Fundamentals of Computer Systems Project 1

ECE 5484 (Fall 2019)  Project 1 Page 1 of 7

Virginia Tech  ECE 5484: Fundamentals of Computer Systems  Fall 2019

Project 1 Assignment (updated 9/19/2019)

Preface

Before you start this project, please be sure that you have completed all of the following

activities.

 Read the project all the way through before starting. For example, there are some

suggestions in the last section.

 Complete all reading and watch all videos for Modules 1, 2, and 3. Ensure that you

understand number systems, codes, Boolean logic, and combinational logic circuits and

that you are familiar with Logisim.

 Note the grading policies, including policies for submitting assignments, in the syllabus.

 Review the course schedule. Note the due dates for course assignments including this

one.

Please note the following.

 All submissions of graded work in this class are subject to the Graduate Honor System.

Work on this project is to be completely your own. You are welcome to discuss high-

level aspects of the project with others and you are encouraged to the Project 1

discussion area on the class website for this. Any questions concerning design details

must be directed to the instructor or teaching assistant.

 Submit your assignment using the Assignments area of the class website. You must

submit your assignment by 11:55 p.m. on the due date.

1. Introduction

The objective of this project is to reinforce your understanding of binary codes, combinational

logic design, and logic simulation. You must:

a) design a combinational logic circuit that displays the decimal value of an Aiken (or

“2421”) code input according to the specifications given below;

b) debug and test your design by simulating it using the Logisim simulator; and

c) document your work in a short report.

2. Aiken Codes

Computer systems usually represent decimal and hexadecimal numbers in standard radix-2

form. The four bits representing a decimal or hexadecimal digit have weights 8-4-2-1. For

example, the value 9 decimal is represented as 1001 (18 + 04 + 02 + 11). Some systems

use different codes, with different weights for the digits, to achieve special properties.

Converters can translate from or to standard radix-2 representation.

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One example of such a special code is the Aiken (or 2421) code1 which uses weights 2-4-2-1

instead of 8-4-2-1 to represent decimal digits using four binary digits. Consider a decimal

number N with binary representation B using the Aiken code. Using the Aiken code, the 9’s

complement2 of N is represented in binary form as the 1’s complement of B. For example, the

decimal number 2 is represented as 0010 (just like in standard radix-2 representation). The 9’s

complement of 2 is 7. Using the Aiken code, 7 is represented as 1101 (and not 0111 as it is in

radix-2). Note that 1101 is the 1’s complement of 0010. The Aiken code makes it easier to

perform decimal arithmetic with the decimal digits represented in binary form. The Aiken code

is used in inherently decimal devices such as calculators and digital clocks. These devices use

decimal, rather than binary, arithmetic. Table I shows how decimal values 0 through 9 are

represented using the Aiken code as well as the standard binary (radix-2) code.

Table I. Decimal Values and Associated 4-bit Aiken Code and Standard Binary Code

Decimal

Digit

Aiken (2421)

Code

Binary (8421)

Code

0 0000 0000

1 0001 0001

2 0010 0010

3 0011 0011

4 0100 0100

5 1011 0101

6 1100 0110

7 1101 0111

8 1110 1000

9 1111 1001

One might think you could represent some decimal numbers in two different ways, such as

both 1011 and 0101 for decimal 5. But, the Aiken code is defined so that it maintains the

complementation property described above. Note that there are six combination of four bits

that are not included in the table as an Aiken code, namely 0101, 0110, 0111, 1000, 1001, and

1010. These six values are considered undefined or disallowed for the Aiken code.

3. Design Specification

You are to design a combinational logic circuit that accepts a decimal value represented as a

four-bit Aiken code (X3 X2 X1 X0) as its input and that creates a four-bit output (Y3 Y2 Y1 Y0) that

uses standard binary (radix-2) encoding to represent the same decimal value. In other words,

the circuit translates between the Aiken code input and the standard binary code output as

indicated in Table I. For example, if X3X2X1X0 = 1110, then output Y3Y2Y1Y0 = 1000.

1 More information is at https://en.wikipedia.org/wiki/Aiken_code. 2 For more information, see: https://www.geeksforgeeks.org/9s-complement-decimal-number/ and

https://en.wikipedia.org/wiki/Method_of_complements.

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Figure 1 provides a block diagram of the converter function.

Figure 1. Block diagram of the Aiken-to-binary code converter function.

Note that not all input combinations of X3 X2 X1 X0 will occur. The six disallowed inputs

described above will never be input to the circuit. In designing the logic circuit, we do not care

what the output values Y3 Y2 Y1 Y0 are for these six disallowed inputs since they never occur.

We can use these “don’t care” conditions to our advantage to simplify the design. We may be

able to reduce the amount of logic needed by assuming they are a logic 1 or a logic 0. In a truth

table, we use “X” to represent a don’t care value.

Note that Table I is not a true truth table, although it specifies all that we need to know to

create the truth tables for the four outputs (Y3 Y2 Y1 Y0). Table 1 specifies only 10 of the 16

possible input combinations of inputs X3 X2 X1 X0. From the discussion above, we know that we

can assign a don’t care, or “X,” output for the six disallowed input combinations.

For each of the four outputs, you can construct a standard truth table with inputs X3 X2 X1 X0

appearing in order from 0000, 0001, 0010, …, 1111. The 6 disallowed input combinations can

be specified as don’t cares. You can create a separate truth table for each output signal, or you

can merge the four truth tables into one truth table with four output columns for Y3 Y2 Y1 Y0.

For this project, you are not required to minimize the logic function or associated circuit, but

you may choose to do so. Reducing the complexity of the logic function will make the logic

circuit simpler and, hence, easier to simulate in Logisim.

4. Modeling the Circuit in Logisim

Use the Pin device in Logisim’s Wiring library to control the four inputs (X3 X2 X1 X0) 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 Aiken 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.

The circuit’s four output bits should be used to control a hexadecimal display to show values 0

through 9, inclusive. Use the Hex Digit Display device in Logisim’s Input/Output library. It

accepts a 4-bit binary encoded value as input and displays the decimal digit. Note that the

display is capable of showing hexadecimal digits A through F, but these should not appear in

this circuit since the Aiken code inputs only represent digits 0 through 9. Use the Splitter device

in Logisim’s Wiring library to interface the four individual single bits produced by the

Aiken Code to

Binary Code Converter

X0

X1

X2

X3

Y0

X1

X2

X3

ECE 5484 (Fall 2019)  Project 1 Page 4 of 7

combinational circuit (Y3 Y2 Y1 Y0) to the four-bit wide input to the Hex Digit Display. The Hex

Digit Display device has a second input to control the decimal (hexadecimal) point. The decimal

point input can be left unconnected.

Figure 2 shows a possible layout for part of the design to implement the output Y3. The

associated Logisim circuit file is provided with this assignment.

Figure 2. Possible circuit layout including logic to produce output Y3 (input is for

Aiken code value 1110 which produces binary output 1000 or decimal 8).

5. Simulation

After you create your design, use Logisim to simulate the code conversion circuit. You should

test all 10 possible valid input combinations (0 through 9) and verify that the correct values of

Y3, Y2, Y1, and Y0 are produced and that the correct decimal value is displayed.

ECE 5484 (Fall 2019)  Project 1 Page 5 of 7

6. Submission

6.1. Report

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 (or you can provide four separate truth tables with one for each of the four outputs).

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 have 16 rows instead of 10 and must be in the proper order.

Section 3 – Logic Expressions: Specify the Boolean logic expressions for Y3, Y2, Y1, and Y0. Show

any work that led to the expressions. Cite any tools you have may have used in deriving the

expressions. (Note that you can just state the expression for Y3 given above, assuming you

implement Y3 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 = 1110 (decimal value 8) 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 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.)

6.2. Submission

Carefully follow these instructions when submitting your project.

ECE 5484 (Fall 2019)  Project 1 Page 6 of 7

 Create a single PDF file for your report. Name the PDF file lastname_firstname_P1.pdf,

where lastname is your last or family name and firstname is your first or given name.

Submit this file.

 Save your Logisim circuit with file name lastname_firstname_P1.circ. This file will be

used to test your design for grading. Submit this file in addition to the PDF report file.

 Submit your assignment in the Assignments area of the class website. You must submit

both files by 11:55 p.m. on the due date.

7. Grading

The project will be evaluated based on the following criteria. Also, see the grading rubric on

the Project 1 assignment page on the class Canvas site.

 Overall Presentation (15 points)

o Complete, clear, and well organized report

o Mechanics (spelling, grammar, etc.)

 Technical Merit (40 points)

o Discussion of design objectives (Section 1)

o Correct and complete truth table (Section 2)

o Correct and complete logic expressions and brief discussion of how they were

derived (Section 3)

o Correct and complete circuit design that follows from the logic expressions

(Section 4)

o Brief discussion of conclusions (Section 5)

 Correct operation (45 points)

o Correct operation as verified using the circuit simulation file

8. Suggestions and Tools

8.1. Design Process Hints

You need to use a systematic approach for this design and the project. Here are key steps and

some suggestions.

1) Be sure you understand the design objectives including how the Aiken code relates to

the standard binary code. Be sure you understand Table I.

2) Develop the truth table. Check the entries against Table I.

3) Develop the four expressions for the outputs. Try a few input combinations to be sure

that the outputs match the correct ones in your truth table and in Table I. Look at the

tools suggestions below before starting this step.

4) Create a circuit diagram in Logisim. Follow the instructions given in Section 4. Starting

with the provided circuit file is probably best although it is not required. Build the

circuit incrementally by creating the logic diagrams for one output at a time and testing

ECE 5484 (Fall 2019)  Project 1 Page 7 of 7

to ensure that it operates correctly. After you have tested that output’s logic, add the

next to the diagram. Test the circuit thoroughly for all 10 valid input combinations.

5) Write your report and submit it and your circuit file.

8.1. Tools

While some work with pencil, paper, and brain power is needed (especially some brain power),

tools are also very helpful in the design and synthesis of logic functions and larger systems. For

this project, you can use any helpful tool that can take your work as input and create outputs to

help you complete the project. Be sure to cite any tools that you do use for any part of this

project other than Logisim (and Microsoft Word, Google Docs, or other word processing

software used to create the report itself). Here are some tools that you may find useful.

 Logisim is a must. You should already have some experience using Logisim from

previous work in this class.

 An online synthesis tool or a synthesis application you run on your computer may be

helpful. Here’s a specific tool that allows you to input a truth table (including “x” for

“don’t care” outputs) and outputs a Boolean expression.

Online Minimization of Boolean Functions: http://tma.main.jp/logic/index_en.html

You would need to use four-input truth table and run the tool four times, once for each

input. Remember the old saying, “garbage in, garbage out.” So, you will get correct

expressions from the tool only if the input truth table is correct.

Note that there are other tools and some may be better than this one, but this one is

very helpful.

 Remembering another old saying, “Excel is the second best tool for everything,” you

may find Microsoft Excel is a useful tool for this project if you have good Excel skills. You

can create truth tables, convert between different bases, create logic functions, etc.

Other than Logisim, use of other tools is optional. But, you will likely other tools can be very

helpful in successfully completing this project.