essay Example | Topics and Well Written Essays - 1250 words

Law of Evidence. write of silence - Essay Example However, as observed in R v Beckles, such inferences cannot be used to establish guilt. The House of Lords in R v Webber of 2004 that pursuant to Section 34 facts may include any fact that is an issue at the trial and tendered by the defendant in his or her defence. Moreover, facts will include any explanation or fact that the defendant would have logically raised at an earlier stage of the criminal proceedings. According to the ruling in R v Ali, the only recourse a defendant may have is to either deny culpability at the police station or to prepare a statement setting out his or her defence so as to preserve the right to raise the defence at trial. The right to a fair trial guaranteed by Article 6 of the ECHR demands however, that prosecutors bear the burden of proof. It was ruled in R v Condron that directions to the jury must be given with caution emphasizing the right to silence. The Judicial Studies Board established 6 points intended to ensure that adverse inferences contained in section 34 do not contradict Article 6. The 6 points correspond with the 6 requirements for adverse inferences as laid doing in R v Argent and are: There must be proceedings. Failure to mention a fact must predate the charge or when being charged. The omission must have occurred while being questioned under caution. The questions must have related to determining who committed the offence. The omitted fact must be one subsequently used in defence at the trial. The omitted fact must be one that accused was logically expected to mention. The courts have tried to set limits to what amounts as a new fact and to preserve the defendant’s right to remain silent. For example in R v McGarry, the defendant was charged with causing grievous bodily harm. In a written statement taken by the police, the defendant claimed that he acted in self-defence and did not answer police questions. At his trial, the defendant testified to facts substantiating and building on his claim of self-defen ce. The trial judge said that he was not inviting the jury to draw an adverse inference since D had not raised a new fact but did state that it was up to the jury to determine whether or not they wished to draw an adverse inference. The defendant was convicted and appealed. The appeal was allowed because the trial judge had a duty to direct the jury that they were not at liberty to hold the defendant’s failure to answer police questions since he did not rely on a new fact. R v B (MT) partially deals with circumstances in which a defendant may not be aware that a new fact may provide him or her with a defence. In this case the defendant was accused of sexual raping his stepdaughter, a minor and another girl under the age of 16. When questioned by the police, the defendant could not identify a motive for the girls to lie. However, at trial, his stepdaughter testified that she resented the defendant and did not want him to live with her mother. The defendant used this informatio n in his defence. The trial judge directed the jury that they could draw an adverse inference from this if they felt that it was reasonable for the defendant to raise the issue of motive while being questioned by police. The defendant was convicted and upon appeal, the Court of Appeal allowed the appeal on the grounds that the fact relied on was not a fact that the defendant could have known when questioned by the police. Likewise in Murray v UK before the European Court of Human Rights it was held

Understanding The Business Environment Term Paper

Understanding The Business Environment - Term Paper Example The capital comes from the treasury or the local rates. The public limited aim at providing services to the nation, and in case of profit generation, it has handed hack to the government or the local authority. The government appoints a minister to take responsibility. The minister then appoints a chairperson and the board of directors who respond to daily activities in running the industry. The chairperson and board of directors then give an annual report to the minister who presents it to the parliament for public debate. The information then published for public. The private limited companies are businesses owned by private people. The owners do control and management. They are the directors and managers. The private people raise capital, and their aim is to generate profit. The profit or losses made equally distributed according to the number of shares one own in the company. The voluntary group is an organization consisting of people who offer unpaid services to the organization . Its resources (cash, labor and services) obtained through voluntary means. The co-operatives form when a group works together to accomplish a common need. They are significant status in the tax law in most countries. The co-operatives assist members with their primary business e.g. selling of milk or other farm products. Type of organization Examples- Name of organization and why it exist What sector does this organization operate within Public limited company CDC – A centre for Disease Control ministry of Public health Private limited company Fly Emirates Transport industry Voluntary DISABLED AMERICAN VETERANS AUXILLARY- facilitate medical treatment of veterans Medical industry Co-operatives BONGARDS’ CREAMERIES CO-OPERATIVE Milk processing industry US CDC; CENTRE FOR DISEASE CONTROL CDC is a division of the public health systems and workforce development based in Atlanta, Georgia USA. Its strategy is to work with partners with the aim of strengthening public health systems and the public health workforce. It applies public health sciences and practices to demonstrate health impact. Vision, mission and goals Its vision is to enable countries worldwide have efficient and equitable public health systems to protect communities. It also visualizes the enablement of persons to live productive and healthy lives. It has a mission of working with Ministries of Health (MOH), and various health partners to strengthen public health systems. They collaborate to develop the workforce using innovative programs and science. The aim at building sustainable capacity maintaining strong public health systems and responding to the changing and increasing health challenges. They have a mission of coming together with public health partners to diversify global health problems, practices experiences and resources. (Allison, M & Kaye J 2001) Their main goal is to use system development programs to help the Ministry Of Health worldwide build strong, effective and sust ainable programs. The system development programs include; FETP, Field Epidemiology Training Programs, Field Epidemiology, Laboratory and Training Programs (FELTP), Global Public Health information program (GPHIP),Sustainable Management Development Program (SMDP) and the Integrated Disease Surveillance and Response (IDSR). They thus help the MOH to improve public health systems locally, regionally and nationally. The internal and external stakeholders of the CDC Stakeholders include persons or organizations invested in a program. They are interest in the results and evaluation of the program where their interests and requirements considered and budgeted for in the planning process. These

The one who is in the sun Essay Example for Free

The one who is in the sun Essay The manipulation of the regular repetition creates contrast and opposition, which produces emotions and makes the story appealing. The contrast also tends to unsettle the readers and make them pay more attention. The rhythm of the story is manipulated by excluding proverbs from the end of the story to prevent monotony and predictability and makes it more memorable. This interruption of the rhythm creates aesthetic tension by means of the fulfillment and defiance of the readers expectations. The repetition of the proverbs creates a pattern, but the pattern is interrupted by the omission of the proverbs. There are also other elements repeated throughout Zabi Naka. The themes of evil, poverty, death, stealing, fighting and righteousness are recurring. The repetition of these components gets vital concepts before the reader more than once and emphasizes the key ideas of this piece of writing. These themes are repeated to accentuate the meaning of the story. The repetition of both the proverbs and the themes in the story creates layers. The layering gives depth and texture to the story. Having the obvious story, then other themes and issues woven in creates the layering. The layering is an embellishment taking something and adding a dimension to it. This tends to instill a sense of wholeness in the reader. The layers of the story make it complete. I believe that interruption also makes the story extraordinary. The proverbs themselves are an interruption of the storyline. The repetition of the pattern of the story, then a proverb, then back to the story is also interrupted by the absence of the proverbs in the second part of the story when the war occurs. The rhythm of the story is interrupted by the lack of proverbs. This constant disturbance throughout the story creates a multitude of layers, making the story more whole. The combination of interruption, layering, repetition, and proverbs make Zabi Naka the incredible work of art that it is. They add meaning and emotion to the story and also make it complete. These artistic characteristics have thoroughly deepened the story and made it interesting.

Gender Constructions in The Hours

Gender Constructions in The Hours TITLE: Gender Constructions in The Hours (Daldry. S, 2002) AIM/OBJECTIVE: To illustrate gender as being a social construction rather than a biologically determined entity and to evaluate how heteronormativity influences the several layers of identity. METHODOLOGY Drawing upon the evolution of gender construction in The Hours, I intend to use feminist theory and the social construction on gender to obtain a preview of a society devoid of the restrictions in terms of heteronormativity. LITERATURE REVIEW: Judith Butler’s (1988) ‘Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory’ asserts that â€Å"gender identity is a performative accomplishment compelled by social sanction and taboo†. Butler (1988) argues that gender is constituted through a series of â€Å"acts† that have been actualized by individuals in repetition over time. She further argues that gender is something that is not a concrete â€Å"social fiction† but is constantly being reproduced, shifted and moved. In short, she theorizes that gender is not a set of concrete identities, but it is always reproduced over and over by the body. â€Å"One is not born, but rather becomes, a woman.† This emblematic quote of Simone de Beauvoir in ‘The Second Sex’ (1949) demonstrates that â€Å"no biological, psychological, or economic fate determines the figure that the human female presents in society†¦Ã¢â‚¬  Gender must be understood as a process of taking on or realizing possibilities, a process of interpreting the body and giving it a cultural form. In other words, to be a woman is to become a woman through an active practice of appropriating, interpreting and reinterpreting received cultural possibilities. In so doing, women are relegated to the category ‘the other’ through cultural construction, which Butler identifies as being the key to women’s oppression. Gender identity, advocates Simone de Beauvoir, â€Å"rests on unstable bedrock of human invention.† Drawing on Laura Mulvey’s work ‘Visual Pleasure and Narrative Cinema’, Anneke Smelik’s ‘Feminist Film Theory’ (1999) indicates a prolific diversity which echoes the multitude of voices, manifold points of view, and cinematic styles and genres that indicate womens triumphant endeavor for self-representation on the silver screen. However, a restriction such as the reproduction of a male/female dichotomy is questioned and the need for a deconstruction is expressed. The renewed interest in the sex/gender distinction that Gayle Rubin had introduced in 1975 is given much importance. The term gender usually seemed to point to a more lucid distinction between anatomy (sex) and social construction (gender), and equally between sexual practice and gender identity. This distinction contributes to the critical appreciation of movies where gender constructions are depicted as being unusual. BACKGROUND: Society has been, most of the time, portrayed as being a patriarchal one. One representation that can be recurrently seen in texts is that man is the norm, and woman is ‘the other’, or as stated by Culler (2007), â€Å"Men have aligned the opposition male/female with rational/emotional, serious/frivolous, or reflective/spontaneous†. In such a scenario, the woman feels restricted to particular roles dictated by men and at some point, she feels stifled by the various impositions levied upon her. This research topic gives a discerning stance of the struggle of women of the 20th century who have been constantly seeking for more meaningful lives. In order to question the whole issue of gender construction as well as the hierarchy of the opposing attributes, this tale of women will be considered. These heroines of everyday lives will be analysed in terms of the construction of a patriarchal society as they make heart breaking and defining choices that eventually influence their whole life. INTRODUCTION: The Hours is a 2002 drama film – a screenplay by David Hare based on the 1999 Pulitzer Prize-winning novel of the same title by Michael Cunningham. Starring Meryl Streep, Nicole Kidman and Julianne Moore, the movie relates the life of women of three different generations, who are interconnected by Virginia Woolf’s novel, Mrs. Dalloway. The character of Virginia Woolf, magnificently portrayed by Nicole Kidman, lives against her will in Richmond, England, 1922. Laura Brown is a pregnant housewife living in 1951 in Los Angeles. Played by Julianne Moore, she feels suffocated in her so-called â€Å"perfect life†. Lastly, Clarissa Vaughan, expertly acted by Meryl Streep, is a contemporary version of Mrs. Dalloway and leads a somewhat happy life with her homosexual partner, Sally, in New York City, 2001. DISCUSSION: In The Hours, Virginia Woolf is seen to be delving into her imagination to create Mrs. Dalloway – a woman who, like herself, embodies liberal thoughts, but nonetheless, enjoys a more expansive freedom in her lifestyle. Through her creation, she craftily plays on the notion of what gender identity should represent. This idea is once again explored through Mrs. Brown, who engages herself in reading the novel Mrs. Dalloway in her moments of solitude and depression. Virginia Woolf thus gives birth to Mrs. Dalloway, who in turn, becomes a source of inspiration to Laura Brown. Woolf turns many cultural gender stereotypes and generalizations on their heads, and seems to do so more in an effort to expose how gender is a socially constructed concept rather than promoting an exclusively feminist agenda. The character of Clarissa is yet another portrayal of construction related to gender identity. The contrast between Mrs. Dalloway in the novel and Clarissa Vaughan in the movie shows how the process of deconstruction occurred over time. The fact that Mrs. Dalloway could only be allowed to reminisce about her love for Sally shows that there are some limitations for her to live her femininity and sexuality as compared to Clarissa who is in a committed relationship with her homosexual lover. The construction of identity as portrayed in Clarissa goes beyond sexual orientation and constricted roles for women. It focuses on how the concept of the self develops in a society defined by social norms. CONCLUSION: With each upcoming generation, the characters demonstrate that they are given license to broaden their horizons. This evolving pattern shows a deconstruction of heteronormativity and at the same time does not restrict women to being portrayed as the other. BIBLIOGRAPHY: Ahmed, S. (2010). ‘Killing Joy: Feminism and the History of Happiness’. The University of Chicago Press. Vol. 35, No. 3, pp. 571-594 Beauvior, S. D. (1949). ‘The Second Sex’, trans. and ed. H. M. Parshley. New York: Knoph. Butler, J. (1986). Sex and Gender in Simone de Beauvoirs Second Sex .Witness to a century. 72 (3), 40-42. Butler, J. (1988). ‘Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory’. The John Hopkins University Press: Theatre Journal, Vol. 40, No. 4 (Dec., 1988), pp. 519-531 Butler, J. (1988). ‘Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory’. The John Hopkins University Press: Theatre Journal, Vol. 40, No. 4 (Dec., 1988), pp. 519-531 Butler, J. (1990) ‘Gender Trouble: Feminism and the Subversion of Identity’. London and New York: Routledge. Butler, J. (1993). ‘Bodies that Matter: On the Discursive Limits of â€Å"Sex†. London and New York: Routledge. Cott, F. N. (1987). ‘The Grounding of Modern Feminism.’ Yale University Press Culler, J. D. (2007). ‘On Deconstructionà ¢Ã¢â€š ¬Ã‚ ¬: Theory and Criticism After Structuralismà ¢Ã¢â€š ¬Ã‚ ¬Ã¢â‚¬â„¢. Cornell University Press.à ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬Ãƒ ¢Ã¢â€š ¬Ã‚ ¬ Daldry. S (Director).The Hours[Motion picture]. Miramax Films, 2002. Fausto-Sterling, A. (2000). ‘Sexing the Body: Gender Politics and the Construction of Sexuality’. New York: Basic Books. Flax, J. (1990). ‘Postmodernism and gender relations in feminist theory’. In Nicholson, L. J., editor, Feminism/Postmdernism. London and New York: Routeldge, 39-62. Foucault, M. (1961). ‘Madness and Civilization: A History of Insanity in the Age of Reason.’ Howard, R., translator. New York: Pantheon Books. Hjersing, C (2009).‘Representations of Clarissa and Septimus in Virginia Woolf’s Mrs Dalloway A deconstructive approach combined with aspects of feminist and psychoanalytical criticism’ Molyneux, M. (1986).‘No God, No Boss, No Husband: Anarchist Feminism in Nineteenth-Century Argentina.’ Sage Publications. Latin American Perspectives, Vol. 13, No. 1, Latin Americas Nineteenth-Century History, pp. 119-145 Motashery, I. (2012). ‘A Feminist Reading of Virginia Woolf’s Mrs Dalloway’. International Journal of Applied Linguistics English Literature. Vol. 1 No. 3. Offen, K. (1988). ‘Defining Feminism: A Comparative Historical Approach’The University of Chicago Press. Vol. 14, No. 1, pp. 119-157 Probyn, E. (1993). ‘Sexing the Self: Gendered Positions in Cultural Studies’. London and New York: Routledge. Shihada, M, I. ‘A Feminist Perspective of Virginia Woolf’s Selected Novels: Mrs. Dalloway and To the Lighthouse.’ Shor, M. et. al (1999).‘Contemporary Feminism: Art Practice, Theory, and ActivismAn Intergenerational Perspective’. College Art Association. Art Journal, Vol. 58, No. 4, pp. 8-29 Smelik, A. (1999). ‘Feminist film theory.’ Warner, M. (1991). ‘Introduction: Fear of a Queer Planet’. Duke University Press. Social Text, No. 29 (1991), pp. 3-17

The Second Sex by Simone de Beauvoir Essay -- Essays on The Second Sex

Simone de Beauvoir, in her 1949 text The Second Sex, examines the problems faced by women in Western society. She argues that women are subjugated, oppressed, and made to be inferior to males – simply by virtue of the fact that they are women. She notes that men define their own world, and women are merely meant to live in it. She sees women as unable to change the world like men can, unable to live their lives freely as men can, and, tragically, mostly unaware of their own oppression. In The Second Sex, de Beauvoir describes the subjugation of woman, defines a method for her liberation, and recommends strategies for this liberation that still have not been implemented today. De Beauvoir, in attempting to define the subjugation experienced by woman, notes that women lag behind other oppressed groups of her epoch, like Jews and blacks. She argues that women are behind in terms of civil rights mainly because they have not identified that they are indeed being oppressed, despite their lack of social and professional status. De Beauvoir writes that â€Å"the epithet of female has the sound of an insult,† (1) meaning that women experience discrimination and social inequity. Further, she asserts that man is responsible for the construction of a world based upon his values, his norms, and his capabilities. She is unsurprised by the fact that woman has achieved comparatively less – in a male-oriented culture, how could anyone possibly expect woman to accomplish as much as man? This societal commentary transcends legal status. The acquisition of civil rights will not be enough to right the wrongs perpetrated upon woman as a whole, according to de Beauvoir. Liberalism, therefore, is also insufficient to address the problems wom... ...ated socialism as a method of societal structure based on reciprocity, but our current system of capitalism fosters aggression and competition instead. The quest for material possessions and wealth as signs of power and success leads to endless competition. This runs counter to the induction of reciprocity into our society and therefore means that reciprocal relationships, defined by de Beauvoir as requisite to the emancipation of woman, are not the culturally accepted norm. To truly state that de Beauvoir’s vision has been realized, Western society would need to entirely scrap its capitalist system and redefine itself in terms of community, reciprocity, and sharing. This has definitely not happened yet, and until it does the world will continue to be defined on male terms. Works Cited Beauvoir, Simone De. The Second Sex;. New York: Knopf, 1953. Print.

Faulkners Light in August - Themes :: Light August Essays

Light in August - Themes    1. RACISM    The Southern concern with racial identity is one of Light in August's central themes. When people think that Joe Christmas has even a trace of black ancestry, they treat him completely differently from the way they treat white people. Many of the characters in Light in August seem twisted by their preoccupation with race. Joe Christmas, Joanna Burden, Nathaniel Burden, Doc Hines, and, ultimately, Percy Grimm are among these. But even many of the characters who don't share this mania assume that treating blacks inhumanly is acceptable. The Jefferson sheriff, Watt Kennedy, seems a decent man, yet he whips a randomly chosen black in an interrogation that was unnecessary in the first place.    2. THE SOUTHERN PAST       Two of Light in August's five major characters live in the shadow of their dead ancestors. But you could interpret their relation to these forebears in different ways. On the one hand, you could point to a pattern of decline and say that the present doesn't live up to the heroic days of yesteryear. On the other hand, you could say that the problems of the present come from a failure to shake off the burdensome grip of the past. Here is how you could argue each point of view.    a. The Heroic Past    Gail Hightower's grandfather was a robust lover of life, and his father was a helper of his fellow human beings. But Hightower fails both his wife and his congregation and spends the rest of his life cut off from other people.    Though Joanna Burden's forefathers were not originally from the South, their emigration to Jefferson makes them part of the Souths history too. And like Gail Hightower, Joanna compares badly to both her father and grandfather. They were rebellious wanderers and vigorous family men. She spends most of her time in her house, feels homesick whenever she leaves Jefferson, and never marries or has children.    b. The Burdensome Past    Gail Hightower's problems stem from his obsession with his grandfather, who was not even worth this worship. After all, he died stealing chickens. Likewise, Joanna Burden is the victim of the stern religion and patronizing racism that her father taught her and that he learned from his father before him.

About Specific Moments

Eng 119 10/16/12 My life tragedy I remember that cold November like it was yesterday. It was so cold that I felt the breeze going through my skin. I remember waking up to my mom and sisters crying. I can tell that my father was trying his hardest not to cry. I’ve always felt safe at home, it’s a place to feel peace and joy with family but this was different. I just wanted everything to be like the normal days where my mom fusses at me for not waking up earlier for school or forgetting to do the laundry. Everybody was so sad but trying there hardest to be strong in front of me.Everybody surrounded me as I was getting ready, it seemed like they were following my every move. I tried my hardest not to cry or just fall apart because I know that it would only make things worse and break everyone into pieces. I had to remain strong and remember that I’ve been through this before and that God is always by my side. Sitting on the dining table was pointless; the food was j ust there for show. Nobody seemed to have an appetite. It seemed as if they were the one going through this tragedy but I can’t blame them. If anything happened to them, I would feel the same way.I had left my house a billion times before but that morning was by far one of the hardest things I’ve ever done in my life. I kissed my sisters goodbye and told them to be strong for me and regardless of what happens, that they’ll always be in my heart. I have 3 sisters and not seeing there beautiful faces again would destroy me. Getting into the car was like moving to a new house. It was so quiet driving to the hospital with my parents. It was the longest drive of my life although I didn’t want the drive to end. I had to be strong though and remember that I am no longer 4 years old anymore.I was only 17 and I already been through this life trial before. Everything seemed to be playing in slow motion. I started to remember every childhood memory I had. I remember ed the first time I went to the zoo with my family and I fell and scraped hurt my knee and had to get stiches. I was terrified and so scared about getting stiches but nothing can possibly be worse than this life trial. I remembered the first day my baby sister was born. I remembered the going on a trip to Niagara Falls and how much fun I had with my family and friends. A million memories and thoughts were running through my mind.My mother sighed once we arrived to the hospital, but this wasn’t a sigh of relief, this was more like pure sadness. Before walking into the hospital, I took one last glance at the world outside. Walking into the Oakwood hospital, I was able to recall every memory I had within every step I took. I was asked to sit down for 5 minutes till they call me up. My mom was telling me a story about my grandma and how she also had an open heart surgery. She told me that she had an open heart surgery 7 times in her life and survived all 7 but she was a very heav y smoker and that’s how she passed away.She had recently passed away from cancer. She said I reminded her of my grandma because she was a very strong woman. The nurse called my name and told me that the doctor was ready for me. I was getting closer and closer to the operating room. At the same time, I was so focused on everything. I could stare at the plant that I was walking by for hours and hours. The more closer I got to the operating room, the more scared and freaked out I was getting. my lips were so dry because the hospital told me I wasn’t supposed to eat anything. I felt choked up. I could hear a baby crying after the mother giving birth.That made me smile. To think God takes life but brings another life to the world. That’s just the way life is. I got to the operating room and changed into the hospital gown. I always hated the hospital gowns. There were closed from the front but open from the back. It just didn’t make sense to me. Sitting on the hospital bed, I was so nervous. The nurse even noticed and gave me some medication to calm down my nerves. I always wanted to be a nurse when I grow up. I started to think if I can ever actually fulfill that dream, but I had faith in God and knew he wouldn’t let me down.The nurse told me she can see me as being a nurse because I love to help people. The medication didn’t seem to work so well especially when you’re almost going to have an open heart surgery. I couldn’t believe this was actually happening to me again. It felt like a dream, I dream that I wanted to just wake up from so badly. I started to imagine myself sitting home watching TV like a normal teenage girl with nothing to worry about but homework and drama. I knew I had no way out of this though. It’s now or never, I thought to myself. My father held my hand and said, â€Å"come on sweetie, you can do this†.I kissed my parents goodbye and couldn’t help but cry. I started t o think to myself that this may be the last time that I’ll ever see there beautiful faces. I trusted my surgeon with my life because this isn’t the first time he has done this to me before. He told me that he always loved seeing my face vbecause I was all smiles but this was such a fake smile I had on. My anesthesiologist gave me some medicine and told me to count to ten. â€Å"One, two, three, four, five, then I was gone. The next thing you know I was waking up to my families faces.My mom was sitting by me holding my hand. I thought I was dreaming. Everything was so blurry but I can still see a little. I had survived. I survived an open heart surgery for the second time. After that moment, I knew that I was going to appreciate every minute of my life. There isn’t a day that goes by that I don’t remind myself of the strength I have within me. My seven inch scar reminds me that I am alive and strong. I feel like I'm capable of giving a lot to the world. I appreciate my family and friends even more because I don’t know where I would be without them.

Simplification of Switching Function

EEN1036 Digital Logic Design Chapter 4 part I Simplification of Switching Function 1 Objective s s s s Simplifying logic circuit Minimization using Karnaugh map Using Karnaugh map to obtain simplified SOP and POS expression Five-variable Karnaugh map 2 Simplifying Logic Circuits †¢ †¢ †¢ A A Boolean expression for a logic circuit may be reduced to a simpler form The simplified expression can then be used to implement a circuit equivalent to the original circuit Consider the following example: B C A B C + A BC Y AB C + AB C Y = A B C + A BC + AB C + AB C 3 Continue †¦Checking for common factor: Y = A B C + A BC + AB C + AB C = A C ( B + B ) + AB (C + C ) Reduce the complement pairs to ‘1’ Y = A C ( B + B ) + AB (C + C ) = A C + AB Draw the circuit based on the simplified expression A B C Y 4 Continue †¦ †¢ A Consider another logic circuit: B C Y Y = C( A + B + C ) + A + C Convert to SOP expression: Y = C( A + B + C ) + A + C = AC + B C + AC C hecking for common factor: Y = A(C + C ) + B C = A + BC 5 Continue †¦ †¢ †¢ Simplification of logic circuit algebraically is not always an easy task The following two steps might be useful: i.The original expression is convert into the SOP form by repeated application of DeMorgan’s theorems and multiplication of terms ii. The product terms are then checked for common factors, and factoring is performed wherever possible 6 Continue †¦ †¢ Consider the truth table below: A 0 0 0 0 1 B 0 0 1 1 0 C 0 1 0 1 0 Y 0 0 1 0 0 Minterm Boolean expression: Simplify to yield: Y = A BC + ABC + AB C Y = BC ( A + A) + AB C = BC + AB C 1 0 1 1 1 1 0 1 1 1 1 0 †¢ If minterms are only differed by one bit, they can be simplified, e. g.A BC & ABC 7 Continue †¦ †¢ More example: A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 1 1 0 0 1 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Minterms 1 and 5, 2 and 6 are only differ by one bit: Y = B C ( A + A) + BC ( A + A) = BC + B C A B C Y 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Checking and factoring minterms differed by only by one bit: Y = A C ( B + B ) + AC ( B + B ) = A C + AC = C ( A + A) =C 8 Continue †¦ †¢ †¢ †¢ Though truth table can help us to detect minterms which are only differed by one bit, it is not arranged in a proper way A Karnaugh map (K-map) is a tool, which help us to detect and simplify minterms graphically It is a rearrangement of the truth table where each adjacent cell is only differed by one bit By looping adjacent minterms, it is similar to grouping the minterms with a single bit difference on the truth table 9 Karnaugh Map †¢ †¢ A K-map is just a rearrangement of truth table, so that minterms with a single-bit difference can be detected easily Figure below shows 4 possible arrangement of 3-variable K-map A BC 0 0 01 1 11 3 10 2 C AB 00 0 01 2 11 6 10 4 0 1 4 5 7 6 0 1 1 3 7 5 AB C 0 0 1 1 BC A 0 0 1 4 00 01 2 3 00 01 1 5 11 6 7 11 3 7 10 4 5 10 2 6 10 Continue †¦ †¢ Figure below show two possible arrangement of 4variable K-map CD AB 00 0 01 1 11 3 10 2 AB 00 CD 01 4 11 12 10 8 00 01 4 5 7 6 00 0 01 1 5 13 9 11 12 13 15 14 11 3 7 15 11 10 8 9 11 10 10 2 6 14 10 †¢ Notice that the K-map is labeled so that horizontally and vertically adjacent cells differ only by one bit. 11 Continue †¦ †¢ The K-map for both SOP and POS form are shown below: C D C D CD C D AB AB AB 0 1 3 2C+D C+ D C + D C +D A +B 0 1 3 2 4 5 7 6 A+B A+B A +B 4 5 7 6 12 13 15 14 12 13 15 14 AB 8 9 11 10 8 9 11 10 SOP form (minterm) POS form (maxterm) †¢ †¢ The simplified SOP expression can be obtained by properly combining those adjacent cells which contains ‘1’ This process of combining adjacent minterms is known as 12 looping Continue †¦ †¢ †¢ Each loop of minterms will form a group which can be represented by a product term When a variable appears in both complemented and uncomplemented form within a group, that variable is eliminated from the product term C D C D CD C DAB AB AB AB 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 group 2 group 1: C D( AB + AB ) = AC D group 2: AB(C D + CD ) = ABD Simplified SOP expression: Y = AC D + ABD 13 group 1 Continue †¦ †¢ Consider another K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 group 1 C D C D CD C D AB AB AB AB 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 14 group 1: ( A B + AB )(C D + CD ) = BD Simplified SOP expression: Y = BD group 1: C D ( A B + A B + AB + AB ) = C D Simplified SOP expression: Y = CD group 1 From truth table to K-map †¢ The content of each cell can be directly plot on the Kmap according to the truth table Consider the following example: 0 1 2 3 4 5 6 7 A 0 0 0 0 1 1 1 1 B C Y 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 B C B C BC B C A A 1 0 1 1 0 3 1 2 0 4 0 5 0 7 1 6 AB BC Simplif ied SOP expression: Y = A B + BC 15 Continue †¦ †¢ Consider the following 4-variable K-map A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C D Y 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 C D C D CD C D AB AB AB 0 0 0 1 1 1 0 1 0 0 1 0 3 0 0 0 ACD 2 4 5 7 6 12 13 15 14 AB 0 8 9 11 0 10 ABD Simplified SOP expression: Y = A C D + ABD 16 Continue †¦ †¢ Some guidelines: i. Construct K-map and fill it according to the truth table ii. Only loop cells in the power of 2, i. e. 2 cells, 4 cells, 8 cells and so on iii. Always start by looping the isolated minterms iv. Look for minterms which are adjacent to only one minterm and loop them together v. Proceed on to loop the largest possible groups, from eight minterms (octet), 4 minterms (quad) to 2 minterms (pair) vi.Obtain the product term for each group vii. The sum of these product terms will be the simplified SOP expression 17 Continue †¦ Exam ple: a. Obtain the simplify SOP expression for the truth table: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Y 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 C D C D CD C D AB AB AB AB A B CD 0 0 0 0 0 0 1 1 0 1 0 1 1 3 1 0 0 0 2 4 5 7 6 12 13 15 14 8 9 1 11 10 BD ACD Simplified SOP expression:Y = A B CD + ACD + BD 18 Continue †¦ b. Obtain the simplify SOP expression from the K-map: ACD C D C D CD C D AB AB ABC 0 0 1 0 1 1 1 0 0 1 1 1 ACD 0 1 0 0 A BC AB AB Simplified SOP expression: Y = A C D + A BC + ACD + ABC 19 Continue †¦ c. Obtain the simplify SOP expression from the K-map: alternative solution: C D C D CD C D AB AB AB C D C D CD C D AB A CD 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 AB D 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 B CD A CD AB AB AB AB Y = A CD + AC D + AB D Y = A CD + AC D + B CD 20 General Terminology for Logic Minimization †¢ †¢ Here, we define four terms to provide the basis for general function minimization techniques These terms are implicant, prime implicant, essential prime implicant and cover We refer to the K-map below in explaining each term B C B C BC B C A A 1 0 1 1 3 2 1 4 1 5 1 7 6 †¢ †¢ An implicant is a product term that could be used to cover minterms of the function In the K-map above, there are 11 implicants: 5 minterms: {A B C , A BC , AB C , AB C , ABC} 5 group of two adjacent minterms: {AB , AC , A C , B C , BC} 1 group of four adjacent minterms:{C} 21 Continue †¦ †¢ †¢ †¢ A prime implicant is an implicant that is not part of any other mplicant In the K-map, there are two prime implicant: C and AB An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicants Prime implicant AB is essential as it is the only prime implicant that covers minterm 4 Prime implicant C is also essential as it is the onl y prime implicant that covers minterm 1, 3 and 7 A cover of a function is a set of prime implicants for which each minterm of the function is contained in (covered by) at least one prime implicant All essential prime implicants must be used in any cover of a function 22 †¢ †¢ †¢ Continue †¦ †¢ †¢ For the K-map above, the set of implicants { AB , C} represents a cover of the function A minimum cover contains the minimum number of prime implicants which contains all minterm in the function Consider the 4-variable K-map below: C D C D CD C D AB AB AB AB 1 1 Prime implicants †¢ C D C D CD C D AB AB AB 1 1 1 1 1 1 1 1 1 AB AB AB AB C D C D CD C D 1 1 1 1 Minimum cover 1 1 1 1 1 1 1 1 1 1 1 1 AB Essential prime implicants 23 Continue †¦ †¢ Consider another K-map C D C D CD C D AB AB AB AB 1 1 1 1 1 1 1 Prime implicants C D C D CD C D AB 1 1 1 1 1 1 1 1 1 1 AB AB 1 ABEssential prime implicants (minimum cover) 24 Don’t Care Conditions â₠¬ ¢ †¢ †¢ †¢ Some logic circuit will have certain input conditions whereby the output is unspecified This is usually because these input conditions would never occur In other words, we â€Å"don’t care† whether the output is HIGH or LOW Consider the following example: An air conditioning system has two inputs, C and H: – C will be ‘1’ if temperature is too cold (below 15 °C) Otherwise, it will be ‘0’ – H will be ‘1’ if temperature is too hot (above 25 °C) Otherwise, it will be ‘0’ – Output Y will be ‘1’ if temperature is too cold or too hot.If the temperature is acceptable, Y will be ‘0’ 25 Continue †¦ As there are two inputs, there are 4 possible logical conditions: C 0 0 1 1 H 0 1 0 1 Y 0 1 1 X meaning just nice too hot too cold ? Input condition C = 1, H = 1 has no real meaning, as it is impossible to be too hot and too cold at the same time We put a ‘X’ at the output corresponds to this input condition as this input condition cannot occur 26 K-map and Don’t Care Term †¢ Don’t care term, ‘X’ can be treated as ‘0’ or ‘1’ since they cannot occur In K-map, we can choose the don’t care term as ‘0’ or ‘1’ to our advantage A B C D Y 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 X 0 1 0 0 1 0 1 0 1 X 0 1 1 0 0 0 1 1 1 X 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 X 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 X C D C D CD C D AB AB AB 0 1 1 0 1 X 1 0 X X X X 0 0 1 0 AB Simplified Boolean expression: Y = AB + BC + A D 27 More examples †¦ C D C D CD C D AB AB AB AB C D C D CD C D AB AB AB AB 1 1 X 1 0 1 X 1 0 0 X X 0 1 X X 1 0 X 1 0 0 X 0 0 0 X X 1 X X Y = C D + BC + BD + A C D C D CD C D AB AB AB Y = B D + CD C D C D CD C D AB AB AB 0 0 1 0 1 X 1 1 0 1 X 0 0 0 0 0 1 1 X 0 1 X X 1 0 1 X X 0 0 X X 28 AB AB Y = ABC + C D + BD Y = A C + BD + AD Plo tting function in Canonical Form †¢ Logic function may be expressed in many forms, ranging from simple SOP/POS expression to more complex expressions However, each of them has a unique canonical SOP/POS form If a Boolean expression is expressed in canonical form, it can be readily plotted on the K-map Consider the following Boolean expression: †¢ †¢ †¢ Y = ABC + B CConvert to canonical SOP expression: Y = ABC + B C ( A + A) = ABC + A B C + AB C 29 Continue †¦ Y = ABC + A B C + AB C Plotting the canonical SOP expression onto K-map B C B C BC B C A A 1 1 0 0 BC 0 0 0 1 AC Simplified SOP expression: Y = B C + AC †¢ Consider plotting the following Boolean expression on K-map: Y = C ( A ? B) + A + B 30 Continue †¦ First, convert to SOP expression Y = C ( A ? B) + A + B = C ( AB + A B) + A B = AB C + A BC + A B (C + C ) = AB C + A BC + A B C + A B C B C B C BC B C A A 1 0 AB 1 1 1 0 BC 0 0 AC ?Y = A B + B C + A C 31Plotting K-map from SOP expression â₠¬ ¢ †¢ It is sometime too tedious to convert a Boolean expression to its canonical SOP form Consider the following Boolean expression: Y = AB (C + D )(C + D ) + A + B Convert to SOP form: Y = ( AB C + AB D )(C + D ) + A B = AB C D + AB CD + A B Convert to canonical form: Y = AB C D + AB CD + A B (C + C )( D + D) = AB C D + AB CD + ( A B C + A B C )( D + D) = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD 32 Continue †¦ Y = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD Plot the minterm on K-map: C D C D CD C D AB ABAB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB B CD BC D Simplified SOP expression: Y = B C D + B CD + A B 33 Continue †¦ †¢ †¢ †¢ †¢ †¢ Boolean expression can be plotted on to the K-map from its SOP form Product terms with four variables are the minterms and correspond to a single cell on the K-map Product term with three variables corresponds to a loop of two adjacent minterms Product term with only two variables is a quad ( a loop of four adjacent minterms) Product term with a single variable is an octet (a loop of eight adjacent minterms) 1 cell 2 cellsY = A + BC + B CD + ABCD 4 cells 8 cells 34 Continue †¦ †¢ Consider the previous example: Y = AB C D + AB CD + A B minterms 4 cells †¢ †¢ †¢ Both minterms are directly plotted on the K-map The loop which corresponds to A B is drawn on the K-map The cells inside the loops are filled with ‘1’ C D C D CD C D AB AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB C D A B CD 35 Continue †¦ †¢ Consider the following Boolean expression: Y = ( A + B )( AC + D ) Convert to SOP form: Y = AC + AD + ABC + BD Plot the SOP onto K-map C D C D CD C D AB AB AB AB AC BD C D C D CD C D AB AB ill cells in loops with ‘1' 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 36 ABC AB AB AD Continue †¦ Obtain the simplified SOP expression from K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 Simplified SOP expression: Y = AC + AD + BD 37 Continue †¦ Example: Redesign the logic circuit below from its simplified SOP expression: A B C D Z Z = ( B + D )( B + D ) + B(CD + A D ) 38 Continue †¦ Z = ( B + D )( B + D ) + B(CD + A D ) = B + D + B + D + BCD + A BD = BD + B D + BCD + A BD C D C D CD C D AB AB AB 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 AB Z = BD + B D + A B 39 Simplification of Switching Function EEN1036 Digital Logic Design Chapter 4 part I Simplification of Switching Function 1 Objective s s s s Simplifying logic circuit Minimization using Karnaugh map Using Karnaugh map to obtain simplified SOP and POS expression Five-variable Karnaugh map 2 Simplifying Logic Circuits †¢ †¢ †¢ A A Boolean expression for a logic circuit may be reduced to a simpler form The simplified expression can then be used to implement a circuit equivalent to the original circuit Consider the following example: B C A B C + A BC Y AB C + AB C Y = A B C + A BC + AB C + AB C 3 Continue †¦Checking for common factor: Y = A B C + A BC + AB C + AB C = A C ( B + B ) + AB (C + C ) Reduce the complement pairs to ‘1’ Y = A C ( B + B ) + AB (C + C ) = A C + AB Draw the circuit based on the simplified expression A B C Y 4 Continue †¦ †¢ A Consider another logic circuit: B C Y Y = C( A + B + C ) + A + C Convert to SOP expression: Y = C( A + B + C ) + A + C = AC + B C + AC C hecking for common factor: Y = A(C + C ) + B C = A + BC 5 Continue †¦ †¢ †¢ Simplification of logic circuit algebraically is not always an easy task The following two steps might be useful: i.The original expression is convert into the SOP form by repeated application of DeMorgan’s theorems and multiplication of terms ii. The product terms are then checked for common factors, and factoring is performed wherever possible 6 Continue †¦ †¢ Consider the truth table below: A 0 0 0 0 1 B 0 0 1 1 0 C 0 1 0 1 0 Y 0 0 1 0 0 Minterm Boolean expression: Simplify to yield: Y = A BC + ABC + AB C Y = BC ( A + A) + AB C = BC + AB C 1 0 1 1 1 1 0 1 1 1 1 0 †¢ If minterms are only differed by one bit, they can be simplified, e. g.A BC & ABC 7 Continue †¦ †¢ More example: A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 0 1 1 0 0 1 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Minterms 1 and 5, 2 and 6 are only differ by one bit: Y = B C ( A + A) + BC ( A + A) = BC + B C A B C Y 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 Minterm Boolean expression: Y = A B C + A BC + AB C + ABC Checking and factoring minterms differed by only by one bit: Y = A C ( B + B ) + AC ( B + B ) = A C + AC = C ( A + A) =C 8 Continue †¦ †¢ †¢ †¢ Though truth table can help us to detect minterms which are only differed by one bit, it is not arranged in a proper way A Karnaugh map (K-map) is a tool, which help us to detect and simplify minterms graphically It is a rearrangement of the truth table where each adjacent cell is only differed by one bit By looping adjacent minterms, it is similar to grouping the minterms with a single bit difference on the truth table 9 Karnaugh Map †¢ †¢ A K-map is just a rearrangement of truth table, so that minterms with a single-bit difference can be detected easily Figure below shows 4 possible arrangement of 3-variable K-map A BC 0 0 01 1 11 3 10 2 C AB 00 0 01 2 11 6 10 4 0 1 4 5 7 6 0 1 1 3 7 5 AB C 0 0 1 1 BC A 0 0 1 4 00 01 2 3 00 01 1 5 11 6 7 11 3 7 10 4 5 10 2 6 10 Continue †¦ †¢ Figure below show two possible arrangement of 4variable K-map CD AB 00 0 01 1 11 3 10 2 AB 00 CD 01 4 11 12 10 8 00 01 4 5 7 6 00 0 01 1 5 13 9 11 12 13 15 14 11 3 7 15 11 10 8 9 11 10 10 2 6 14 10 †¢ Notice that the K-map is labeled so that horizontally and vertically adjacent cells differ only by one bit. 11 Continue †¦ †¢ The K-map for both SOP and POS form are shown below: C D C D CD C D AB AB AB 0 1 3 2C+D C+ D C + D C +D A +B 0 1 3 2 4 5 7 6 A+B A+B A +B 4 5 7 6 12 13 15 14 12 13 15 14 AB 8 9 11 10 8 9 11 10 SOP form (minterm) POS form (maxterm) †¢ †¢ The simplified SOP expression can be obtained by properly combining those adjacent cells which contains ‘1’ This process of combining adjacent minterms is known as 12 looping Continue †¦ †¢ †¢ Each loop of minterms will form a group which can be represented by a product term When a variable appears in both complemented and uncomplemented form within a group, that variable is eliminated from the product term C D C D CD C DAB AB AB AB 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 group 2 group 1: C D( AB + AB ) = AC D group 2: AB(C D + CD ) = ABD Simplified SOP expression: Y = AC D + ABD 13 group 1 Continue †¦ †¢ Consider another K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 group 1 C D C D CD C D AB AB AB AB 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 14 group 1: ( A B + AB )(C D + CD ) = BD Simplified SOP expression: Y = BD group 1: C D ( A B + A B + AB + AB ) = C D Simplified SOP expression: Y = CD group 1 From truth table to K-map †¢ The content of each cell can be directly plot on the Kmap according to the truth table Consider the following example: 0 1 2 3 4 5 6 7 A 0 0 0 0 1 1 1 1 B C Y 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 B C B C BC B C A A 1 0 1 1 0 3 1 2 0 4 0 5 0 7 1 6 AB BC Simplif ied SOP expression: Y = A B + BC 15 Continue †¦ †¢ Consider the following 4-variable K-map A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C D Y 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 C D C D CD C D AB AB AB 0 0 0 1 1 1 0 1 0 0 1 0 3 0 0 0 ACD 2 4 5 7 6 12 13 15 14 AB 0 8 9 11 0 10 ABD Simplified SOP expression: Y = A C D + ABD 16 Continue †¦ †¢ Some guidelines: i. Construct K-map and fill it according to the truth table ii. Only loop cells in the power of 2, i. e. 2 cells, 4 cells, 8 cells and so on iii. Always start by looping the isolated minterms iv. Look for minterms which are adjacent to only one minterm and loop them together v. Proceed on to loop the largest possible groups, from eight minterms (octet), 4 minterms (quad) to 2 minterms (pair) vi.Obtain the product term for each group vii. The sum of these product terms will be the simplified SOP expression 17 Continue †¦ Exam ple: a. Obtain the simplify SOP expression for the truth table: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Y 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 C D C D CD C D AB AB AB AB A B CD 0 0 0 0 0 0 1 1 0 1 0 1 1 3 1 0 0 0 2 4 5 7 6 12 13 15 14 8 9 1 11 10 BD ACD Simplified SOP expression:Y = A B CD + ACD + BD 18 Continue †¦ b. Obtain the simplify SOP expression from the K-map: ACD C D C D CD C D AB AB ABC 0 0 1 0 1 1 1 0 0 1 1 1 ACD 0 1 0 0 A BC AB AB Simplified SOP expression: Y = A C D + A BC + ACD + ABC 19 Continue †¦ c. Obtain the simplify SOP expression from the K-map: alternative solution: C D C D CD C D AB AB AB C D C D CD C D AB A CD 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 AB D 0 0 0 0 AC D 0 0 1 1 1 1 0 1 0 0 0 0 B CD A CD AB AB AB AB Y = A CD + AC D + AB D Y = A CD + AC D + B CD 20 General Terminology for Logic Minimization †¢ †¢ Here, we define four terms to provide the basis for general function minimization techniques These terms are implicant, prime implicant, essential prime implicant and cover We refer to the K-map below in explaining each term B C B C BC B C A A 1 0 1 1 3 2 1 4 1 5 1 7 6 †¢ †¢ An implicant is a product term that could be used to cover minterms of the function In the K-map above, there are 11 implicants: 5 minterms: {A B C , A BC , AB C , AB C , ABC} 5 group of two adjacent minterms: {AB , AC , A C , B C , BC} 1 group of four adjacent minterms:{C} 21 Continue †¦ †¢ †¢ †¢ A prime implicant is an implicant that is not part of any other mplicant In the K-map, there are two prime implicant: C and AB An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicants Prime implicant AB is essential as it is the only prime implicant that covers minterm 4 Prime implicant C is also essential as it is the onl y prime implicant that covers minterm 1, 3 and 7 A cover of a function is a set of prime implicants for which each minterm of the function is contained in (covered by) at least one prime implicant All essential prime implicants must be used in any cover of a function 22 †¢ †¢ †¢ Continue †¦ †¢ †¢ For the K-map above, the set of implicants { AB , C} represents a cover of the function A minimum cover contains the minimum number of prime implicants which contains all minterm in the function Consider the 4-variable K-map below: C D C D CD C D AB AB AB AB 1 1 Prime implicants †¢ C D C D CD C D AB AB AB 1 1 1 1 1 1 1 1 1 AB AB AB AB C D C D CD C D 1 1 1 1 Minimum cover 1 1 1 1 1 1 1 1 1 1 1 1 AB Essential prime implicants 23 Continue †¦ †¢ Consider another K-map C D C D CD C D AB AB AB AB 1 1 1 1 1 1 1 Prime implicants C D C D CD C D AB 1 1 1 1 1 1 1 1 1 1 AB AB 1 ABEssential prime implicants (minimum cover) 24 Don’t Care Conditions â₠¬ ¢ †¢ †¢ †¢ Some logic circuit will have certain input conditions whereby the output is unspecified This is usually because these input conditions would never occur In other words, we â€Å"don’t care† whether the output is HIGH or LOW Consider the following example: An air conditioning system has two inputs, C and H: – C will be ‘1’ if temperature is too cold (below 15 °C) Otherwise, it will be ‘0’ – H will be ‘1’ if temperature is too hot (above 25 °C) Otherwise, it will be ‘0’ – Output Y will be ‘1’ if temperature is too cold or too hot.If the temperature is acceptable, Y will be ‘0’ 25 Continue †¦ As there are two inputs, there are 4 possible logical conditions: C 0 0 1 1 H 0 1 0 1 Y 0 1 1 X meaning just nice too hot too cold ? Input condition C = 1, H = 1 has no real meaning, as it is impossible to be too hot and too cold at the same time We put a ‘X’ at the output corresponds to this input condition as this input condition cannot occur 26 K-map and Don’t Care Term †¢ Don’t care term, ‘X’ can be treated as ‘0’ or ‘1’ since they cannot occur In K-map, we can choose the don’t care term as ‘0’ or ‘1’ to our advantage A B C D Y 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 X 0 1 0 0 1 0 1 0 1 X 0 1 1 0 0 0 1 1 1 X 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 X 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 X C D C D CD C D AB AB AB 0 1 1 0 1 X 1 0 X X X X 0 0 1 0 AB Simplified Boolean expression: Y = AB + BC + A D 27 More examples †¦ C D C D CD C D AB AB AB AB C D C D CD C D AB AB AB AB 1 1 X 1 0 1 X 1 0 0 X X 0 1 X X 1 0 X 1 0 0 X 0 0 0 X X 1 X X Y = C D + BC + BD + A C D C D CD C D AB AB AB Y = B D + CD C D C D CD C D AB AB AB 0 0 1 0 1 X 1 1 0 1 X 0 0 0 0 0 1 1 X 0 1 X X 1 0 1 X X 0 0 X X 28 AB AB Y = ABC + C D + BD Y = A C + BD + AD Plo tting function in Canonical Form †¢ Logic function may be expressed in many forms, ranging from simple SOP/POS expression to more complex expressions However, each of them has a unique canonical SOP/POS form If a Boolean expression is expressed in canonical form, it can be readily plotted on the K-map Consider the following Boolean expression: †¢ †¢ †¢ Y = ABC + B CConvert to canonical SOP expression: Y = ABC + B C ( A + A) = ABC + A B C + AB C 29 Continue †¦ Y = ABC + A B C + AB C Plotting the canonical SOP expression onto K-map B C B C BC B C A A 1 1 0 0 BC 0 0 0 1 AC Simplified SOP expression: Y = B C + AC †¢ Consider plotting the following Boolean expression on K-map: Y = C ( A ? B) + A + B 30 Continue †¦ First, convert to SOP expression Y = C ( A ? B) + A + B = C ( AB + A B) + A B = AB C + A BC + A B (C + C ) = AB C + A BC + A B C + A B C B C B C BC B C A A 1 0 AB 1 1 1 0 BC 0 0 AC ?Y = A B + B C + A C 31Plotting K-map from SOP expression â₠¬ ¢ †¢ It is sometime too tedious to convert a Boolean expression to its canonical SOP form Consider the following Boolean expression: Y = AB (C + D )(C + D ) + A + B Convert to SOP form: Y = ( AB C + AB D )(C + D ) + A B = AB C D + AB CD + A B Convert to canonical form: Y = AB C D + AB CD + A B (C + C )( D + D) = AB C D + AB CD + ( A B C + A B C )( D + D) = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD 32 Continue †¦ Y = AB C D + AB CD + A B C D + A B C D + A B CD + A B CD Plot the minterm on K-map: C D C D CD C D AB ABAB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB B CD BC D Simplified SOP expression: Y = B C D + B CD + A B 33 Continue †¦ †¢ †¢ †¢ †¢ †¢ Boolean expression can be plotted on to the K-map from its SOP form Product terms with four variables are the minterms and correspond to a single cell on the K-map Product term with three variables corresponds to a loop of two adjacent minterms Product term with only two variables is a quad ( a loop of four adjacent minterms) Product term with a single variable is an octet (a loop of eight adjacent minterms) 1 cell 2 cellsY = A + BC + B CD + ABCD 4 cells 8 cells 34 Continue †¦ †¢ Consider the previous example: Y = AB C D + AB CD + A B minterms 4 cells †¢ †¢ †¢ Both minterms are directly plotted on the K-map The loop which corresponds to A B is drawn on the K-map The cells inside the loops are filled with ‘1’ C D C D CD C D AB AB AB AB 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 AB AB C D A B CD 35 Continue †¦ †¢ Consider the following Boolean expression: Y = ( A + B )( AC + D ) Convert to SOP form: Y = AC + AD + ABC + BD Plot the SOP onto K-map C D C D CD C D AB AB AB AB AC BD C D C D CD C D AB AB ill cells in loops with ‘1' 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 36 ABC AB AB AD Continue †¦ Obtain the simplified SOP expression from K-map: C D C D CD C D AB AB AB AB 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 Simplified SOP expression: Y = AC + AD + BD 37 Continue †¦ Example: Redesign the logic circuit below from its simplified SOP expression: A B C D Z Z = ( B + D )( B + D ) + B(CD + A D ) 38 Continue †¦ Z = ( B + D )( B + D ) + B(CD + A D ) = B + D + B + D + BCD + A BD = BD + B D + BCD + A BD C D C D CD C D AB AB AB 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 AB Z = BD + B D + A B 39