Algorithm design as it relates to time complexity problems like Research Paper

Algorithm design as it relates to time complexity problems like reducing fractions without using the euclidean algorithm for GCD - Research Paper Example The main difference of Algorithms both circuit implementation, testing and results expected. Modern processors that perform calculations need Algorithm design for present and future programmers. The paper also explains some key terms as used in the text in relation to computer design. It covers the need to maintain optimal code for future programmers due to complexity of testing circuits. Key words: Euclid’s Algorithm, Stein’s Algorithm, Built-In-Self-Test and Linear Feedback Shift Register. Algorithm Design Review of steps involved in solving time complexity problems 1. Euclidean algorithm Euclidean algorithm is an ancient efficient method used in computing the greatest common divisor (GCD) of two integers. The simplest Euclid’s algorithm starts with two positive integers. This then form a new pair that consists of the smaller number and the difference between the smaller and larger numbers. The process repeats until the numbers are equal. The resultant number t hen is the greatest common divisor of the original two integers. Euclid algorithm is described as GCD(a, 0) = a GCD(a, b) = GCD(b, a mod b) If and b>0, then GCD(a, a) = a GCD(a, b) = GCD(a - b, b) ; if b < a GCD(a, b) = GCD(a, b - a) ; if a < b For example, GCD(20, 0) is 20. Similarly, GCD(20, 10) is same as GCD((20-10), 10) = GCD(10, 10) = 10. 2. Stein’s Algorithm This algorithm is also a binary GCD algorithm. It computes the greatest common divisor of two nonnegative integers (Purdy, 1983). It is more efficient over the ancient Euclidean algorithm because it replaces multiplication and divisions with shifts, which are cheaper when operating on the binary representation used by modern computers. This is critical on embedded platforms available that do not have direct processor support for calculations of division. Stein’s algorithm is described as GCD(0, v) = v GCD(u, 0) = u GCD(0, 0) = 0 When v and u are even, then GCD(u, v) = 2.GCD(u/2, v/2) For an even u and an odd v, then GCD(u, v) = GCD(u/2 v) Similarly, if v is even and u is odd, then GCD(u, v) = GCD(u, v/2) In case, v and u are both odd, and if u ? v, then GCD(u, v) = GCD((u – v)/2, v) In case, both are odd, and u < v, then GCD(u, v) = GCD((v – u)/2, u) When initially solving a problem, how might one detect that a solution needs extra attention with respect to an efficient algorithm vs standard solutions where a highly efficient solution may be indistinguishable from an inefficient one? Identification of a problem is the first step towards solving a given mathematical equation. It involves examining for complexity to be able to simplify before any other complex operations take place. Time requirements spell complexity and attention are hence worth considering. Built-In Self Test (BIST) Modern computers have a built in IC for testing. This technique integrates the functionality of an automated test system within a chip. It is a Design where testing is accomplished by the help of built in hardware features. BIST has test controller, response verification and test generator. Test generator is responsible for generating test address sequence that compares the output from memory with the expected correct data. The BIST controller can be either hardwired logic, microcode controller or based on processor (Rekha Devi, 2011). Specifically discuss the potential tradeoff between an easy to understand inefficient solution vs a difficult to follow efficient solution. By employing Linear Feedback Shift

Predictably Irrational Research Paper Example | Topics and Well Written Essays - 1250 words

Predictably Irrational - Research Paper Example As a philosophical example, one could agree that there are many religions. Most all of them profess faith in God or a god, and yet none of them can completely agree on a universal doctrine which clearly expresses shared values. If that is not an example of people being predictably irrational, there are certainly more examples to follow. However, that is just an idea to illustrate the point that there can be many different viewpoints, but only one truth viewed from multiple avenues. These truths certainly stem from pluralism, as, we live in a pluralistic society to be sure in the 21st century all around the globe. Also, the fact that Cartesian dualism plays a major role in making this cliche of â€Å"predictably irrational† a phrase which some people may regard with diffidence—one naturally distrusts conflicting ontological meanings, when they can coexist together as a phrase and make sense. II. Thesis (90 words) No doubt, it is difficult to accurately pinpoint this seem ingly cliche phrase describing someone who is predictably irrational. Although somewhat of an unusual phrase, one person can completely be irrational as well as predictably so. This extended definition, if you will, is going to be broken up into manageable sections t oread. Predictable irrationality will be proven by: giving an extended definition of predictability; what predictability is not; what irrationality is; what an extended definition of rationality is; and, finally, what is the definition of someone who is predictably irrational. III. The Nature of Predictability Part I (115 words) To introduce the idea of predictability, predictability is usually the assumption that a pattern is set. People count on predictability—the prediction that the stock market will rise, that the sun will rise in the east and set in the west, and that they will have three square meals per day. Predictability governs the land. Schedules, timetables, and clocks dictate where we are and what we do, most of the time. Predictability itself is cliche. â€Å"[W]e might adjust our definition and instead term cliche a predictable or unoriginal turn of phrase or action.†1 This is why predictability would fit in so well with the idea of irrationality—but more on that point later soon ahead. IV. The Nature of Predictability Part II (85 words) Another issue that concerns predictability is that something or someone predictable is never vague or indeterminate. â€Å"The existence of widespread predictability is a potential embarrassment to claims of radical indeterminacy†¦Ã¢â‚¬ 2 Thus, the very nature of predictability is one’s ability to describe what is going to happen when. Predictability directly contradicts unpredictability precisely because of the fact that it leads to concrete evidence of forming types of patterns. When something is unpredictable, it has the tendency to be vague. This leads us to our next point. V. The Nature of Unpredictability (10 0 words) Unpredictability is, by its very nature, in contra of predictability. However, by studying what unpredictability is, we can find out more about predictability. Unpredictability is precluded by the inability to be predictable. Thus, surprises become commonplace. There are no patterns, everything is in flux, constantly. Now, if everything was that unpredictable in the world, think about how horrible

Appraisal of Laura Poppo and Todd Zenger Article

Appraisal of Laura Poppo and Todd Zenger - Article Example The paper introduces one means by which other factors to a company’s transaction cost economics (TCE) in addition to the widely recognized and tested boundary choice theory might be measured in the information services field. After explaining the concepts involved with efficiency models based on boundary choice, the authors reveal the weaknesses introduced in the results of these models as a result of an inability to test for performance-level data. By testing the influence of exchange attributes on the performance levels of markets and firms independently, the authors are able to incorporate production and governance efficiency within their models. The literature review, presented in conjunction with the development of the various hypotheses to be tested, is well-rounded, examining various aspects of the theories that have presented, including their strengths and weaknesses. This provides a very informative background introduction to the subject as well as establishes how the various hypotheses were developed. The sample selected for the study is similarly based upon the work of previous scholars, concentrating on the same group of professionals as being the most involved with the factors under consideration. However, this study differed from others in that it attempted to include a much broader selection of informants than previous studies.