Assignment 5: Boolean Algebra March 31, 2015 Abstract Assignment Five covers boolean algebra and computer hardware. As with previous labs, you will need to complete a lab report. In this lab report, you should write the introduction, method, results, discussion and conclusion sections. Other sections will already be filled in for you. For the results and discussions sections in the report template, you will find headings for the individual tasks. Please fill in the details under these headings, and leave the headings as they are. Note: the submission deadline for this lab report is Wednesday, April 8th at midday. As always, you must submit your lab report as a PDF file. Any late submissions — without prior agreement of the course coordinator — will be penalised with the penalty system discussed in the course outline. NOTE: The University is closed between Friday, April 2nd and Tuesday, April 7th. You should not expect to be able to get access to Cotton 145 on these days. 1 Marks for the Assignment Parts of the Assignment: 1. A Core part, which involves programming the Arduino to perform simple tasks using the basic concepts and constructs, 2. A Completion part, which extends the Core part and involves more difficult thinking and may cover additional concepts and constructs, 3. A Challenge part, which usually involves substantially more difficult programming and problem solving, and 5. Documenting your work in a formal Lab Report. Successfully performing of all the Core tasks will enable you to get awarded up to 65% of the lab marks. By successfully performing all the Completion tasks enables you to be awarded a maximum of 80%, the Challenge tasks can take you up to 100%. But simply performing the tasks will not ensure that you get the marks. You must clearly document your work in a lab report, and you must make sure you include code for every task with brief explanations in your report. 1 Actual questions are boxed: Please note that the CORE , COMPLETION and CHALLENGE tasks have a note attached to them guiding you as to which of the Results or Discussion sections that you should write them in. You will also need to write an introduction, method and conclusions section, although these do not need to be broken down by specific tasks, and you have more flexibility in how you structure you’re writing here. However, you must adhere to the Task structure in the Results and Discussion sections. Some questions require you to submit a screenshot of the circuit you have created. You can achieve this via the ”export image” feature in the ”file” menu of Logisim, and you MUST include these screenshots in the PDF. DO NOT submit them separately. 2 Core Core 1 RESULTS Section: Using logisim confirm truth tables of AND, OR and NOT gates. Run simulations. Include a screen-shot of the circuit and truth tables in your report. Core 2 RESULTS Section: Using logisim confirm boolean identities A + A = 1 and A · A = 0. Run simulations. Include a screen-shot of the circuit and truth tables in your report. Core 3 DISCUSSION Section: Using logisim build XOR gate A · B + A · B Enter your circuit in Logisim. Compare your results with the truth table for the Logisim library XOR gate. Include a screen-shot of the circuit and truth tables in your report. 2 Core 4 RESULTS Section: Using logisim confirm DeMorgan rules (A + B) = A · B and A · B = A + B . Enter the circuit in Logisim for each equation. Run simulations. Confirm DeMorgan’s rule using the truth tables. Include screen-shot of the circuit and truth tables in your report. Core 5 RESULTS Section: Build a half adder in Logisim for two binary numbers, where each binary number is one bit long. Start from truth table and work your way to the circuit, explaining your reasoning. Include a screen-shot of the circuit in your report. 3 3 Completion Completion 1 RESULTS Section: Build a full adder in Logisim for two binary numbers, where each binary number is two bits long. Start from truth table and work your way to the circuit, explaining your reasoning. Include a screen-shot of the circuit in your report. Completion 2 DISCUSSION Section: Derive the circuit to implement the following truth table, using Karnaugh Maps: 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 1 1 0 0 1 0 0 0 Enter the circuits in Logisim for the equation. Run simulations. Check truth table. Include a screen-shot of your circuit in your report, and discuss how Karnaugh Maps can assist in this process. 4 4 Challenge A 7-segment LED display can be used to display numbers and letter. Each segment can be turned ON if 1 is provided for the corresponding input. You Figure 1: LED display can find pins description in Logisim help. Challenge 1 DISCUSSION Section: Make a circuit that: • takes 3 bits as an input • converts number to decimal • displays decimal number using LED You can use any facilities of Logisim that are available Include screenshot of the circuit in your report, and discuss why it works. 5
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