Design and testing of systolic array multiplier using fault injecting schemes

Computer Science and Information Technologies
Vol. 3, No. 1, March 2022, pp. 1~9
ISSN: 2722-3221, DOI: 10.11591/csit.v3i1.pp1-9  1
Journal homepage: http://iaesprime.com/index.php/csit
Design and testing of systolic array multiplier using
fault injecting schemes
Kurada Verra Bhoga Vasantha Rayudu1
, Dhananjay Ramachandra Jahagirdar1
, Patri Srihari Rao2
1
Scientist’G’Head, Reliability Engineering Division, Research Centre Imarat, Kurmalguda, India
2
Department of Electronics and Communication Engineering, NIT Warangal, Hanamkonda, India
Article Info ABSTRACT
Article history:
Received Aug 20, 2021
Revised Dec 12, 2021
Accepted Jan 26, 2022
Nowadays low power design circuits are major important for data
transmission and processing the information among various system designs.
One of the major multipliers used for synchronizing the data transmission is
the systolic array multiplier, low power designs are mostly used for
increasing the performance and reducing the hardware complexity. Among
all the mathematical operations, multiplier plays a major role where it
processes more information and with the high complexity of circuit in the
existing irreversible design. We develop a systolic array multiplier using
reversible gates for low power appliances, faults and coverage of the
reversible logic are calculated in this paper. To improvise more, we
introduced a reversible logic gate and tested the reversible systolic array
multiplier using the fault injection method of built-in self-test block observer
(BILBO) in which all corner cases are covered which shows 97% coverage
compared with existing designs. Finally, Xilinx ISE 14.7 was used for
synthesis and simulation results and compared parameters with existing
designs which prove more efficiency.
Keywords:
BILBO
BIST
MISR
Reversible gates
SAM
This is an open access article under the CC BY-SA license.
Corresponding Author:
Kurada Verra Bhoga Vasantha Rayudu
Scientist’G’Head, Reliability Engineering Division, Research Centre Imarat
Vignyanakancha Po, Hyderabad-500069, Kurmalguda, India
Email: kvbvr1@gmail.com
1. INTRODUCTION
Many multipliers are used to achieve low power and high-speed performance, In DSP systems, most
of the DSP applications are designed for power dissipation and components used as multipliers [1]–[5] and to
perform various high-speed operations multiplications play a major role in winding up the design. Mainly
multiplication is an algorithm used at a structural level. Multi-dimension multiplication is done by the
systolic array multipliers, those multipliers are a sequence of channels and it’s a pipe lining process with a
linear arrangement. When the multiplication process happens, it stores the information itself and processes it
to the next pipeline level, and maintains a pipelining process, each block of the systolic array multiplier is
fixed and looks similar. The simultaneous process performs in systolic arrays which increases the speed of
the system and reduces the processing time with perfect efficiency of the output. Systolic array Multipliers
are used for sorting and convolution techniques.
In this paper, we developed a systolic array design with the new model gate which decreases the
delay and increases the speed of the operation, first of the multiplicand and multiplier are arranged in an
array structure, and from the both of each bit is collected and do multiplicand, and its processes to the later
pipeline stage, partial products, and carry generation done in the later stages. From the statement of the great
scientist Landauer energy is dissipated at each bit of lost when transmits data with a particular amount of
energy, the basic formula for calculating the loss of each bit of energy dissipated as KT*log2, T defines

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Comput Sci Inf Technol, Vol. 3, No. 1, March 2022: 1-9
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absolute temperature and K Defines Boltzmann’s Constant. Reversible logic proved that we can minimize the
dissipation of the heat by Charles Bennet [6], [7]. Reversible design is the future for developing circuits for
low power and high-speed operations with very few system designs used. The main structures of the
reversible gates are designed in such a way that the number of inputs is equal to the number of outputs. By
this, it improves the overall performance of the systems [8]–[10]. In this paper systolic array multiplier is
designed using reversible technology; it means all the components of the design use reversible gates to
achieve the low power targets. Most of the system designs are being developed by reversible gates but testing
was more complex and to reach the time to market it depends on the way of testing.
In the existing paper [11], [12] developed the systolic array multiplier with reversible gates, and
proposed a multiplier for 4x4 systolic array design which calculates partial products and passes the partial
products for carrying select generation, the testing to be done but simulated the design using the design tools
and verified only parts of the design through simulations. In this paper [13], [14] they have proposed a new
level of testing using BILBO logic where we can find the number of faults, but they have tested for Baugh
Wooley multiplier designs. Most of the Baugh Wooley designs are used for high-speed operations, and also
when we change the increased number of the bits for operations, we required more logic for the testing and
implementation. The researchers [15], [16] addressed fault analysis techniques for computing multipliers by
reviewing different methodologies of converting matrix algorithms to a predefined systolic array designs and
then introduces array structure of the systolic part designs which was originally designed by the Lang and
Moreno. Morghade et al. [17] Proved the design was correct by using the simulations and all the logic that
implemented was algorithms for multiplication, division and direct multiplications methods, have examined
various methods of testing they come up with LFSR technique which generates the random number of values
for testing and applied and got succeeded and then moved for shift register designs which actually increases
the area of the chip. The researchers [18]–[20] proposes a new method of approach for reducing the power
consumption on an irreversible array multiplier and also using the reversible logic designs for the systolic
array multiplier designs, which they expected to get high-end of the efficiency of the output in which
compared with existing they end up with good results and also tested with 90ns CMOS nanometer
technology. The researchers [21]–[24] which comes over a GF has made a bright application over the
security of the multiplications and developed systolic array multiplier design over GF multiplier designs with
full pattern generator using a six-bit counter and generate number of patterns required for the testing of the
system designs for GF multiplier designs where it increases delay in the circuit and in the proposed system,
we have overcome the issue of the delay removal of GF in the proposed system. The Proposed system of the
research is to design an advanced systolic array multiplier with a new modified gate and test using fault
injection method using BILBO logic for generating different patterns of test vectors.
2. RESEARCH METHOD
Nowadays many low-power applications use reversible gate designs for low area and power.
Because the logic present in reversible gates like no of input variables is equal to the number of output
variables [25] where the utilization of power is used equally for fan outs, it is used for low power relevance
designs. Quantum cost also reduces with the main logic involved in reversible designs. The majority plays an
important role in reducing power dissipation due to the garbage and constant inputs used, when the circuit
has garbage outputs power utilization is reduced due to which power loss is less. Reversible logic design
selected for the project for low power dissipation and the reversible gate has been modified and is used for
full adder design circuit, namely modified Islam gate shown in Figures 1 and 2. Modified Islam gate has 4
inputs and 4 outputs which output reflect as full adder model designs usage.
We have used controlled operational gate design which is used for getting full adder to carry select
block, COG gate has now inputs and outs are equal i.e., 3, where logic completely depends on the second and
third input variables, based on the status of that variables logic changes and works for full adder carrier
output. Mostly COG reversible designs used for low power circuits in DSP Application for having the
number of multiplier designs to get partial products intern to get resultant carry generation blocks, in our
project we defined for the usage of carrier output.
Figure 1. Reversible modified Islam gate Figure 2. Reversible controlled operational gate

Comput Sci Inf Technol ISSN: 2722-3221 
Design and testing of systolic array multiplier using fault … (Kurada Verra Bhoga Vasantha Rayudu)
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By Integrating the above two reversible gates MIG and COG we get a complete adder and
subtractor, which is used for systolic array multiplication, in systolic array multiplication it is used for
multiplication, the process will be briefed in section 2.2. Mostly reversible full adder in Figure 3 plays a
major role in any of the applications like video, medical, and many digital world systems
Figure 3. Reversible full adder /full subtractor
2.1. Systolic array multiplier cell block
Systolic array multiplier cell block is the special block for multiplication operation in which
integration of sub designs like COG, MIG, and a complete formation of full adder block used for getting the
resultant of the partial product of the design. For the function of the gate, the operation used the Toffoli gate
which perfectly fits to reduce the power of the circuit. Multiplier cell block starts by taking individual bits of
each of the Toffoli gate block as multiplicand and multiplier and generates the partial products with the usage
of the reversible full adder design block. It is also a pipelining process in the systolic array multiplication
model. Proposed full adder using reversible gates used for generating resultant and carry. Many of the
instances of the block are used for reducing the coding of the design and re-use method performed, when one
gets inputs other will be in the processing stage, and the Same way the process continues whole instances
gets inputs and generate sums and carries. We are using a 4-bit multiplication process in which 16 multiplier
cells are used for getting the full results of the systolic array multiplier. All the operations will be in the
pipeline process and scheduled with each block to perform to get the value of the assigned bit and send to the
other block and vice versa. Need to be very careful at the time of integrating the output of one block carry to
the other multipliers cell block as shown in Figure 4, it may mislead the design for the wrong operation, it
should be according to Endian format righted to left addition or connecting of the designs to the previous
block of the carry bit.
Figure 4. Multiplier cell block
2.2. System design & testing method
Proposed system systolic array multiplier design and testing are to verify the multiplier corner cases
as it is very complexing in finding the faults and compare the faults with existing system designs and
improvement over the area, speed, power and find the faults. The proposed system mainly consists of four
main blocks DUT, GRM, BILBO, and a checker as shown in Figure 5. Design under test which is proposed
systolic array design, where mainly multiplication process goes on, Systolic Array multiplier developed using
reversible gates and compared to the existing design we have proposed a new gate which performs faster than
existing systolic array multiplier design. Multiple data bits are used for multiplication purposes. Mainly in
systolic array multiplier design consists of 4 stages, whereas in 3 stages carry generated by the multiplier cell
blocks were moved to the other stage multiplier cellblock design, whereas in stage 4 side by side the carrier
moves to generate the final results of the multiplier block. Golden reference models are used for many of the

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testing and verification SOC designs, GRM the coding part can be user-defined and it can be of any
language, but it should work exactly as DUT, In this project reference model is taken as VHDL model for
easy understanding of the flow of the multiplier at each stage of the block, when BIBLO generates the
patterns, GRM also picks up the values and used for generating the outputs, the main focus is to get injected
with the sum of the faults into the reference design, with the BILBO logic to get compared with the signature
values to get the exact faults where has injected.
Figure 5. The proposed system with DUT and all required components
DUT Circuit which is used for testing could be placed in middle of the BILBOs, which are mostly
working in the relevant modes as Linear feedback shift register and MISR modes. To test the circuit of SAM,
a 4-bit multiplier design and an 8-bit BILBO were used. YAG gate design [26] is used for generating sum
and product terms simultaneously. Input signal always in SCAN Mode If the BILBO uses LFSR mode, it
generates the no of patterns required for the multiplier and the multiplier takes the inputs and intakes the
output to the BILBO, which performs the operations to generate the signature like MISR Mode. If there is a
signature produced for no-fault injection circuits called a good signature. Now the process begins will inject
the faults in the design and generate the LFSR mode and gets patterns and generates the signature and that
signature compares with the existing signature. If both matches, it proves testing did not happen correctly or
fault is not identified by BILBO, if not BILBO detected fault. Checkers are most common in verification
areas; checkers are named as scoreboard logics in which the two different data received from two blocks are
to be compared and verified whether matched or mismatched to get the resultant of usage of DUT. Checkers
are coded in the environment and tested the SAM circuit by injecting faults and by not injecting faults. In this
project, a comparison is done between GRM and DUT outputs and storing the resultant for future usage.
As the process starts BILBO starts generating the patterns using modes, those patterns carried out
within the environment and given to reversible systolic array multiplier, it processes the number of patterns it
receives as it works as a pipeline stage multiplier, it generates the resultant and gives to the checker logic
whereas simultaneous process happens in reference model used and also BILBO starts generating patterns at
the same time, from the environment we are injecting the faults, one time stuck at 0/1 fault injected, and we
see resultant is wrong than expected as in the Same BILBO logic gives a significant value as false, then the
design will be corrected if BILBO passes as good signature it is failed to verify the design, hence the design
should be modified depends on logic preferred.
Hence, the process of testing continues with various injections of faults, and results are compared
using a checker. According to the research, many BIST architectures had been proposed but BILBO has
played a vital role in the present generation as in SAM Project, we can configure it as an input generation of
patterns in a full environment as shown in Figure 6, and also can be configured as output analyzer.
Depending on the selection of inputs like b1 and b2, the mode can be selected. Various fault models
discussed in [27]–[29] Compare to all techniques BIST technique is more popular because of its low power
and less time of execution, complex designs also get testing done very fast, BILBO called LOGIC BIST
because of using BIST as the main component in it and used for operating modes. Mainly in this project, a
reversible multiplier is used for testing using the reversible BILBO logic applied for finding two main faults
SAF, MSAF, and MGF faults of the design. Stuck at faults are rare faults that occur in designs and can be
more complexes to find the faults whether to zero or one, Multiple stuck at faults also a rare finding of faults
in conventional designs and Missing gate fault changes the output of the design, finding these types of faults
are the most important nowadays to make fault free system designs [30], [31].

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Figure 6. Full environment and testing with proposed systolic array multiplier using fault injection schemes
3. RESULTS AND DISCUSSION
Figure 7 shows the systolic array multiplier resultant using the new modified Islam gate and the
resultant can be calculated from the below fig as 1111*1111=011100001. From Figure 8 we can say that
various patterns have been generated for the Sam circuit which gets resultant true as it is mentioned in
decimal 14*15=210. Internal blocks of the design gates output resultant are shown in Figure 9.
In Figure 10, the concept of injection logic tried to inject the faults by missing some of the gates in
the design which resulted in missing gate fault but here we can see the output does not break because of the
reversible logic gates usage. Figure 11 shows the pattern generated from BILBO logic of LFSR mode, which
generates random patterns as shown.
From Figure 12 and comparison values generated from the BILBO logic which proves stuck at fault
findings at nearest value, as the design gets tested and compared with the existing signature after injecting
faults.
Figure 7. Resultant of reversible systolic array multiplier using pattern generator from BILBO logic design
Figure 8. Resultant systolic array multiplier
Figure 9. Resultant of SAM internal blocks COG and MIG gates

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Figure 10. Resultant of missing gate fault
Figure 11. Resultant of BILBO LFSR mode
Figure 12. Resultant of BILBO MISR mode signature comparison
Finding test vector of the resultant at stuck at 0/1 is FAILED----The output is correct at required places
x1=1, x2=0, x3=0, x4=1, x5=0, scan_in=1, out=1, 3100
Finding test vector of the resultant at stuck at 0/1 is PASSED
x1=0, x2=0, x3=1, x4=0, x5=0, scan_in=0, out=0, 3200
x1=1, x2=0, x3=0, x4=0, x5=0, scan_in=0, out=0, 3300
x1=0, x2=1, x3=1, x4=0, x5=0, scan_in=0, out=1, 3400
x1=1, x2=0, x3=0, x4=1, x5=0, scan_in=1, out=0, 3500
x1=0, x2=0, x3=1, x4=0, x5=0, scan_in=0, out=1, 3600
x1=1, x2=0, x3=0, x4=0, x5=0, scan_in=0, out=0, 3700
x1=0, x2=1, x3=1, x4=0, x5=0, scan_in=0, out=0, 3800

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x1=1, x2=0, x3=0, x4=1, x5=0, scan_in=1, out=1, 3900
x1=0, x2=0, x3=1, x4=0, x5=0, scan_in=0, out=0, 4000
Table 1 and Table 2 have been shown a comparison of different multipliers for fault analysis of
conventional and proposed design and also fault analysis at stuck-at faults, table values are collected using
synthesis process of Xilinx ISE, where we have used vertex family for FPGA designs and improved the
execution time unit.
Table 1. Comparison of multipliers from BILBO logic
Fault analysis Conventional multiplier [10] Proposed multiplier
Good signature 200 200
No of faults 138 138
No of faults detected 130 134
Fault coverage 96% 97%
Table 2. Comparison of multipliers after synthesizing the design using XILINX ISE 14.7
Local utilization Conventional multiplier [10] Proposed multiplier
No of slices 76.11% 70.2%
No of 4 input LUTs 26% 25%
Time delays 28.24% 28%
Area covered 75% 68%
4. CONCLUSION
Compared to the existing system designs, we proved that the design of the modified gate of systolic
array multiplier design works faster because of reversible gate which has equal no of inputs and outputs
which process the information faster and used for many low power high-speed applications. There is much
scope to optimize the designs using the new reversible gates implementation. The proposed MIG gate
reduces the gate count by 10% compared to the conventional designs and all other parameters to optimization
mark. Most efficient testing was also done for SAM circuit to find the convenient faults as SAF and MGF
preferably, we achieved coverage of patterns generation tested as 100%. Moreover, BILBO logic is
implemented and is used for finding various faults for various system designs. Fault coverage using BILBO
logic achieved 97% higher than the convention system designs. Future designs of SOC or subsystems can
integrate and use for the detection of fault blocks of the design.
ACKNOWLEDGEMENTS
The authors would like to thank Shri B H V S N Murthy, DS &Director, RCI and Dr. Bheema Rao,
HOD, ECE Dept., Present HOD Dept ECE Prof L Anjaneyulu and also DRC members NITW for their
constant encouragement, valuable suggestions, and support for carrying out this work as a part of my Ph.D.
work.
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BIOGRAPHIES OF AUTHORS
Kurada Verra Bhoga Vasantha Rayudu graduated from Institution of
Electronics and Telecommunication Engineers (IETE), New Delhi during Dec 1990 and
obtained MS (Electronics &Control) from BITS, Pilani. Served as Scientist up to 2002 at ISRO
Satellite Centre and currently as Scientist at Research Centre Imarat (RCI), DRDO, Hyderabad
in R&QA activities of MRSAM, LRSAM, PDV Mk-02(Mission Shakti ASAT) Missile and
Weapon Systems and related Avionic Systems. Contributed significantly in Parts Management,
Qualification, Testing, Failure Analysis, reliability Analysis & Screening Policy of Electronic
Components & Systems for Aerospace Applications. Planned and Played Key role for ISO
9001:2015 Certification and Aerospace Quality Management System AS 9100:2016
certification to RCI, Hyderabad. His Research Interests include VLSI Testing, VLSI Fault
Simulation, Modeling & Diagnosis, Reliability Analysis, Failure Analysis, Quality
Management System Certifications, applications of ANN, GA, SVM for optimization etc.
Received Lal C Verman Award (2015) from IETE, New Delhi for significant contributions in
Quality & Reliability assurance of Missile Systems. He can be contacted at email:
kvbvr1@gmail.com
Dhananjay Ramachandra Jahagirdar received his B.E. degree in Electronics
Engineering in 1990, from Govt. College of Engineering, Amravati University, Maharashtra,
India. He received M. Tech. in Microwave Engineering in 1992, from Indian Institute of
Technology, Kharagpur, West Bengal, India. He was a Research Assistant at Sponsored
Research and Industrial Consultancy at IIT, Kharagpur. Later, he joined Antenna Products
Division of Electronics Corporation of India Ltd, Hyderabad. He obtained Ph. D. in 1997 from
the Department of Electronics and Computer Science, University of Southampton, UK. He
received scholarship from the Commonwealth Scholarship Commission UK to pursue PhD. He
joined Research Centre Imarat, DRDO, Hyderabad in May 2000. He has won ‘Best Paper
Award’ at the University of Leeds, UK organized by IEEE UKRI section. He has received
Prof. S.K. Mitra memorial award for ‘Best research-oriented paper’ from IETE in 2002. He
received young scientist award at IETE-IRSI International Radar symposium Bangalore in
2005. He also received laboratory scientist of the year award for 2006. He is a Fellow of IETE
and senior member of IEEE, Antennas and Propagation Society and Microwave Theory and
Techniques Society. He is also a member of URSI. Recently he has been listed in Marquis’
Who’s who in the world. His area of interest is microwave antennas and arrays for radars. He
can be contacted at email: DR.Jahagirdar@rcilab.in
Patri Srihari Rao is working as Assoc Prof at NIT Warangal in the dept. of ECE.
His Research interests include RFIC Design, VLSI Testing, Fault Diagnosis Analog/digital IC
design, VLSI Testing Fault Diagnosis Analog/Digital IC Design, DSP Architecture, Analog
LDO’s. He has published numerous technical papers in Reputed international
journals/Presented in Conferences. He has conducted various training courses and
Workshops/Seminars at National/Internal Level and guided many PhD students. He can be
contacted at email: patri@nitw.ac.in

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