The Principle Of Duality States Computer Science Essay

The Principle Of Duality States Computer Science Essay To simplify a SOP for a Boolean expression using a K map, first identify all the input combinations that produce an output of logic level 1 and place them in their appropriate K map cell. Consequently, all other cells must contain zero (0). Second, group the adjacent cells that contain 1 in a manner that maximizes the size of the groups but also minimizes the total number of groups. All 1s in the output must be included in a group even if the group is only one cell. Third, as each SOP term represents an AND expression, each (AND) grouping is written with only the input variables that are common to the group. Finally, the simplified expression is formed by ORing each of the (AND) groups. To illustrate let us consider the function X =ABC+ABC+ABC whose truth table and K map are illustrated below: Truth table specifications for a logic function may not to include all possible combinations of the input binary digits for the input variables, yet they may still be complete specifications of the logic function for the prescribed application. In these situations certain input combinations will not occur due to the nature of the application. When the input combinations are irrelevant or cannot occur, the output states are in the Truth table and the K map are filled with an X and are referred to as dont care states. When simplifying K maps with dont care states, the contents of the undefined cells (1 or 0) are chosen according to preference. The aim is to enlarge group sizes thereby eliminating as many input variables from the simplified expression as possible. Only those Xs that assist in simplifying the function should be included in the groupings. No additional Xs should be added that would result in additional terms in the expression. THE TABULATION METHOD The K-map method is convenient as long as the number of variables does not exceed five or six, but when the number increases it becomes difficult to use this method. The tabulation method overcomes this difficulty, besides it is suitable for computer mechanisation. It was first formulated by Quine and later improved by McCluskey. It is also known as the Quine-McCluskey method. The tabular method of simplification consits of two parts: Determination of Prime Implicants. Selection of Essential Prime Implicants. The first part is covered in the software provided, the second part is not. Each minterm and its combined cells are included in the Minterm record, and linked lists techniques are used. Linked lists are the best way to manage unknown amount of data at run time instead of using a large array which is a waste of memory. The record used is: Pminterm = ^Minterm; Minterm = Record Number : Word; {This is to hold the decimal equivalent of the minterm} NumberOfOnes : Byte; {This is to hold the no. of 1s in the field Number} Selected : Boolean; {used as a tick when this term is selected} CellStr : String; { a string to hold all minterms that form a cell with this term } DashPlaceStr : String {a string to hold the place of the dash } Next : Pminterm { a pointer to the next record to form a linked list} End; The software procedure summarise as follows: The user enters the minterms in decimal equivalent. The program sorts minterms in the number of ones included in the binary equivalent (SortMinTerms). Any two minterms that differ from each other by only one variable are combined (done in FirstTabulation procedure), two minterms fit into this category if the number in the lower group is greater than that in the upper one, and the two numbers differ by a power of 2 e.g. ( 2d = 0010b and 10d = 1010b the difference is 8d which is a power of 2). Then the two numbers are copied to the second linked list ( First, Second, Vertex : Pminterm;). This procedure is carried for all the minterms. Matching groups are copied to second linked list while first one deleted. Then a second tabulation is carried in the SecondTabulation procedure, here each cell contained in the CellStr field of the Minterm record are compared together, a matching is found if the numbers in one cell are greater than the other one and they differs by a power of 2 e.g. (0,2 and 8,10 differs by 8 which is a power of two) . This procedure is carried for all the records in the second linked list and matching cells are copied to the first linked list, and any incomparable cells are copied to the Vertex linked list. Then the second linked list is deleted. The step 4 is repeated m 1 time where m is the number of inputs, transferring cells between first and second linked lists. The last linked list and the vertex linked list prime implicants are printed in the ABC equivalent using the WMterm procedure. My program architecture can be used to simplify any number of inputs, but practical limitations are in the Number field in the Minterm record which is a word i.e. 16 bits (16 inputs). Bearing in mind as well the simplified expression is contained in a string which is only 255 characters. Some inputs and corresponding outputs to try on the program: Boolean Expression Simplified Boolean Expression F(A,B,C) = S(0,6,7) ABC + AB F(A,B,C) = S(0,4,6,7) BC + AB + AC F(A,B,C,D,E,F) = S(4,5,6,7,36,37,38,39) BCD F(A,B,C,D,E,F,G,H) = S(16,17 up to 31,144,145 up to 159) BCD VARIABLE ENTERED METHOD (VEM) The conventional logic minimization is time consuming easy only for 4-5 variables. It becomes difficult to solve using conventional K-map method when number of variables goes on increasing. In that case Variable Entered Method will be good idea to use. It represents values of functions in terms of its variables called map entered variables. A new method for obtaining a compact subsumptive general solution of a system of Boolean equations is presented. The method relies on the use of the variable-entered Karnaugh map (VEKM) to achieve successive elimination through successive map folding. It is superior in efficiency and simplicity to methods employing Marquand diagrams or Conventional Karnaugh maps; it requires the construction of significantly smaller maps and produces such maps in a minimization-ready form. Moreover, the method is applicable to general Boolean equations and is not restricted to the two-valued case. Combinational Sequential Circuits Combinational logic circuits implement Boolean functions. Boolean functions are mappings of input bitstrings to output bitstrings. These circuits are functions of input only. What does that mean? It means that if you feed in an input to a circuit, say, 000, then look at its output, and discover it is, say, 10, then the output will always be 10 for that circuit, if 000 is the input. 000 is mapped to 10. If that value were not the same every single time, then the output must not completely depend on 000. Something else must be affecting the output. Combinational logic circuits always depend on input. Another way to define something that is a function of input is to imagine that you are only allowed to use input variables xk-1,,x0, i.e. data inputs, cm-1,,c0, i.e., control inputs, to write the function. This function can not depend on global variables or other variables. Like combinational logic circuits, a sequential logic circuit has inputs (labelled with x with subscripts) and outputs (labelled with z with subscripts). Unike combinational logic circuits, a sequential logic circuit uses a clock. Also, there is a box inside the circuit called State. This box contains flip flops. Assume it has k flip flops. The flip flops basically store a k-bit number representing the current state. The output z is computed based on the inputs (x with subscripts) and the state coming out of the state box (q with subscripts). The state may be updated at each positive clock edge. When theres not a positive clock edge, the state remains unchanged. The information needed to update to the state (called the next state) comes from the current state (the current value of q) and the input, which is fed through combinational logic, and fed back into the state box, telling the state box how to update itself. A sequential circuit uses flip flops. Unlike combinational logic, sequential circuits have state, which means basically, sequential circuits have memory. The main difference between sequential circuits and combinational circuits is that sequential circuits compute their output based on input and state, and that the state is updated based on a clock. Combinational logic circuits implement Boolean functions, so they are functions only of their inputs, and are not based on clocks. The S-R Latch A bistable multivibrator has two stable states, as indicated by the prefix bi in its name. Typically, one state is referred to as set and the other as reset. The simplest bistable device, therefore, is known as a set-reset, or S-R, latch. To create an S-R latch, we can wire two NOR gates in such a way that the output of one feeds back to the input of another, and vice versa, like this: http://sub.allaboutcircuits.com/images/04173.png The Q and not-Q outputs are supposed to be in opposite states. I say supposed to because making both the S and R inputs equal to 1 results in both Q and not-Q being 0. For this reason, having both S and R equal to 1 is called an invalid or illegal state for the S-R multivibrator. Otherwise, making S=1 and R=0 sets the multivibrator so that Q=1 and not-Q=0. Conversely, making R=1 and S=0 resets the multivibrator in the opposite state. When S and R are both equal to 0, the multivibrators outputs latch in their prior states. The Clocked D-Latch Since the enable input on a gated S-R latch provides a way to latch the Q and not-Q outputs without regard to the status of S or R, we can eliminate one of those inputs to create a multivibrator latch circuit with no illegal input states. Such a circuit is called a D latch, and its internal logic looks like this: http://sub.allaboutcircuits.com/images/04181.png Note that the R input has been replaced with the complement (inversion) of the old S input, and the S input has been renamed to D. As with the gated S-R latch, the D latch will not respond to a signal input if the enable input is 0 it simply stays latched in its last state. When the enable input is 1, however, the Q output follows the D input. Since the R input of the S-R circuitry has been done away with, this latch has no invalid or illegal state. Q and not-Q are always opposite of one another. Master-Slave Flip-Flops A master-slave flip-flop is constructed from two seperate flip-flops. One circuit serves as a master and the other as a slave. The logic diagram of an SR flip-flop is shown in figure below. The master flip-flop is enabled on the positive edge of the clock pulse CP and the slave flip-flop is disabled by the inverter. The information at the external R and S inputs is transmitted to the master flip-flop. When the pulse returns to 0, the master flip-flop is disabled and the slave flip-flop is enabled. The slave flip-flop then goes to the same state as the master flip-flop. http://wearcam.org/ece385/lectureflipflops/flipflops/fig9.gif Logic diagram of a master-slave flip-flop The timing relationship is shown in Figure below and is assumed that the flip-flop is in the clear state prior to the occurrence of the clock pulse. The output state of the master-slave flip-flop occurs on the negative transition of the clock pulse. Some master-slave flip-flops change output state on the positive transition of the clock pulse by having an additional inverter between the CP terminal and the input of the master. http://wearcam.org/ece385/lectureflipflops/flipflops/fig10.gif Timing relationship in a master slave flip-flop Edge Triggered Devices Another type of flip-flop that synchronizes the state changes during a clock pulse transition is the edge-triggered flip-flop. When the clock pulse input exceeds a specific threshold level, the inputs are locked out and the flip-flop is not affected by further changes in the inputs until the clock pulse returns to 0 and another pulse occurs. Some edge-triggered flip-flops cause a transition on the positive edge of the clock pulse (positive-edge-triggered), and others on the negative edge of the pulse (negative-edge-triggered). The logic diagram of a D-type positive-edge-triggered flip-flop is shown in figure below: http://wearcam.org/ece385/lectureflipflops/flipflops/fig11.gif D-type positive-edge triggered flip-flop When using different types of flip-flops in the same circuit, one must ensure that all flip-flop outputs make their transitions at the same time, ie., during either the negative edge or the positive edge of the clock pulse.

Progressive Movement Essay

The period from 1890 to 1917 in the history of United States is known as Progressive era. This period is marked by an all-encompassing and intensive change in all spheres of American life viz. political, economic and social. According to Nevin and Commager, this period was â€Å"marked by revolt and reform in almost every department of American life. Old political leaders were ousted and new one enlisted; political machinery was overhauled and modernized; political practices were subject to critical scrutiny and those which failed to square with the ideals of democracy were rejected.† (p. 382) These leaders from middle class pleaded for government regulation of big businesses to prevent exploitations pf the weaker sections. Stressing on the needs for reforms, Theodore Roosevelt said, â€Å"†No hard-and-fast rule can be laid down as to the way in which such work [reform] must be done; but most certainly every man, whatever his position, should strive to do it in some way and to some degree.† (Roosevelt) Most of the problems that Progressives wanted to tackle was an outcome of the industrial expansion and the political-industrial coalitions of the Gilded Age. During the Progressive almost every department of American life was overhauled and modernized. Thus Progressivism was a movement with â€Å"predominantly middle class objectives and viewpoint, deriving much of its support from small businessmen, farmers and professional people.† ( Parkes, p.544) At the federal level, the Progressive movement set in with the inauguration of the President Roosevelt curtailed the powers of the large organizations was epitomized through the suite against The Northern Securities Company in 1903. He introduced other legislative measures to breakdown the monopoly of the large corporations. Trust-Busting was the first radical step taken by Roosevelt that was aimed at the breaking of monopolies in any form and its abuses. Second major proponent of Progressivism at the Federal level was President William Howard Taft (1909-1913) who accomplished more progressive legislation than the Roosevelt. He introduced and enacted law to check corrupt practices during the elections. He dissolved ninety trusts under the Sherman Anti-Trust Act (these trusts were saving huge taxes in the name of charity and were involved in certain illegal activities). He strengthened the cause of democracy when he propagated the idea of direct elections for the senators and introduced 17th amendments in the U.S. constitution. Woodrow is the next in the row for progressive presidents. He introduced far-reaching economic reforms and adopted a number other progressive measure to capacitate the entire American spirit with purpose. Hs foremost priority was the revision of tariff and introduction of viable reforms. Secondly, he introduced another Act to reconstruct the monetary and banking sector. Although his program of more progressive reforms were cut short but the outbreak or WW II but two more constitutional amendment (18th and 19th) became effective in his presidency.[1] Progressives could not bring about the revolutionary transformation of the political and economic system. The evident disappointment of the Progressive movement was its disinclination to deal with racial discrimination. Although it had a national agenda but it was meant for Whites only. The Afro-American suffered from the victimization at the social and state level through disfranchisement, Jim Crow laws, and poverty.   Additionally, it failed to address the questions of class conflict and ended in despair for small owners and businessmen. Yet it cannot be denied that through their reforms they tried to revitalize democracy and made the rulers responsible and accountable to the public. â€Å"Perhaps the best known results of this era are the 18th and 19th Amendments, Prohibition and woman suffrage respectively. But this legislation really came at the tail end of the period that has come to be known as the â€Å"Age of Reform.† The amendments were actually the byproducts of an immense social and political upheaval which changed forever the expectations of the role government would play in American society.† (PBS) References Nevins, Allan& Commager, Henry S. 1966. A short history of the United States. New   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   York: A. Knopf. Parkes, Henry B. 1959. The United States of America—A History. New York: Knopf. PBS. The Progressive Era 1900-1918. On-line. Available from Internet, http://www.pbs.org/wgbh/amex/eleanor/peopleevents/pande08.html, accessed 23 March   2008. [1] 18th Amendment of U.S. Constitution the process of introduction of Prohibition was completed whereas 19th Amendments granted the right of vote to the women on equal terms with men.

The Ultimate Guide to Advertisement Analysis Essay Topics

The Ultimate Guide to Advertisement Analysis Essay Topics The Start of Advertisement Analysis Essay Topics There's an endless number of different essay topics that may be analyzed. Apparently, writing an essay on the subject of marijuana is too general. Be mindful of the size it must be and get started writing the narrative essay outline. So as to write a decent rhetorical analysis essay, however, you have to first pick a great topic. Analysis essays are known to be among the hardest to write. An analysis essay is a type of persuasive essay. At times it is often quite difficult to consider analysis essay topics, let alone compose the essay. It can be challenging to work out what is going to make a great topic for a rhetorical analysis essay. The Start of Advertisement Analysis Essay Topics Therefore, process analyses can be quite detailed and at times quite long. Once you choose the procedure you wish to concentrate on, you then need to earn a list of steps needed to attain the aims of the activity. In case you haven't already mastered the process, it is going to be really hard to learn and compose all at one time. The process essays are generally written for companies or people who need tutorials. The Honest to Goodness Truth on Advertisement Analysis Essay Topics Quality over quantity goes a very long way here. Don't be afraid to find some additional aid to create your paper stick out! It is wise to look for the one which has a great reputation and offers high-quality papers at very affordable prices. The absolute most important guarantee we offer is that in the event that you are dissatisfied with your completed order, and in the event that you can show us where it does not fulfill the requirements which you stated clearly when you placed the order, we'll redo the paper at no cost. The Downside Risk of Advertisement Analysis Essay Topics The conclusion needs to be strong and clear. Write in such a fashion, that you are going to be interested to read it. It's possible to insert thesis statement at any portion of the introduction if you truly feel confident about it. To end the full essay, it's crucial to make an overall concluding statement. Be certain the body of the text contributes to the conclusion logically. You have to reveal the end result of the author's speech and its impact. The data set used to finish the analysis is dependent upon the question the analysis is trying to reply. When you have taken an issue apart, you must describe its components, explain how they're interrelated, and produce your own conclusions. The Upside to Advertisement Analysis Essay Topics In case the essay isn't preassigned to you by your instructor, it is wise to write about a topic in a topic of your interest. When selecting a topic for an important essay make sure you take a topic you'll be able to manage. To begin writing your assignment you would want to encounter an interesting and promising topic. A superb collection historical analysis essay topic which will be suitable to anybody is difficult to find, because everyone has their own preferences. Together with the topics, you'd come across loads of papers at no cost. There are lots of topics to choose at and dissect. Flip through of any parenting magazine and you're going to be astonished at the quantity of knowledge you will receive. You're able to even locate a funny method to teach your readers how to modify their settings. Therefore, it's ok to receive a bit personal here and convey your viewpoint. Everyone needs to discover how to modify a Facebook setting at some time in their lives. In an exact way that you will only have to establish whether the thing you're speaking about is serving the goal. The Benefits of Advertisement Analysis Essay Topics It is possible to discover lots of them to select from, therefore it's recommended to produce your final decision based on your likes and assignment specifics. The writer ought to be very keen to prevent confusion. He should avoid any unnecessary information such as the background, history or origin. If you are abl e to analyze any book for your rhetorical assignment, choose the work you recognize well. You might have to be somewhat careful. One of the most typical forms of analysis that college and higher school students perform. It's possible to also talk about the issues that arrive with having a football program. There are several methods in which you are able to write a rhetorical paper. It's possible for you to create a process analysis essay on the best way to make the ideal potatoes pie. It is an impossible task to produce a good, impressive introduction before you know the remainder of the paper's content. There are special words and word combination utilized for analytical purposes which ought to be learned also. The cost of an essay is dependent upon the total amount of effort the writer has to exert. Therefore, an analytical essay is a bit of writing that offers an informative observation about the particular topic or idea. What's more, the author should vary their usage of transitional words such as after, then, next in order to make certain that the essay doesn't become repetitive. The conclusion plays a crucial role in the feeling it ties up the whole essay.

The Problem Of Teen Drinking - 1450 Words

Every 51 minutes in America, someone is killed in a drunk driving crash. A dangerous issue facing society today is the problem of teen drinking and driving. Currently an approximate of 10,076 people die in drunk driving crashes per year. If positive progress to ceasing this act does not happen, teens will continue to drink and drive putting everybody on the road at risk. Teens who drink and drive put everyone on the road at risk, causing serious crashes that could be preventable. Background of the Problem A major factor contributing to alcohol-related car accidents is binge drinking. Teenage drinking is not legal, therefore teens usually cannot drink whenever they want. When teens do drink, they often times drink to get drunk on the†¦show more content†¦Fake IDs are often very effective because they are not always taken seriously in the bouncer world. There are approximately more fake IDs than real that are used on college campuses. A Her Campus survey found that â€Å"54.5% of readers surveyed had or currently have a fake ID† (Collins, 2012, p. 2). The people guarding the doors at clubs and bars aren’t always equipped to spot fake IDs. In an interview, FIRST NAME Shubaly, a New York bouncer, quoted â€Å"I never received any formal how-to-spot-a-fake-ID training† (Goldberg, 2009, p. 5). The rate that underaged people are getting into clubs factors into how easy it is for teens to get alcohol, which only increases the risk of a teen to get behind the whee l while under the influence, even if they were not planning on drinking that night. Teens who take on the responsibility of being a designated driver are sometimes still pressured into drinking. Teens who get peer pressured into drinking when they know they had a responsibility to drive later often still do. Some teens decide to drink a little bit at parties so it looks like they are trying to get drunk to other teens around them in order to look or feel cool. â€Å"While 71% of teens have tried alcohol by the end of high school, far fewer drink to get drunk† (Barker, 2013, p. 6). When a teen gives into peer pressure or takes â€Å"just one sip,† they do not always know what they are getting themselves into. Most kids wildly overestimate the prevalence of