International Journal of Recent Advances in Engineering & Technology (IJRAET)
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An Efficient Implementation of 4X4 Vedic Multiplier using Power Gating Method
1Pathan Johnkhan, 2B. Nageswara Rao Naik
1PG Student (M.Tech), Dept. Of ECE, KKR & KSR Institute of Technology & Sciences, Guntur
2Assistant Professor, Dept. Of ECE, KKR & KSR Institute of Technology & Sciences, Guntur
Abstract— This paper proposed a various multipliers implemented using CMOS logic style and their comparative analysis on the basis of power and PDP (Power delay product). A variety of multipliers have been reported in the literature but power dissipation and area used by these multiplier circuits are relatively large. This paper proposed a high performance and power efficient 8x8 multiplier design based on Vedic mathematics using CMOS logic style. . In this paper, XNOR gates with MTCMOS and without MTCMOS technique are compared taking power consumption as parameter by varying voltage, frequency and temperature. The designs are tested in 45nmtechnology. The XNOR gate design with MTCMOS technique gives least power consumption Keywords— Multi-Threshold Voltage CMOS (MTCMOS), Vedic multiplier, XNOR Gate, Power analysis.
I. INTRODUCTION
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 are not commensurate with the advances in electronic devices.
So the designers are faced with more constraint; high speed, high throughput and at the same time, consumption of power as minimal as possible. The levels, such as the architectural, circuit, layout, and the process technology level. At the circuit design level, the possibility for power savings exists by means of proper choice of a logic style for implementing combinational circuits. In the absence of low-power design techniques such applications generally suffer from very short battery life, while packaging and cooling them would be very difficult and this is leading to an unavoidable increase in the cost of the product. Historically, VLSI designers have used speed as the performance metric.
High gains, in terms of performance and silicon area, have been made for Digital circuits. In general, small area and high performance are two conflicting constraints. The power consumption for any given function in CMOS circuit must be reduced for either of the two different reasons: The most important reason is to reduce heat dissipation in order to allow a large density of functions to be incorporated on an IC chip.
Any amount of power consumption is worthwhile as
long as it doesn‘t degrade overall circuit performance [4]. The other reason is to save energy in battery operated instruments same as electronic watches where average power is in microwatts
Power dissipation can be reduced by scaling the supply voltage. The scaling of supply voltage linearly with feature size was started from half-micron technology.
But the power supply scaling affects the speed of the circuit the need of the time is to put efforts in designing low-power and high speed circuits. MTCMOS technology has emerged as a promising alternative to build logic gates operating at a high speed with relatively small power dissipation as compared to traditional CMOS. MTCMOS is an effective circuit- level technique that provides a high performance and low-power design by utilizing both low and high- threshold voltage transistors. This technology is used for reducing sub threshold currents in standby mode while maintaining circuit performance.
Vedic mathematics is a part of four Vedas (books of wisdom). It is part of Sthapatya- Veda, which is an upaveda (supplement) of Atharva Veda. It encompasses the explanation of numerous modern mathematical terms that includes arithmetic, geometry, trigonometry, quadratic equations, factorization and even calculus. The word ―Vedic‖ was coined from the word ―Veda‖ which means the repertoire of all knowledge.
Vedic mathematics is commonly based on 16 Sutras (or aphorisms) dealing with different types of mathematics like arithmetic, algebra, geometry etc. The essence of Vedic mathematics is the fact that it reduces the otherwise ponderous calculations in conventional mathematics that slows down the calculation process considerably. This is because the Vedic formulas are predicated on the principles which are generally used my humans. This is a very enticing field and presents some efficient algorithms which can be applied to numerous branches of engineering such as computing, image processing and digital signal processing.
When the physical design of the MTCMOS circuits is done, it is vital to consider the large current flowing through the current stopping transistors in active mode and the electro-migration in the wires should be taken
into account. The channel width is also very important due to the large current. There is a trade-off between the local and global sleep devices. The bottleneck with local sleep devices is that there will be a large area overhead due to the fact that there will be a lot of extra transistors.
MTCMOS
The MTCMOS approach is easy on combinatorial circuits, but it can be tricky on sequential circuits.
Should the power supply be turned off, all data stored in the circuit will be irreversibly lost. This is the main problem with MTCMOS circuits. To deal with this problem complex timing scheme must be used or extra circuits have to be added. Because of these added items the performance of the circuit would be degraded.
This will also require a larger die area and impose higher power losses. MTCMOS (multithreshold CMOS) reduces leakage current during standby mode and attains high speed in active mode.
In this technique high threshold voltage transistor are used to isolate the low threshold voltage transistor from supply and ground during standby mode. However by including extra transistor, MTCMOS circuit faces performance penalty compared to CMOS circuits, if the transistor are not sized properly. The high threshold voltage transistor are turned off during standby (sleep mode) , this result very low sub threshold passes from Vcc to ground. MTCMOS includes high Vt transistor to gate power and ground of a low Vt logic blocks as shown in figure 1.when the high Vt transistor are off resulting in a very low sub threshold leakage current.
When the high Vt transistor are turned on, low Vt are connected to virtual ground and Vdd.
Figure 1 Power gating structure
Figure 2 Schematic diagram of Existing XNOR Gate However there are three drawbacks in MTCMOS sequential circuits that is need to be eliminated: first is
sequential circuit will lose data when sleep transistor are turned off, second is timing is critical for sleep signal and third is sizing of sleep transistor is very difficult task.
The existing design of XNOR gate is shown in Fig.2. It consists of 3 transistors as one pMOS and two nMOS.
When ab=00, nMOS (both) are OFF and pMOS is ON due to high gate voltage than threshold. As pMOS is strong ‗1‘ device it will pass complete logic ―high‖
signal at the output. When ab=01, one nMOS is OFF and other nMOS is ON. As nMOS is strong ‗0‘ device it will pass complete logic ―low‖ signal at the output.
When ab =10, nMOS (second) and pMOS are ON. As mobility of nMOS is nearly three times greater than pMOS, hence it will drive the output ignoring the effect of ON pMOS transistors which results into zero output.
When ab=11, both the nMOS transistors are ON and only nMOS will be responsible for driving the output.
II. VEDIC MATHEMATICS
The proposed Vedic multiplier is based on the Vedic multiplication formulae (Sutras). These Sutras have been traditionally used for the multiplication of two numbers in the decimal number system. In this work, we apply the same ideas to the binary 6number system to make the proposed algorithm compatible with the digital hardware.
Urdhva Tiryakbhyam
The multiplier is based on an algorithm Urdhva Tiryakbhyam (Vertical & Crosswise) of ancient Indian Vedic Mathematics. Urdhva Tiryakbhyam Sutra is a general multiplication formula applicable to all cases of multiplication. It literally means ―Vertically and crosswise‖. It is based on a novel concept through which the generation of all partial products can be done with the concurrent addition of these partial products.
The parallelism in generation of partial products and their summation is obtained using Urdhava Triyakbhyam explained in fig.3. The algorithm can be generalized for n x n bit number. Since the partial products and their sums are calculated in parallel, the multiplier is independent of the clock frequency of the processor. Thus the multiplier will require the same amount of time to calculate the product and hence is independent of the clock frequency.
The net advantage is that it reduces the need of microprocessors to operate at increasingly high clock frequencies. While a higher clock frequency generally results in increased processing power, its disadvantage is that it also increases power dissipation which results in higher device operating temperatures. By adopting the Vedic multiplier, microprocessors designers can easily circumvent these problems to avoid catastrophic device failures.
The processing power of multiplier can easily be increased by increasing the input and output data bus widths since it has a quite a regular structure. Due to its regular structure, it can be easily layout in a silicon chip.
The Multiplier has the advantage that as the number of
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bits increases, gate delay and area increases very slowly as compared to other multipliers. Therefore it is time, space and power efficient. It is demonstrated that this architecture is quite efficient in terms of silicon area/speed.
Multiplication of two decimal numbers- 325*738:
To illustrate this multiplication scheme, let us consider the multiplication of two decimal numbers (325 * 738).
Line diagram for the multiplication is shown in fig2.1.
The digits on the both sides of the line are multiplied and added with the carry from the previous step. This generates one of the bits of the result and a carry. This carry is added in the next step and hence the process goes on. If more than one line are there in one step, all the results are added to the previous carry. In each step, least significant bit acts as the 7result bit and all other bits act as carry for the next step. Initially the carry is taken to be zero. To make the methodology more clear, an alternate illustration is given with the help of line diagrams in figure where the dots represent bit „0‟ or
„1‟ .
Figure 3 Multiplication of two decimal numbers by Urdhva Tiryakbhyam
Consider an example of a 4x4-bit Vedic multiplier unit as shown in Fig. 4 which multiplies two 4-bit numbers (A and B), each number can be expressed as (A0–A3, B0– B3); A3 and B3 being the most significant inputs.
Figure 4 4x4 bit Vedic multiplication method Each square shape block in the above figure shows a 2x2 bit Vedic multiplier unit. First 2x2 bit Vedic multiplier has inputs as A1A0 and B1B0. The last block is also 2x2 bit Vedic multiplier with inputs A3 A2 and B3 B2. The blocks in the middle are 2x2 bit multipliers with inputs A3 A2 & B1B0 and A1A0 & B3 B2. So the
final result of multiplication will be of 8 bit as S7S6S5S4S3S2S1S0. To understand the concept, the Block diagram of 4x4 bit Vedic multiplier is shown in Fig. 5. To get final product (s7 s6 s5 s4 s3 s2 s1 s0), four 2x2 bit Vedic multipliers and three 4-bit Ripple-Carry (RC) Adders are required.
Figure 5 Block diagram of 4X4 bit Vedic multiplier Analysing 4X4 multiplications, inputs are a3-a0 and b3- b0 and the output is given by s7 s6 s5 s4 s3 s2 s1 s0.The inputs of 1st 2X2 multiplier are a1a0 and b1b0, 2nd 2X2 multiplier are a1a0 and b3b2, 3rd 2X2 multiplier are a3a2 and b1b0 and that of 4th 2X2 multiplier are a3a2 and b3b2.
As compared to Array Multiplier, Proposed Vedic Multiplier is efficient in terms of delay and speed. The Proposed Vedic Multiplier can be used to reduce Delay.
This 4X4 Multiplier Module is the Basic Building Block of 8X8 Vedic Multiplier.
The module of 8X8 bit Vedic multiplier shown in Fig. 6 can be implemented by using four 4X4 bit Vedic multiplier modules [12]. Analyzing 8X8 multiplications, inputs are a7- a0 and b7-b0 and the multiplication‘s 16 bits output will be s15-s0.In this , four 4X4 bit Vedic multipliers and three 8 bit RC Adders(having 2 input of 8 bits) are required. Inputs are given to the 4x4 bit Vedic multipliers and the output of multiplier is of 8 bits.
Now, the input of the 1st RC Adder is the output of the 2nd and 3rd 4x4 bit multipliers which gives output of 8 bits (7-0) + one carry. The 2nd RC Adder will add the output of 1st RC Adder (7-0) and 4 bits (7-4) output of 1st 4x4 bit Vedic multiplier, other 4bit of are considered as 0.So output is of 8-bits(7-0) and one carry(carry is discarded).
The 3rd RC Adder will add the output of 4th 4x4 bit multiplier (7-0) and 4 bits of output of 2nd RC Adder (7- 4), other 4 bits are carrying of 1st RC Adder and 0. Now, the output of 8x8 multiplier is s(3-0) output of 1st 4x4 bit multiplier(3- 0), s(7-4) is output of 2nd RC Adder (3- 0) and s(15-8)=8 is output of 3rd RC Adder(7-0).
Figure 6 Block diagram of 8X8 bit Vedic multiplier
III. VEDIC MULTIPLIER USING MTCMOS
CMOS technology when scaled helps in the attainment of reduced supply and threshold voltages. When the threshold voltages are lowered the sub threshold current begins to wax precipitously. Leakage current plays a pivotal role in modern high performance integrated circuits (ICs) as more than 40% of the total active mode energy is associated with these currents. Integrating more transistors on-chip, causes the leakage current to dominate the high performance IC‘s total energy consumption. Additionally, it is the leakage current which is the prime source of energy consumption in an idle circuit.
In various hand-held battery-operated gadgets like mobile phones, laptops etc. employs long standby periods thus reducing the leakage current is highly important to provide longevity to the battery. The highly recommended circuit technique for the leakage current reduction is the Multi- Threshold Voltage CMOS (MTCMOS).
In MTCMOS technology, efficient power management is obtained by allowing the circuit to operate in two modes: 1) Active Mode 2) Sleep Mode. The conventional circuit works using a single threshold voltage (Vt) whereas the circuits employing the MTCMOS technique works on two different threshold voltage switches i.e. the Low Vt and High Vt . The circuit makes use of two different set of transistors – one being the High Vt transistors known as the ―sleep‖
transistors and other being the Low Vt transistors which forms the logical circuit. The sleep transistors helps in the reduction of leakage current thus providing the high performance and the Low Vt transistors are used to boost the circuit‘s speed performance.
Figure 7 Power Gating Techniques using MTCMOS The Fig.7 shows the power gating technique used in MTCMOS. The above circuit comprises of two sleep transistors S1 and S2 which possess the higher Vt . The logical circuit between S1 and S2 comprises of the Low Vt transistors is not connected directly to the real supply, Vdd and ground, GND but is connected to virtual supply and ground lines Vddv and Gndv. The sleep transistors are provided with complementary inputs S and SBAR.
The circuit works in the active mode when, S=0 and SBAR=1 thus making both the sleep transistors S1 and S2 to remain ON and the virtual supply and ground lines Vddv and Gndv works as real supply lines and the logic circuit performs its operations normally at higher speed.
But when S=1 and SBAR=0, the circuit works in the sleep mode making S1 and S2 sleep transistors to go in OFF state which results in the floating of virtual power supply lines and sleep transistors S1 and S2 suppresses the large leakage current present in the circuit. This reduces the power consumption as the leakage current has been lowered. Fig.8 represents the implementation of XNOR using the MTCMOS technique. Here a high Vt transistor i.e. the sleep nMOS transistor is incorporated at the bottom of the logical circuit design which during the sleep mode helps in the abatement of the leakage current present in the circuit thus reducing the overall power consumption.
Figure 8 XNOR using MTCMOS Technique.
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IV. RESULTS AND CONCLUSIONS
This paper introduces a novel and high performance design of an 8x8 multiplier using ancient Indian mathematics called Vedas. We have presented three different designs of the 8x8 Vedic multiplier using the CMOS technology, PTL and finally concoct the Vedic Multiplier using the Multi-Threshold Voltage CMOS (MTCMOS) and proved that the MTCMOS implementation of Vedic Multiplier is the best among all the implementations.
The Below schematic represent the gate design of the proposed substractor .the schematic is drawn using DSCH software.
Figure 9 Schematic of substractor
Figure 10 Simulation of the substractor
The above simulation shows the A,B,C input of the substractor .d is the difference calculated and the borrow is the carry left .
A full subtractor subtracts 3input bits and gives the output in the form of difference and borrows. We design the transistor level full subtractor using cadence virtuoso tool in 45 nm technology and simulate it giving the inputs and get output. By applying the MTCMOS technique in 45nm technology reduction in current and power.
Figure 11 MTCMOS paired with the proposed substractor
Figure 12 Simulation of the MT CMOS substractor The multi threshold CMOS technology has two main parts. First, ―active‖ and ―sleep‖ operational modes are associated with MTCMOS technology, for efficient power management. Second, two different threshold voltages are used for N channel and P channel MOSFET in a single chip.
Figure 13 Layout Design
Figure 14 RTL Schematic of the TOP Module Figure 13 and 14 shows the Layout and RTL Schematic of the Proposed System.
The multiplier and the adder-subtractor units used for the implementation of Vedic multiplier are adopted from ancient methodology of India mathematics called as Vedas. The use of Vedas not only abates the carry propagation taking place from lsb to msb but also produces the partial product and there sums in the same step. Vedic mathematics based multipliers thus causes least delay and consume least power than any other type of multipliers in the literature. The functionality of all the three designs and there PDP and total power consumptions at two different frequencies and three different voltages were calculated
REFERENCES
[1] Himanshu Thapliyal and M. B. Srinivas,―An efficient method of elliptic curve encryption using Ancient Indian Vedic Mathematics,‖48th
IEEE International Midwest Symposium on Circuits and Systems, 2005, vol. 1, pp. 826- 828.
[2] M. Pradhan and R. Panda, ―Design and Implementation of Vedic Multiplier,‖ A.M.S.E Journal, Computer Science and Statistics, France vol. 15, July 2010, pp. 1-19.
[3] Sen-Maw Kuo and Woon-Seng Gan, ―Digital Signal Processor, architectures ,implementations and applications,‖ Pearson Prentice Hall, 2005, pp. 253-323.
[4] S. S. Kerur, Prakash Narchi, Jayashree C .N., Harish M.Kittur and GirishV.A.―Implementation of Vedic Multiplier for Digital Signal Processing,‖ International Journal of Computer Applications, 2011, vol. 16, pp. 1-5.
[5] D. Zuras, On squaring and multiplying large integers, In Proceedings of International Symposium on Computer Arithmetic, IEEE Computer Society Press, pp. 260-271, 1993.
[6] Shripad Kulkarni, ―Discrete Fourier Transform (DFT) by using Vedic Mathematics‖Papers on implementation of DSP algorithms/VLSI structures using Vedic Mathematics, 2006, www.edaindia.com, IC Design portal.
[7] S.G. Dani, Vedic Maths‘: facts and myths, One India One People, Vol 4/6,January 2001, pp. 20- 21; (available on www.math.tifr.res.in/ dani).
[8] M.C. Hanumantharaju, H. Jayalaxmi, R.K.
Renuka, M. Ravishankar, "A High Speed Block Convolution Using Ancient Indian Vedic Mathematics," ICCIMA, vol. 2, pp.169-173, International Conference on Computational Intelligence and Multimedia Applications, 2007.
[9] Himanshu Thapliyal, ―Vedic Mathematics for Faster Mental Calculations and High Speed VLSI Arithmetic‖, Invited talk at IEEE Computer Society Student Chapter, University of South Florida, Tampa, FL, Nov 14 2008.
Authors Profile:
Pathan John Khan is pursuing his Master degree M.Tech in VERY LARGE
SCALE INTEGRATION (VLSI)
SYSTEMS in KKR & KSR Institute of Technology & Science.
B. Nageswara Rao Naik is working as Assistant Professor in KKR & KSR Institute of Technology & Science.. he has over 6 years of Teaching experience.
