Design of 64 bit error tolerant adder

INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July-December (2012), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print) IJARET
ISSN 0976 - 6499 (Online)
Volume 3, Issue 2, July-December (2012), pp. 235-247
© IAEME: www.iaeme.com/ijaret.asp
©IAEME
Journal Impact Factor (2012): 2.7078 (Calculated by GISI)
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DESIGN OF 64 BIT ERROR TOLERANT ADDER
1A.S.Prabhu, 2V.Elakya,3A.Andamuthu and 4 N.Vignesh
1 Asst Prof, VLSI Design, EBET Group of Institutions, Kangayam, Tamil Nadu, India.
Mail id: prabhu.mevlsi@gmail.com
2 Asst Prof, VLSI Design, Angel College of Engineering and Technology, Tirupur, Tamil Nadu, India.
Mail id: elakya17@gmail.com
3
Asst Prof, VLSI Design, Muthayammal Engineering College, Rasipuram, Tamil Nadu, India.
Mail id : andamuthuece@gmail.com
4 Asst Prof, VLSI Design, Karpagam College of Engineering and Technology, Tamil Nadu, India.
Mail id : vickee76@gmail.com

ABSTRACT

Adders are the core element of complex arithmetic operations like addition, multiplication, division,
exponentiation etc. In most of these systems adder lies in the critical path that affects the overall speed of
the system. This project introduces the design of low power error tolerant adder which acquires less area
with the lowest transistor count. Enhanced performance of the proposed Error Tolerant adder in terms of
power makes it suitable for portable image processing applications where minimum percentage of error
is tolerable. The low power error tolerant adder circuit design and the simulation have been carried out on
T a n n e r EDA tool. The result shows that t h e proposed low power error tolerant adder is an
efficient adder cell with less MOS transistor count that reduces the high power consumption and it
considerably increases the speed.

Index Terms—Adders, Error Tolerant adder, low power, error tolerant

INTRODUCTION
The design of error tolerant adder consists of accurate part and inaccurate part. in accurate part the
conventional ripple carry adder is replaced by the ripple carry adder designed using 8 transistor full
adder. In the inaccurate part the 3 transistor XOR logic is used in the modified XOR gate. The power
comparison is made between the existing design and the proposed method [2].
PROPOSED METHOD OF ETA BLOCK DIAGRAM
The block diagram of the hardware implementation of such an ETA that adopts our proposed
addition arithmetic is provided in Figure 4.1. This most straightforward structure consists of two parts: an
accurate part and an inaccurate part. The accurate part is constructed using a conventional adder such
as the RCA. The carry-in pin of this adder is connected to ground. The inaccurate part constitutes two
blocks: a carry-free addition block and a control block. The Control block is used to generate the control

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signals, to determine the working mode of the carry-free Addition block. A 64-bit adder is used as an
example for illustration of the design methodology and circuit implementation of an ETA [1].

Figure 1: Hardware Implementation of the Proposed ETA.

DESIGN OF 64 BIT ERROR TOLERANT ADDER

Strategy of Dividing the Adder
The first step of designing a proposed ETA [2] is to divide the adder into two parts in a specific
manner. The dividing strategy is based on a guess- and-verify stratagem, depending on the requirements,
such as accuracy, speed, and power. First, we define the delay of the proposed adder as Td = max (Th,
Tl), where Th is the delay in the accurate part and Tl is the delay in the inaccurate part. With the
proper dividing strategy, we can make Th approximately equal to Tl and hence achieve an optimal time
delay. With this partition method defined, we then check whether the accuracy performance of the adder
meets the requirements preset by designer/ customer. This can be checked very quickly via some
software programs. For example, for a specific application, we require the minimum acceptable
accuracy to be 95% and the acceptance probability to be 98%. The proposed partition method
must therefore have at least 98% of all possible inputs reaching an accuracy of better than 95%. If
this requirement is not met, then one bit should be shifted from the inaccurate part to the accurate
part and have the checking process repeated. Also, due to the simplified circuit structure and the
elimination of switching activities in the inaccurate part, putting more bits in this part yields more
power saving. Having considered the above, we divided the 64-bit adder by putting 24 bits in the
accurate part and 40 bits in the inaccurate part. Design of the Accurate Part

In our proposed 64-bit ETA [1], the inaccurate part has 40 bits as opposed to the 24 bits used in
the accurate part. The overall delay is determined by the inaccurate part, and so the accurate part need
not be a fast adder. The ripple-carry adder, which is the most power-saving conventional adder[7],
has been chosen for the accurate part of the circuit. The conventional ripple carry adder is
replaced by the ripple carry adder designed using 8 transistor full adder. The power is drastically
reduced by using 8 transistor full adders [8].

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Design of the Inaccurate Part
The inaccurate part is the most critical section in the proposed ETA [1] as it determines the
accuracy, speed performance, and power consumption of the adder. The inaccurate part
consists of two blocks: the carry free addition block and the control block. The carry-free addition
block is made up of 40 modified XOR gates, and each of which is used to generate a sum bit. The block
diagram of the carry-free addition block and the schematic implementation of the modified XOR gate
are presented in Figure 1. In the modified XOR gate [6], three extra transistors, M1, M2, and M3,
are added to a 3 transistor XOR gate. CTL is the control signal coming from the control block of Figure
2 and is used to set the operational mode of the circuit. When CTL = 0, M1 and M2 are turned on, while
M3 is turned off, leaving the circuit to operate in the normal XOR mode. When CTL = 1, M1 and
M2 are both turned off, while M3 is turned on, connecting the output node to DD, , and hence
setting the sum output to “1”.

Figure 2: Carry-Free Addition Block. (a) Overall Architecture and (b) Schematic Diagram of a
Modified XOR Gate.

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The function of the control block is to detect the first bit position when both input bits are “1,”
and to set the control signal on this position as well as those on its right to high. It is made up of 40
control signal generating cells (CSGCs) and each cell generates a control signal for the modified XOR
gate at the corresponding bit position in the carry-free addition block. Instead of a long chain of 40
cascaded GSGCs [3], the control block is arranged into ten equal-sized groups, with additional
connections between every two neighboring groups. Two types of CSGC, labeled as type I and II in
Figure 2 (a) are designed, and the schematic implementations of these two types of CSGC are provided in
Figure 2(b). The control signal generated by the leftmost cell of each group is connected to the input of
the leftmost cell in next group. The extra connections allow the propagated high control signal to “jump”
from one group to another instead of passing through all the 40 cells.

Figure 3: Control Block. (a) Overall Architecture and (b) Schematic Implementations of CSGC.
3T XOR Gate
The design of 3T XOR gate is shown in figure 4. The heart of the design is comprises of two
PMOS and one NMOS. The output signal for inputs AB= 01 and 11 will be complete. Both M2 and M3
will be on and will pass a poor “HIGH” signal level to the output for AB= 10, the reason is that when
M2 and M3 will be on the resistance of both devices will come in parallel and the total resistance will
decrease which will lead to the degradation in output voltage and as the aspect ratio of M2 is larger
than that of M3, the voltage at OUT terminal will be reflected as per the functioning of transistor M2.
However, the threshold drop occurs across M2 for AB=00 and consequently the output Y degrades with
respect to the input. The voltage degradation due to threshold drop can be minimized considerably by
increasing the W of M3.

Figure 4: 3T XOR Gate

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Power Consumption in Adders

Addition is a common operation in circuits designed for portable equipment and is typical of the
digital processing carried out in computer systems. In CMOS circuits most of the energy consumed is
due to switching activity[6], with the number of nodes in the circuit, the stored energy per node
and the number of switching operations per second all contributing to the total power consumption.
Power consumption was paid more and more attention to by IC designers. The motive of low
power design comes from two reasons: For those chips used in products supplied by battery, such as
portable computers and hand-held devices, lower power consumption is one of the key features
surpassing their competitors [2]With the steadily increasing of chip’s capacity and density, low power
consumption becomes a vital feature for chip’s functionality and reliability. High power density will
make chip’s temperature increasing, thus cause path delay increasing and problem of metal immigration
Building low power VLSI system has emerged as significant performance goal because of the fast
technology in mobile communication and computation. The advances in battery technology have not
taken place as fast as the advances in electronic devices. So the designers are faced with more constraint;
high speed[4], high throughput and at the same time, consuming as minimal power as possible.
The goal is to extend battery life span of portable electronics is to reduce the energy expended
per arithmetic operation, but low power consumption does not necessarily result in low energy
dissipation. To execute an arithmetic operation, a circuit can consume very low power by clocking at
extremely low frequency but it may take a very long time to complete the operation. We measure the
energy consumption by the product of average power and worst case delay (power delay-product).Thus
ETA is found to have less delay and have less power consumption [2].

IMPLEMENTATION OF 64-BIT ETA
The simulation results of 64-bit ETA are obtained using Tanner EDA tool.
Comparative analysis on the error tolerant adders has been done.

239


Figure 5: Design of Accurate Part of Existing Method
Figure 5 shows the design of accurate part of existing method. The design is created using S-
Edit in Tanner. The ripple-carry adder, which is the most power-saving conventional adder, has been
chosen for the accurate part of the circuit [5], [7]. Among the 64 bits input the first 24 bits are given to
Figure 5 shows the design of accurate part of proposed method. The ripple carry adder is designed
using 8 transistor full adder.

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Figure 6: Design of Accurate Part of Proposed method

Design of existing modified XOR block using conventional XOR gate is shown in Figure 7. In
the modified XOR gate, three extra transistors, m1,m2, and m3, are added to a conventional XOR
gate. CTL is the control signal coming from the control block.

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6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 2, July December (2012), © IAEME
July-December

Figure 7: Design of Existing Modified XOR Block using Conventional XOR Gate

Figure 8 shows the waveform of existing modified XOR block using conventiona XOR gate
ntional
the wave form is viewed using tanner W-Edit. The inputs are A, B and CTL signal [6] and
corresponding SUM output is obtained.
btained.

242


Figure 8 : Waveform of Existing Modified XOR Blok using Conventional XOR Gate

Design of existing modified XOR block using conventional XOR gate is shown in Figure 9. In
the modified XOR gate, three extra transistors, m1,m2, and m3, are added to a 3 transistor XOR
gate. Figure 10 shows the wave form of design of proposed modified XOR block using 3T XOR gate.
The inputs are A, B and CTL [2] signal and corresponding SUM output is obtained[6]. The wave form is
viewed using tanner W-Edit.

Figure 9: Design of Proposed Modified XOR Block using 3T XOR Gate

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Figure10: Waveform of Proposed Modified XOR Block using 3T XOR Gate

Figure 11 shows the design of inaccurate part of existing method. The inaccurate part
consists of two blocks: the carry free addition block and the control block. The carry-free addition block
is made up of 40 modified XOR gates [8], [7].

Figure 11: Design of Inaccurate Part of Existing Method

Waveform of inaccurate part of existing method is shown in figure 12. Among the total 64
bits input, the last 40 bits are given as input to the inaccurate part and corresponding sum output is
obtained. The wave form is viewed using tanner W- Edit.

244


Figure 12: Waveform of Inaccurate Part of existing method

Figure 13 shows the design of inaccurate part of proposed method. The design is created
using S-Edit in Tanner. The carry-free addition block is made up of 40 modified XOR gates. In the
modified XOR gate, three extra transistors, M1, M2, and M3, are added to a 3 transistor XOR gate.

Figure 13: Design of Inaccurate Part of Proposed method

Figure 10 shows the wave form of inaccurate part of proposed method. Among the
total 64 bits input, the last 40 bits are given as input to the inaccurate part and corresponding sum
output is obtained. The input bits are A0 to A39, B0 to B39,CTL0 to CTL39[6] and the outputs are S0
to S39.The wave form is viewed using tanner W-Edit.

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Figure 14: Waveform of Inaccurate Part of Proposed method

Table 1 shows the 64 bit error tolerant adder power comparison. The results of the comparative
analysis reveal that the performance of the proposed Low Power Error Tolerant Adder consumes least
power and acquires least area.

Table 1: Power Comparison of 64 Bit Error Tolerant Adder

Accurate Part
Inaccurate Part
(Ripplecarry adder)

Power Transistor Power Transistor
count count

Existing 53.46 1454 11.923 672
Method 0mW mW

Proposed 13.06 854 25.00 192
Method 8 mW nW

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Chart 1: Power Comparison Chart of 64 bit Error Tolerant Adder

Chart 1 shows the power comparison chart using the power results from tanner simulation. It is observed
that power is reduced when using proposed low power error tolerant; adder consumes low power consumption
and high-speed performance is more important than accuracy. Few such applications are in Digital Image
processing and DSP architectures for portable devices such as cell phones and laptops.

REFERENCES

[1] Ning Zhu, Wang Ling Goh, Weija Zhang, Kiat SengYeo, and Zhi Hui Kong,“ Design of low
power high-speed truncation- error-tolerant adder and its application in digital signal processing
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10.1109/TVLSI.2009.2020591,August 2010.
[2] A. B. Melvin, “Let’s think analog,” in Proc. IEEE Comput. Soc. Annu.Symp , pp. 2–5
,VLSI, 2005.
[3] J. E. Stine, C. R. Babb, and V. B. Dave, “Constant addition utilizing flagged prefix
structures,” in Proc. IEEE Int. Symp. Circuits and Systems (ISCAS), 2005.
[4] L.-D. Van and C.-C. Yang, “Generalized low-error area- efficient fixed width multipliers,”
IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 25,no. 8, pp. 1608–1619, Aug. 2005.
[5] M. A. Breuer, S. K. Gupta, and T. M. Mak, “Design and error- tolerance in the presence of
massive numbers of defects,” IEEE Des. Test Comput., vol. 24, no. 3, pp. 216–227, May-Jun. 2004.
[6] J.-M. Wang, S.-C. Fang, and W.-S. Feng, “New efficient designs for XOR and
XNOR functions on the transistor level,” IEEE J. Solid-State Circuits,vol. 29, no. 7, pp. 780–
786, Jul. 1994.
[7] N. H. E. Weste, and K.Eshraghain, “PRINCIPLES OF CMOS VLSI Design,A Systems
Perspective,” Pearson Education, 2010.
[8] M. Morris Mano, “Digital Design” – Third Edition, Prentice Hall of India private
limited, 2006.

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Design of 64 bit error tolerant adder

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