Reference no: EM131175449

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.

Design Specification

You are to design a combinational logic circuit that accepts a four-bit Balanced Gray code (X₃ X₂ X₁ X₀) as its input and creates a four-bit output (Y₃ Y₂ Y₁ Y₀) that uses standard binary encoding to represent the same hexadecimal value.

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 Y₀ are produced and that the correct hexadecimal value is displayed.

You must document the design, simulation, and outcomes in a brief written report. Your report should contain the following items.

- At the top of the first page of your report, include: your name (as recorded by the university); your email address; and the assignment name (e.g., "ECE 5484, Project 1"). Do not include your Virginia Tech ID number or your social security number.

- 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 X0 and 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 Y0 given above, assuming you implement Y0 as 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.)