Virtual Lab - IIT Kharagpur

Design of Wallace Tree Adders :

There are many cases where it is desired to add more than two numbers together. The straightforward way of adding together m numbers (all n bits wide) is to add the first two, then add that sum to the next using cascading full adders. This requires a total of m − 1 additions, for a total gate delay of O(m lg n) (assuming lookahead carry adders). Instead, a tree of adders can be formed, taking only O(lg m · lg n) gate delays.

A Wallace tree adder adds together n bits to produce a sum of log₂n bits.

The design of a Wallace tree adder to add seven bits (W₇) is illustrated below:

An adder tree to add three 4-bit numbers is shown below:

An adder tree (interconnections incomplete) to add five 4-bit numbers is shown below:

The above block diagrams can be used to design different wallace tree adder.

Design of Wallace Tree Adders :

Basic stage

Multiple choice questions:

Design of Wallace Tree Adders :

Procedure to perform the experiment:Design of Wallace Tree Adder

1. Start the simulator as directed.This simulator supports 5-valued logic.
2. To design the circuit we need 4 full adder, 1 'RCA 4 bit' component, 12 Bit switch(to give input), 5 Bit displays(for seeing output), wires.
3. The pin configuration of a component is shown whenever the mouse is hovered on any canned component of the palette or press the 'show pinconfig' button. Pin numbering starts from 1 and from the bottom left corner(indicating with the circle) and increases anticlockwise.
4. For a full adder input is in pin-5,6,8, output sum is in pin-4 and carry is pin-1
5. For a 'RCA 4 bit' input A0=pin-13 A1=pin-14 A2=pin-15 A3=pin-16, B0=pin-17 B1=pin-18 B2=pin-19 B3=20, C0=21, output S0=pin-12 S1=pin-11 S2=pin-10 S3=pin-9 Cout=pin-8
6. Click on the full adder component(in the Adder drawer in the pallet) and then click on the position of the editor window where you want to add the component(no drag and drop, simple click will serve the purpose), likewise add 3 more full adder(from the Adder drawer in the pallet), 1 'RCA 4 bit'(from the Adder drawer in the pallet,if it is not seen scroll down in the drawer), 12 Bit switches and 5 Bit Displays(from Display and Input drawer of the pallet,if it is not seen scroll down in the drawer).connect the Bit switches with the inputs and Bit displays component with the outputs.
7. To connect any two components select the Connection menu of Palette, and then click on the Source terminal and click on the target terminal. According to the circuit diagram connect all the components. After the connection is over click the selection tool in the pallete.
8. See the output, Bit switches are used to give input so that you can toggle its value with a double click and see the outputs with different inputs.

Circuit Diagram

Components :

To build a wallace tree adder to add three 4-bit input , we need :

1. 4 full adders
2. 4-bit adder
3. Display units to check the outputs.
4. Wires to connect.

Objective of 4 bit wallace tree adder:

This is an adder with less height.

1. understanding behaviour of wallace tree adder from module designed by the student as part of the experiment an dthe working module as well
2. understanding the concept of reducing gate delay by using tree of adders instead of using cascaded full adders
3. the adder will add three 4 bit numbers

Examining behaviour of wallace tree adder for the module designed by the student as part of the experiment (refer to the circuit diagram)

Loading data in the carry lookahead adder (refer to procedure tab for further detail and experiment manual for pin numbers)

• load the three input numbers in the adder units as:
  • 1111, 0001 and 1110

Examining the behaviour:

• check output sum 1110
• check final output carry 1
• check intermediate carry bit and sum bit of the unit adders (refer to theory and circuit diagram)
• probing the any port can be done by verifying the color of the wire coming out of the port
• color configuration of wire for 5 valued logic supported by the simulator:
  • if value is UNKNOWN, wire color= maroon
  • if value is TRUE, wire color= blue
  • if value is FALSE, wire color= black
  • if value is HI IMPEDENCE, wire color= green
  • if value is INVALID, wire color= orange

Examining behaviour of given wallace tree adder for the workng module:

Loading data in the wallace tree adder (refer to procedure tab for further detail and experiment manual for pin numbers) as:

• load the three input numbers as:
  • A(A3 A2 A1 A0): A3=1, A2=1, A1=1, A0=1
  • B(B3 B2 B1 B0): B3=0, B2=0, B1=0, B0=1
  • C(C3 C2 C1 C0): C3=1, C2=1, C1=1, C0=0

Examining the behaviour:

• check output sum:
  • sum(S3 S2 S1 S0): S3=1, S2=1, S1=1, S0=0
• check output carry:
  • cout=1

Recommended learning activities for the experiment: Leaning activities are designed in two stages, a basic stage and an advanced stage. Accomplishment of each stage can be self-evaluated through the given set of quiz questions consisting of multiple type and subjective type questions. In the basic stage, it is recommended to perform the experiment firstly, on the given encapsulated working module, secondly, on the module designed by the student, having gone through the theory, objective and procuder. By performing the experiment on the working module, students can only observe the input-output behavior. Where as, performing experiments on the designed module, students can do circuit analysis, error analysis in addition with the input-output behavior. It is recommended to perform the experiments following the given guideline to check behavior and test plans along with their own circuit analysis. Then students are recommended to move on to the advanced stage. The advanced stage includes the accomplishment of the given assignments which will provide deeper understanding of the topic with innovative circuit design experience. At any time, students can mature their knowledge base by further reading the references provided for the experiment.

Design of Wallace Tree Adders :

• Start the simulator as directed. For more detail please refer to the manual for using the simulator
• The simulator supports 5-valued logic
• To add the logic components to the editor or canvas (where you build the circuit) select any component and click on the position of the canvas where you want to add the component
• The pin configuration is shown when you select the component and press the 'show pinconfig' button in the left toolbar or whenever the mouse is hovered on any canned component of palette
• To connect any two components select the connection tool of palette, and then click on the source terminal and then click on the the target terminal
• To move any component select the component using the selection tool and drag the component to the desired position
• To give a toggle input to the circuit, use 'Bit Switch' which will toggle its value with a double click
• Use 'Bit Display' component to see any single bit value. 'Digital Display' will show the output in digital format
• undo/redo, delete, zoom in/zoom out, and other functionalities have been given in the top toolbar for ease of circuit building
• Use start/stop clock pulse to start or stop the clock input of the circuit. Clock period can be set from the given 'set clock' button in the left toolbar
• Use 'plot graph' button to see input-output wave forms
• Users can save their circuits with .logic extension and reuse them
• After building the circuit press the simulate button in the top toolbar to get the output
• If the circuit contains a clock pulse input, then the 'start clock' button will start the simulation of the whole circuit. Then there is no need to again press the 'simulate' button
• If you are using linux platform then click on 'Linux(32 bit)' or if you are using then click on 'Windows(32 bit)'

Linux(32 bit)

Windows(32 bit)

Back

Back

1. Start the simulator as directed.
2. To design the circuit we need 4 full adder, 1 'RCA 4 bit' component, 12 Bit switch(to give input,which will toggle its value with a double click), 5 Bit displays(for seeing output), wires.
3. The pin configuration of a component is shown whenever the mouse is hovered on any canned component of the palette. Pin numbering starts from 1 and from the bottom left corner(indicating with the circle) and increases anticlockwise.
4. For a full adder input is in pin-5,6,8, output sum is in pin-4 and carry is pin-1
5. For a 'RCA 4 bit' input A0=pin-13 A1=pin-14 A2=pin-15 A3=pin-16, B0=pin-17 B1=pin-18 B2=pin-19 B3=20, C0=21, output S0=pin-12 S1=pin-11 S2=pin-10 S3=pin-9 Cout=pin-8
6. Click on the full adder component(in the Adder drawer in the pallet) and then click on the position of the editor window where you want to add the component(no drag and drop, simple click will serve the purpose), likewise add 3 more full adder(from the Adder drawer in the pallet), 1 'RCA 4 bit'(from the Adder drawer in the pallet,if it is not seen scroll down in the drawer), 12 Bit switches and 5 Bit Displays(from Display and Input drawer of the pallet,if it is not seen scroll down in the drawer).connect the Bit switches with the inputs and Bit displays component with the outputs.
7. To connect any two components select the Connection menu of Palette, and then click on the Source terminal and click on the target terminal. According to the circuit diagram connect all the components. After the connection is over click the selection tool in the pallete.
8. See the output, Bit switches are used to give input so that you can toggle its value with a double click and see the outputs with different inputs.

Circuit Diagram

Click here to download the older version of simulator

Click here to download the new version of simulator

OR

Launch the older version of Simulator

Launch the new version of Simulator

Once the simulator is downloaded, open the command prompt, then go to the directory where you have saved it using cd command and then give the following command to run the simulator:
java -jar coaSimulator.jar

Guideline to perform the experiment:Design of Wallace Tree Adder

1. Start the simulator as directed.
2. To design the circuit we need 4 full adder, 1 'RCA 4 bit' component, 12 Bit switch(to give input), 5 Bit displays(for seeing output), wires.
3. The pin configuration of a component is shown whenever the mouse is hovered on any canned component of the palette. Pin numbering starts from 1 and from the bottom left corner(indicating with the circle) and increases anticlockwise.
4. For a full adder input is in pin-5,6,8, output sum is in pin-4 and carry is pin-1
5. For a 'RCA 4 bit' input A0=pin-13 A1=pin-14 A2=pin-15 A3=pin-16, B0=pin-17 B1=pin-18 B2=pin-19 B3=20, C0=21, output S0=pin-12 S1=pin-11 S2=pin-10 S3=pin-9 Cout=pin-8
6. Click on the full adder component(in the Adder drawer in the pallet) and then click on the position of the editor window where you want to add the component(no drag and drop, simple click will serve the purpose), likewise add 3 more full adder(from the Adder drawer in the pallet), 1 'RCA 4 bit'(from the Adder drawer in the pallet,if it is not seen scroll down in the drawer), 12 Bit switches and 5 Bit Displays(from Display and Input drawer of the pallet,if it is not seen scroll down in the drawer).connect the Bit switches with the inputs and Bit displays component with the outputs.
7. To connect any two components select the Connection menu of Palette, and then click on the Source terminal and click on the target terminal. According to the circuit diagram connect all the components. After the connection is over click the selection tool in the pallete.
8. See the output, Bit switches are used to give input so that you can toggle its value with a double click and see the outputs with different inputs.

Circuit Diagram

Click here to download the older version of simulator

Click here to download the new version of simulator

OR

Launch the older version of Simulator

Launch the new version of Simulator

Once the simulator is downloaded, open the command prompt, then go to the directory where you have saved it using cd command and then give the following command to run the simulator:
java -jar Simulator.jar

Design of Wallace Tree Adder :

References :

Books:

1. Carry-Save Addition - Prof. Loh,CS3220 - Processor Design - Spring 2005,February 2, 2005
2. Digital Logic and Computer Design - M. Morris Mano. Pearson Education - Prentice Hall.
3. Digital Principles Foundation of Circuit Design and Application - Arun Kumar Singh. New Age Publishers.
4. The Art of Electronics - Paul Horowitz and Winfield Hill (1989). Cambridge University Press
5. Modern Dictionary of Electronics - Rudolf F. Graf (1999). Newnes

Web Sites:

• http://en.wikipedia.org/wiki/Wallace_tree
• NPTEL (e-learning courses from IITs and IISC)

Virtual Lab is an initiative of Ministry of Human Resource and Development(MHRD) under National Mission of Education through ICT to provide an interactive environment over the internet for creating and conducting different laboratory experiments by sharing the costly equipments and the resources.

For more information about the Virtual Lab,please visit http://www.vlab.co.in/

Developers of Computer Organization and Architecture Virtual Lab

• Dr. Chittaranjan Mandal
Professor, Computer Science & Engineering
Professor, Information Technology
IIT Kharagpur
• Gargi Roy
Senior Project Assistant
• Devleena Ghosh

Target Audience:

Under graduate students.

Courses Aligned With:

Digital Logic and Computer organization.

Pre-requisite Softwares:

• 32 bit java runtime environment and java 1.6 or above
• Recommended browser: mozilla firefox, google chrome

Feedback:

To give your feedback please visit the following link-

Sponsered by MHRD (NME-ICT) .

Tutorial on UI for lab:

Introduction:

1. The simulator contains a pallete on the right hand side. This pallete contains all the components and tools . Tools are used to act up on the components. Different tools:
   • Selection tool- used for selecting components
   • Marquee tool- used for selecting many components at a time by draggiung the mouse in the design area(editor).
   • Connection tool- used for connecting components
2. Components have been catagorized according to their functionality and put into different drawers in the pallete. The area under every drawer is scrallable, if you are unable to see all the components in a particular drawer just click on the area and scroll. Different drawers:
• Circuits- contains 8 and 16 terminal circuits and flow container which can hold other circuit components.
• Logic gates- contains all kinds of basic logic gates.
• Display and inputs- contains all kinds of component needed to give input to the circuit and displaying outputs of the circuit.
• Adders- contains different types of adder circuits.
• Sequential ckt- contains basic flipflops for designing sequential circuits.
• Other Components- contains different kinds of components like decoders, multiplexers, arithmetic logic units(ALU), memory elements(RAM cell) required to design combinational circuits.
3. To add the components to the editor select any component(first click on the selection tool then click on the desired compoent) then finally click on the position of the editor window where you want to add the component.
4. The pin configuration of a component is shown whenever the mouse is hovered on any canned component of the palette. Pin numbering starts from 1 and from the bottom left corner(indicating with the circle) and increases anticlockwise.
5. To connect any two components select the Connection tool in the palette, and then click on the Source terminal and click on the target terminal(no drag and drop, simple click will serve the purpose). After the connection is over click the selection tool in the pallete.
6. To move any components select the Selection Mode and drag the component after selecting it.
7. If needed select any component in the editor while designing your circuit and use Undo, Redo, Delete, Zoom in, Zoomout buttons to get corresponding functionalities. Open and Save options are under development.
8. As the automated clock is under development and the simulator is under modification for sequencial circuits, for the time being please use individual clock(Bit switch which toggle its value with a double click) for each flipflop.
9. The simulator is currently under modification for sequential circuits, now it is working properly for combinational circuits but may not give proper output for sequential circuits.

Description of Components:

1. Digital display: it can be used to give input and as well as to see the output in the decimal format, its right most terminal is the LSB(least significant bit) and the left most terminal is the MSB(most significant bit), in the editor after selecting a particular digital display you can use 'Increment LED' and 'Decrement LED' buttons in the top left corner of the simulator to increment and decrement its value respectively.
2. Bit display: it displays a single bit value.
3. V+: it gives 1 as input.
4. Ground: it gives 0 as input.
5. Bit switch: it gives 1/0 input, it toggels its value with a double click.

Testing process:

1. To test your circuit give some input(through Digital display or Bit switch or V+ or Ground), if you use the Digital display or Bit switch you can then give different input to you circuit through incrementing/decrementing the Digital display or double clicking the Bit switch, the other two gives constant inputs.
2. to see the output, connect Digital display or Bit display to the output terminals of your circuit.

Frequently Asked Questions:

What is virtual lab?

The Virtual Laboratory is an interactive environment for creating and conducting simulated experiments: a playground for experimentation. It consists of domain dependent simulation programs, experimental units called objects that encompass data files, tools that operate on these objects.

What are the advantages of virtual lab?

Virtual Logic Design and Computer Organisation lab enables students to perform FPGA based prototyping of experiments with support of a virtual environment. The primary need for virtualisation here is multifold.

1. Digital Logic and Computer Organisation are core courses in most of the Undergraduate Curricula of the entire Electrical Sciences Discipline ( Computer Science / Engg., Electronics, Electrical ] etc.
2. Many colleges/institutes cannot procure sufficient number of FPGA boards for their students.
3. Even when such FPGA boards are available, making them available round the clock is difficult.
4. Expert help is required to effectively use these FPGA boards and such help can be easily channeled through a virtual environment.
5. Helps to standardize the set of Experiments to a large extent.

What is eclipse platform?

Eclipse is a Java-based, extensible open source development platform. By itself, it is simply a framework and a set of services for building a development environment from plug-in components. Eclipse comes with a standard set of plug-ins, including the Java Development Tools (JDT).

Which framework is used to develop the application?

We have used the eclipse gef framework. The Graphical Editing Framework (GEF) allows developers to take an existing application model and quickly create a rich graphical editor.

What is platform independent application?

Applications that run under particular operating systems and/or particular hardwares are called platform dependent application whereas platform independent applications can run in any operating environment.

What are the experiments which can be performed by the Virtual Logic Design and Computer Organization lab?

The experiments that will be supported by this lab are given below:

1. Design of a ripple carry adder
2. Design of a carry-look-ahead adder
3. Design of registers and counters
4. Design of a wallace tree adder
5. Design of combinational multipliers
6. Design of a Booth’s multiplier
7. Design of an ALU
8. Design of memory units
9. Design of direct mapped cache
10. Design of associative cache
11. Design of combinational dividers
12. CPU design