Novel Advanced Method for the Square and Cube Architectures Using Vedic Sutras

Contributed by:
Harshdeep Singh
This PDF contains :
I. Introduction,
II. Vedic Mathematics,
III. Proposed Design Methods,
IV. Results And Discussions,
V. Conclusion
1. Research Inventy: International Journal of Engineering And Science
Vol.4, Issue 2 (February 2014), PP -56-59
Issn (e): 2278-4721, Issn (p):2319-6483,
Novel Advanced Method for the Square and Cube Architectures
Using Vedic Sutras
T. Maheshwar1, A Rama1, A Sereesha1,
ECE Department, Sree Dattha Institute of Engineering & Science
Abstract: Square and cube architectures can be uses as element in such applications like DSP, DIP, and
communication and etc .there is different ways for designing this circuit as if with the multiplier. That is not the
ideal approach of designing in present advanced systems with the power, speed and area. We proposes a novel
approach of designing the square and cube architectures by using the one of the fast and less power method
called Anurupyena sutra of Vedic mathematics. These are very efficient because the operation not as with the
normal, and also the have the pipelined execution feature. In proposed design Vedic multiplication method
Urdhwa Tiryakbhyam Sutra is chosen for the sub module design. There by decreases the critical path delay
compare to that of any other alternative method. The designing can done using verilog and simulated using
model-sim and synthesized using Xilinx
Keywords: Square,Cube, Anurupyena, Urdhwa Tiryakbhyam Sutra, Vedic Mathematics
I. Introduction
As expanding the application of the present modern systems high speed architecture are necessitate in
demand. These arithmetic operations needs higher throughput ids desired for the real time processing
applications like image processing (compression and decompression), image encoding and decoding,
communications, adaptive networking, least means square and data encryption and decryption requires square
and cube architectures.
They also requires the time delay and power consumption is more essential Up till now the square and
cube systems are designed using normal methods composes of multiplier. Normally the multiplier is more
power consumed digital design as this internally consists the partial product generation and multi operand
addition and final addition that causes the increases the area and power in advancement of present VLSI features
we cannot accept this type of designing .
Even in for the design of performance increased multiplier the present researches are moving to vedic
mathematic approaches. vedic mathematic is one of the promising alternative for the present ALU requirements.
In this work we have put into effect a high speed and less power square and cube architectures. The
architectures implemented by Anurupyena sutra due to its feature fat operation and multiplier less architecture.
The Urdhwa Tiryakbhyam Sutra used at different levels of design drastically reduces the delay when compared
to conventional designs. The hardware implementation of square and cube Vedic designs using Anurupyena
sutra contributes to adequate improvement of the speed in order to achieve high outturn.
Section II provides a related introduction towards Vedic sutras. Section III describes the proposed architecture.
Section IV simulation results and design analysis of square and cube architectures and proposed design. Section
V represents the conclusions. Followed by references
II. Vedic Mathematics
Vedic math is taken from the traditional Indian Vedas; they are very much used in India for fast oral
calculation without paper and pen. The technique in that the calculation are carried out by using the different
main 16 sutras, different upa sutras and inferences derived from these Sutras. Algebra, arithmetic, geometry or
trigonometry etc any mathematical calculation can be carried out by this sutra efficiently. Vedic Mathematics is
more tenacious than modern mathematics.
Generally the “Vedic mathematics” is comprised of sixteen simple mathematical formulae from the Vedas [5].
1. Ekadhikena Purvena
2. Nikhilam navatascaramam Dasatah
3. Urdhva - tiryagbhyam
4. Paravartya Yojayet
5. Sunyam Samya Samuccaye
6. Anurupye - Sunyamanyat
7. Sankalana - Vyavakalanabhyam
8. Puranapuranabhyam
9. Calana - Kalanabhyam
2. Novel Advanced Method for the Square and Cube Architectures Using Vedic Sutras
10. Ekanyunena Purvena
11. Anurupyena
12. Adyamadyenantya - mantyena
13. Yavadunam Tavadunikrtya Varganca Yojayet
14. Antyayor Dasakepi
15. Antyayoreva
16. Gunita Samuccayah.
III. Proposed Design Methods
a) Square Architecture
There are different sutras for the square calculations but those are limited with some our
proposed method Square Architecture designed using dwandwa yoga property of urdhvatiryagbhyam sutra.
The “Dwandwa Yoga” means the duplex or dual. Here it senses as squaring and cross multiplication. In order to
calculate the square using dwandwa yoga the urdhvatiryagbhyam sutra can be used. It described that first
calculate the square of lower half (LSP) and higher upper half (MSP) and multiply LSP and MSP and twice then
from the final result by concatenating the all internal results. Proposed square architecture is shown in
figure.1.The algorithm steps with example are stated below.
Consider a=1011
Step 1: calculate the square of LSP and MSP
10*10=0100 (MSP square)
11*11=1001 (LSP square)
Step 2: multiply LSP and MSP
Step 3: add multiplication result twice
Step 4: add and concatenate the intermediate results
1. Concatenate MSP square lower half and LSP square upper half (00&10) =0010
2. Add with twice added multiplied result (1100) and concatenated intermediate squares (0010)
Step 5: concatenate the all results
In our proposed architecture we use the advance multi-operand addition method along with parallel
processing of the internal method shown in figure 1. The Vedic square has all the vantages of the Vedic
multiplier.lot more it is degree faster and smaller foot print compared to that of the array, Booth. Rather than
adding the multiplier result twice and then adding to the Concatenate MSP square lower half and LSP square
upper half. We add them together that consumes the less area and increases speed of operation.
b) Cube Architecture
The cube architecture can be designed by using the Vedic sutra called Anurupyena Sutra even though there are
different sutras for the cube calculations but this Anurupyena Sutra is ideal choice. In this method we use the
hierarchy design for the sub modules design. For multiplication we use the urdhvatiryagbhyam sutra.
Fig 1. 8-bit Vedic Square Architecture
3. Novel Advanced Method for the Square and Cube Architectures Using Vedic Sutras
The steps that are involved in Anurupyena Sutra are described below.
Step 1: calculate the cubes of LSP and MSP
Step 2: calculate the squares of LSP and MSP
Step 3: multiply the squared LSP result with MSP and squared MSP result with LSP (Intermediate results)
Step 4: multiply the intermediate results with „3‟ (0011)
Step 5: concatenate the all results
Fig 2: Proposed multiplied by 3 Circuit(3MCM)
For multiple contant multiplication we add the input ( X ) and left shifted input ( 2X) to produce the 3X
output.There by unnesissary multiplier can be avioded. Proposed MCM-3 is shown in fig.2
The proposed mthod can have less foot print and can run very efficient performance with the proposed MCM-3
method ,for designin the left shift operation in MCM-3 we should not uses the any other shifter .
Fig 3. 8-bit Vedic Cube Architecture
For square calculations we use the above square architecture III (a) .and for the intermediate
multiplication with the constant „3‟ can be done with the multiple constant multiplication which is the better
method for multiplication .that causes the only one adder can be used as excess. By that the area can be reduced
and performance also will be increased.*-bit cube architecture is shown in figure.3
IV. Results And Discussions
In our work, 8-bit squaring and cube architectures are designed in Verilog HDL. Simulate using model-
sim and Synthesis is done using Xilinx - Project Navigator and Xilinx ISE simulator. Synthesis results are
compared with previous method. Thus, proposed method outperforms previous method in terms of speed, area
and low power. The proposed squaring architecture may be useful for the design of hardware for computer
arithmetic. Fig 4&5 shows obtained the result of proposed Vedic square and cube. These architectures are faster
than conventional square and cube.
Fig 4: Square design output
4. Novel Advanced Method for the Square and Cube Architectures Using Vedic Sutras
Fig 5: cube design output
V. Conclusion
Vedic square and cube multiplier can be designed with the advanced design methods can be done that
makes the efficient design and reduces the operation time. The extra advanced logic MCM based design can be
done. Rather than using the normal multiplier MCM can uses the very less area. We designed the 8-bit, 16-bit
and 32- bit architectures are designed and comparison evaluation can be carried out in this paper.
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