Reference no: EM131929686
Topic: Fundamentals of Computer Systems
Detailed Question: This homework is all about Logisim, gray codes, binary and circuit layout.
Project Assignment
Preface
Before starting this project, please be sure that you have completed all of the following activities.
Make sure you understand number systems, codes, Boolean logic, and combinational logic circuits.
You will need Logisim to complete this project assignment.
1. Introduction
The objective of this project is to reinforce your understanding of binary codes, combinational logic design, and logic simulation. You must: (i) design a combinational logic circuit that displays the hexadecimal value of a gray code input according to the specifications given below; (ii) debug and test your design by simulating it using the Logisim simulator; and (iii) document your work in a short report.
2. Gray Codes
For this project we consider a special type of Gray code called a Balanced Gray code. In a Balanced Gray code, the number of transitions for each bit position is the same when counting through the values. For example, a four-bit Balanced Gray code can be used to count from 0 to 15 (hexadecimal F). There are 16 transitions as the count goes from 0 to 1 to 2 and so on to 15 and then back to 0. For a Balanced Gray code, there are four-bit transitions for each of the four bit positions during the 16 total transitions. This property is useful in some applications.
Table I below shows the encoding of hexadecimal values 0 through F using a 4-bit Balanced Gray code.
Table I. Hexadecimal Values and Associated 4-bit Balanced Gray Code and Binary Code
| Hexadecimal Value |
Balanced Gray Code (X3X2X1 Xo) |
Binary Code
( Y3 Y2 Y1 Y0)
|
| 0 |
0 |
0 |
| 1 |
1000 |
1 |
| 2 |
1100 |
10 |
| 3 |
1101 |
11 |
| 4 |
1111 |
100 |
| 5 |
1110 |
101 |
| 6 |
1010 |
110 |
| 7 |
10 |
111 |
| 8 |
110 |
1000 |
| 9 |
100 |
1001 |
| A |
101 |
1010 |
| B |
111 |
1011 |
| C |
11 |
1100 |
| D |
1011 |
1101 |
| E |
1001 |
1110 |
| F |
1 |
1111 |
3. Design Specification
You are to design a combinational logic circuit that accepts a four-bit Balanced Gray code (X3X2X1X0 ) as its input and creates a four-bit output (Y3Y2Y1Y0 ) that uses standard binary encoding to represent the same hexadecimal value.
In other words, the circuit translates between the Balanced Gray code input and the binary code output as indicated in Table I. Figure 1 provides a block diagram of the function. You do not need to minimize the logic function or associated circuit, but you may choose to do so.
4. Modeling the Circuit in Logisim
Use the Pin device in Logisim's Wiring library to control the four inputs (X3X2X1X0) to the combinational circuit. The Pin device is also available on Logisim's toolbar. Each pin can be interactively set to 0 or 1 using Logisim's Poke tool to test the circuit for different Balanced Gray code input values. If the proper connections are in place when Logisim is running, signals with logic level 1 appear in bright green and signals with logic level 0 are shown in dark green.
5. Simulation
After you create your design, use Logisim to simulate the code conversion circuit. You should test all 16 possible input combinations and verify that the correct values of Y3, Y2, Y1, and Y0are produced and that the correct hexadecimal value is displayed.
6.Report
You must document the design, simulation, and outcomes in a brief written report. report should contain the following items.
Yourreport should contain the following items.
The body of the report must contain the following sections. Use section numbers and headings to organize your report.
Section 1 - Objectives: Provide a brief summary of the design objectives and general approach to the design.
Section 2 - Truth Table: Provide a truth table with inputs X3, X2, X1, and X0and outputs Y3, Y2, Y1, and Y0. Each row should also be labeled with the corresponding hexadecimal value. The inputs should be in standard truth table order, from "0000" down to "1111." Thus, the truth table will look similar to Table I above, but will be reordered.
Section 3 - Logic Expressions: Specify the Boolean logic expressions for Y3, Y2, Y1, and Y0. Show any work that led to the expressions. (You can just state the expression for Y0given above, assuming you implement Y0as shown in Figure 2.) The Boolean expressions shown in this section for the report should correspond exactly to what is shown in the circuit diagram of the next section.
Section 4 - Circuit Design: Include a schematic diagram of the logic circuit that you created using Logisim. Within Logisim, you can select Export Image from the File menu to produce an image file that can then be incorporated into your report. Uncheck the "Printer View" box when exporting the image from Logisim. Show the circuit with input X3X2X1X0= 0100 (hexadecimal value 9) applied. For full credit, the Logisim schematic must be neat and easy to read. The four input pins and the four output signals should be labeled, as shown in Figure 2. The diagram should also be labeled with a title, your name, and the date.
Section 5 - Conclusions: Briefly discuss the outcome of your design and any problems or aspects that do not work properly; what you learned by doing this project; and any experiences that were particularly good or bad. Also, specify the approximate number of hours that you devoted to the project. (The number of hours is just for the instructor to assess the suitability of this project assignment.)
Submission
Carefully follow these instructions when submitting your project.
Save your Logisim circuit with file. This file will be used to test your design for grading. Submit this file in addition to the report file.
Attachment:- project.rar