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Part 1Simplify the following Boolean expression: AB(A + B)(C + C) Design the combinatorial circuit for: (p’ *r) + q Design the combinatorial circuit for: [(p // q’) V ( r V q)] // s Complete the truth table of the following Boolean expression: p’ // (q V r ) Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof, or complete the two truth tables: (A + C)(AD + AD’) + AC + C? A + C The following is a message coded in ASCII using one byte per character and then represented in hexadecimal notation. What is the message? 4469736372657465204D617468656D617469637320697320434F4F4C21 Convert each of the following signed binary byte representations to its equivalent base-ten representation. What would each byte represent in Binary Coded Decimal? Show your work step by step. 00010001 01011100 1111010 What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work. Convert each of the following base-ten representations to its equivalent two’s complement in 7 bits. Show all of your work. 12 -2 -8 0 Define the highest and lowest integer that can be represented in this 7-bit two’s complement representation. What bit patterns are represented by the following hexadecimal notations? Show all of your work. 9A88 4AF6 DA What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work. Part 2Consider the following graph: Complete this table by finding the degree of each vertex, and identify whether it is even or odd: VertexDegreeEven/OddA??B??C??D??E??F??G??H??What is the order of the graph? Construct the 10 x 10 adjacency matrix for the graph. The graph below illustrates a switching network. The weights represent the delay times, in nanoseconds, travelled by a data packet between destinations, represented by the vertices. Complete the following table by finding the shortest distance and the path for that distance from vertex A to the other vertices: VertexShortest Distance from APath from AB??C??D??E??F??G??H??I??What is the shortest distance between A and J and the path for that distance? The following graph represents a portion of the subway system of a city. The vertices on the graph correspond to subway stations, and the edges correspond to the rails. Your job is to write a program for a cleaning car to efficiently clean this portion of the subway system. Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once. Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once. Is it possible to find an optimal path described in question 3-b that starts on any station? Explain your answer. Is it possible to find an optimal path described in question 3-b that starts and ends at the same station? Explain why or why not. A network engineer lives in City A, and his job is to inspect his company’s servers in various cities. The graph below shows the cost (in U.S. dollars) of travelling between each city that he has to visit. Find a Hamiltonian path in the graph. Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips? Is there another Hamiltonian circuit that will allow the engineer to inspect all of?the servers other than your answer in question 4-b? If so, calculate the cost. Consider the following binary tree: What is the height of the tree? What is the height of vertex H? Write the preorder traversal representation of the tree. Write the array representation of the tree by completing the following table: ? VertexLeft ChildRight ChildA??B??C??D??E??G??H??I??J??K??L??M??N??O??P??Q??R??S??T??Part 3In a survey, 24 IT professionals in Chicago were asked how much their annual salary was for the year 2012. The results are shown below: $109,000$ 65,000$ 65,000$ 59,000$ 180,000$ 101,325$ 130,000$95,000$ 81,500$69,000$71,500$ 74,880$64,000$72,000 $ 71,000$ 82,300$49,000$51,200$ 39,000$48,500$64,330 $ 41,100$52,330$82,000 Construct a frequency distribution with 5 classes. Create a histogram of the data using the frequency table from question 1-a. A software company asked 100 of its programmers to develop a certain program individually. The following histogram shows the time it takes a programmer to finish the task: How many classes are there for the given histogram? What is the class width of the histogram? What percentage of programmers can complete the task in 30 hours? How many hours does it take the majority of the programmers to complete the task? Search the Internet for prices of 11 different laptops. Compute the mean, median, and mode of these prices. Find the first and third quartiles of the prices. In the following image, the memory usage of various processes of a computer running a Windows Operating System is shown: Create a scatter plot of the memory usage of the processes. Find the following measures of central tendency of the memory usage in kilobytes (Kb): Mean Mode Median Find the following measures of dispersion of the memory usage in Kb: Range Variance Standard Deviation? Identify the values that are responsible for the variance of the dataset. Provide a possible solution on how the computer user could decrease the variance of his or her?memory usage. Answer the following questions completely, using proper grammar, complete sentences, and correct terminology: Explain what it means to have a standard deviation of 0. Without doing any calculations, is it possible to tell which of the following 2 sets has a higher standard deviation? Explain your answer. Set 1 = {1,2,3,4,5,6,7,8} Set 2 = {2,4,6,8,10,12,14,16} Part 4This data set (above) is a sample of Web server statistics for a computer science department. It contains the following 11 sections of data:Total successful requests Average successful requests per day Total successful requests for pages Average successful requests for pages per day Total failed requests Total redirected requests Number of distinct files requested Number of distinct hosts served Corrupt logfile lines Total data transferred Average data transferred per day Write an essay of 2–3 pages that contains the following:A complete overview of the data, identifying anomalies in different weeks, and the weeks that the data are not regular. Choose 5 different sections of data, examine these sections, and provide the specific selection process and criteria you used to select this data set. Provide the measures of tendency and dispersion for each of the 5 different sections of data you selected. Provide 1 chart or graph for each of the 5 processed sections. This may be a pie or bar chart or a histogram. Label the chart or graph clearly. Explain why the graph you provided gave a good visual representation of the data. Based on your explanation above, identify some specific advantages why, in general, charts and graphs are important in conveying information in a visual format. Determine the standard deviation and variation, and explain their importance in statistical analysis of a data set. Based on the tasks you performed in this project, research how statistics are used in information technology (IT), and provide references for your research Your essay should include proper citation in APA formatting, both in-text, and in reference pages. Include a title page and use 12-point Times New Roman double-spaced font throughout the text.Part 5High-level computer languages are created to be understood by humans. As a result, the keywords and the commands of these languages are easy to understand. Machine languages are harder to understand and operate.For this assignment, you should assume that the memory cells at addresses F0 to F9 are in the machine described here, and that it contains the hexadecimal bit patterns described in the following table: F020F1C0F230F3F8F420F500F630F7F9F8FFF9FFExplain (in detail) each step of the machine cycle. Show the contents of each of the registers and each of the memory cells after the execution of the code. Compare and contrast machine and high-level languages using resources from the Internet or AIU’s library. Be sure to explain why the hexadecimal and binary codes are important for programming in both languages. ................
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