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1. Artificial Neural Networks are electronic models based on the neural... (DACS Store, Artificial Neural Networks ...
Session B-T2-3
MODELING AND VERIFICATION OF DIGITAL LOGIC CIRCUIT
USING NEURAL NETWORKS
Dr. Reza Raeisi
Indiana State University, Terre Haute, Indiana; Email: [email protected]
1. INTRODUCTION
Artificial Neural Networks are electronic models based on the neural structure of a human brain
(DACS Store, Artificial Neural Networks Technology). Neural Networks have plethora of
applications such as in process control, financial forecasting, voice recognition, pattern
recognition, medical diagnosis and many other areas (Principe, et al; 2000)
The problem of interest to us consists of first, using artificial neural networks for modeling
digital logic circuits based on truth table, logic diagram or Boolean logic expression and second
to contribute specific method and understanding of hardware aspects of neural networks for
modeling and verification of digital logic circuits.
Neural networks are analogous to digital logic circuits because they produce outputs to specific
inputs. But unlike digital logic, a neural network can be trained and is dynamic. Its output values
can change corresponding to its inputs every time it is trained.
In order to test the digital logic, a neural network model is built with specific parameters that
could be trained and tested. This neural network model has the ability to change dynamically its
logic behavior through user inputs.
2. METHODOLOGY
For the purpose of testing digital logic circuits, Java Object Oriented Neural Engine (JOONE)
with back-propagation algorithm is used. In neural network software packages, a neuron is called
a processing element. There are three layers in a neural network, namely, input, hidden and
output layer. The back-propagation algorithm is the most widely used algorithm. It begins by
feeding input values forward through the network. It calculates the output error and propagates it
backward through the network in order to find errors for neurons contained in hidden layers.
This process is repeated until the neural network output falls within the minimum tolerance
value.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
An example of a back propagation to test full adder data is as shown in Figure 1. The required
data Input A, Input B, Input C is fed to the neural network. The neural network needs to learn
this data by experience. It gives the Sum and the Carry error which is then compared with the
desired values. It adjusts the weights that connect different nodes in the layers to give the desired
output. This process takes place until the error is within the minimum tolerance value. The same
concept is used to model wide variety of combinational logic circuits like multipliers,
multiplexers and demultiplexers for different input values.
Figure 1: An example of a back-propagation network to model a full adder data.
Joone is a neural net framework written in Java. It's composed by a core engine, a GUI editor
and a distributed training environment. Neural network that tests digital logic is built using the
GUI editor. The GUI editor is a Graphical User Interface to visually create, modify and test the
neural net. The features of the GUI editor are:
• Creation of any architecture, according to the nature of the core engine
• Neural net save and restore from a file system
• Setting of all parameters for each component of the neural network
• Checking for the correctness of the neural network
• Use of pre-processing and control plug-ins
• A complete macro editor to define and control the scripting code
• A control centre to train the neural network
• A charting component to visualize the output values of the neural network
• A flexible environment based on XML files to add new layers, synapses, etc. to the
editor's palette
• Exporting of the embedded neural network to distribute and run it on external
applications
See (Marrone. P, Java Object Oriented Neural Engine, The GUI editor).
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
This program generates a truth table for a particular logic circuit in order to train its network. The
user can enter the data and try to train and test the network until the optimum values for the
network are reached. The flowchart for the training and testing the neural network that uses a
back-propagation algorithm is as shown in the Figure 2.
Truth table is
evaluated
Enter truth table
The user may
enter the number
of hidden layers,
momentum,
learning rate
Neuron weights
are randomized
Neural network
is being built
Neural network
is being trained
User enters one
input pattern for
testing
Exhaustive
testing
Testing results are
input to a file
Testing result is
being displayed
Program exit
Figure 2: Flowchart for training and testing of neural network using back-propagation algorithm.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
3. TRAINING AND TESTING
For training and testing different digital logical functions like AND, XOR, full adder and other
combinational logic circuits, a neural network model is built that employs a back-propagation
algorithm. The neural network dynamically adjusts itself depending upon the size of the network.
The number of input variables determines the number of input layer neurons. The number of
hidden layers is predicted based on the performance of the network and there is no particular
criterion for choosing the number of hidden layers. Again, the number of output variables
determines the number of output layer neurons. The input and the expected output values are
entered in a text editor. The other parameters that also affect the performance are the momentum,
learning rate, and epoch. Epoch is the number of times the text file is processed. Momentum
determines the speed at which the network runs and the learning rate is the rate at which the
neural network learns all the input and the expected output values. After entering all the values
of the variables, the network is first trained until it reaches its minimum acceptable RMS error
(less than 0.01). If the network has an RMS error less than 0.01, it is then tested for an epoch of
1. The results are displayed in the text editor file specified in the JOONE software. This process
is repeated with different network parameters. A logic 1 is assigned to any output value between
0.5 and 1. A logic 0 is assigned to any output value between 0 and 0.5.
Figure 3 shows the input and expected outputs entry through a notepad file for a full adder
circuit.
Figure 3: Full Adder input entry in the notepad file.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
After the inputs and the expected outputs are entered in the notepad, a full adder circuit is built
using the GUI editor that is available in JOONE software. This is as shown in Figure 4. It
consists of an input layer with three inputs, an output layer with two outputs for sum and carry
and a hidden layer which is chosen through trial and error method. The training set and the
desired data are entered through the file input layers. The teacher layer helps the neural network
to learn in order to reach the expected value of outputs.
The method of building these blocks are explained in the help menu provided at the top of the
neural editor.
Figure 4: Full adder training using Joone neural net editor.
After the neural network is built using the standard GUI editor, the desired parameters are
entered for the training to take place. An example is as shown in the Figure 5.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
Figure 5: Parameter entry for full adder training.
The neural network is trained until the RMSE is close to zero. Once the RMS error becomes
approximately zero, the network is ready for testing. The full adder testing is as shown in Figure
6.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
Figure 6: Full Adder testing.
The testing is carried out using a file output layer that helps in storing the expected values. The
parameters are again entered with epoch of 1 and learning is set to false. This is shown in Figure
7.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
Figure 7: Parameter entry for testing.
The network is tested for best results. The results are displayed on the notepad file stored in the
file output layer as shown in Figure 8.
Figure 8: Results of testing are verified using a notepad file.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
4. RESULTS
The table 1 shows the output of a sample run of the JOONE program for a full adder. The inputs
and the desired outputs are entered and the neural network is tested. The root mean-square error
is then noted for different momentum and learning parameters. In this case, the network consists
of 3 hidden neurons and epoch is set to 1000. The momentum M specified by the user increases
from 0.2 to 0.6 vertically and beta represents the learning rate. Choosing right values of
momentum and learning rate improved the performance of the neural network.
Table 1: RMSE after 1000 epochs.
M/Beta
0.2
0.3
0.4
0.5
0.6
0.2
0.006439
0.006429
0.006182
0.005902
0.005612
0.3
0.006435
0.006395
0.006125
0.005840
0.005548
0.4
0.006398
0.006374
0.006327
0.005770
0.005476
0.5
0.006354
0.006309
0.006049
0.006226
0.005392
0.6
0.006301
0.006230
0.005956
0.005669
0.006080
5. FUTURE RESEARCH
With the rapid development of VLSI, reconfigurable computing and FPGA make fast massively
parallel computations more affordable and neural networks with any architecture can be easily
designed. Since most of the signals in real world are analog in nature, many researchers have
developed analog neural networks (Valle, et al., 1995; Valle, et al., 1996; Brea, et al; 1998). But
problems like noise, power supply instability, cross talk and temperature variations become
inevitable. Due to these reasons, digital logic is used as an alternate solution. With the substantial
advances in FPGA technology, programmable logic provides a new way of designing and
developing systems. The research would help in understanding hardware aspects of neural
networks for modeling and verification of digital logic circuits.
6. DISCUSSION AND CONCLUSION
This paper proposed a neural network for designing digital logic circuits using Joone software.
The software testing provided expected results. This project not only helped the students to grasp
the basics of neural network and digital logic gates but also to solve wide variety of digital logic
design problems using neural models. Motivated by these results, future investigations will
address the design and testing of neural networks using hardware. Today, hardware testing is
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
gaining popularity. Neural networks are inherently massively parallel in nature (Nordstrom, et
al., 1992) which means that they lend themselves well to hardware implementations, such as
Field programmable arrays. With the use of reconfigurable hardware, the performance of the
neural networks can be improved. This advantage will be exploited in the test generation of
combinational and sequential circuits using neural networks.
REFERENCES
Brea, V.M., Vilariño, D.L., and Cabello, D. (1998). Active Contours with Cellular Neural
Networks: An Analog CMOS Realization, Signal Processing and Communications. (J. RuizAlzola ed.), pp.419-422, IASTED/Acta Press.
DACS Store, Artificial Neural Networks Technology,
http://www.dacs.dtic.mil/techs/neural/neural2.html.
Marrone. P, Java Object Oriented Neural Engine, GUI Editor,
http://www.jooneworld.com/docs/guiEditor.html.
Nordstrom, T., Davis, E.W., and Svensson, B. (1992). Issues and applications driving research
in non-conforming massively parallel processors. (In I. D. Scherson, editor, Proceedings of
the New Frontiers, a Workshop of Future Direction of Massively Parallel Processing), pp.
68-78. McLean, Virginia.
Principe, C.Jose., Euliano, R.Neil., and Lefebvre, W.Curt. (2000). Neural and Adaptive Systems:
Fundamentals Through Simulations, John Wiley and Sons.
Valle, M., Chiblé, H., Baratta, D., and Caviglia, D.D. (October, 1995). Evaluation of synaptic
multipliers behavior in the back propagation analog hardware implementation, vol. 2, pp
357-362. Proceedings of ICANN'95 Fifth International Conference on Artificial Neural
Networks, Paris.
Valle, M., Caviglia, D.D., and Bisio, G.M. (1996). An experimental analog VLSI neural network
with on-chip back-propagation learning, Analog Integrated Circuits & Signals Processing,
vol. 9, pp. 25-40. Kluwer Academic Publishers, Boston.
American Society for Engineering Education
April 1-2, 2005 – Northern Illinois University, DeKalb, Illinois.
2005 IL/IN Sectional Conference
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