With the advent of new technology in the fields of VLSI and communication, there is also an ever growing demand for high speed processing and low area design. It is also a well known fact that the multiplier unit forms an integral part of processor design. Due to this regard, high speed multiplier architectures become the need of the day. In this paper, we introduce a novel architecture to perform high speed multiplication using ancient Vedic maths techniques. A new high speed approach utilizing 4:2 compressors and novel 7:2 compressors for addition has also been incorporated in the same and has been explored. Upon comparison, the compressor based multiplier introduced in this paper, is almost two times faster than the popular methods of multiplication. With regards to area, a 1% reduction is seen. The design and experiments were carried out on a Xilinx Spartan 3e series of FPGA and the timing and area of the design, on the same have been calculated.

Novel high speed vedic mathematics multiplier using compressors

In most of the digital signal processing (DSP) applications the critical operations are the multiplication and accumulation Real-time signal processing requires high speed and high throughput Multiplier-Accumulator (MAC) unit that consumes low power, which is always a key to achieve a high performance digital signal processing system In this paper, design of MAC unit is proposed The multiplier used inside the MAC unit is based on the Sutra "Urdhva Tiryagbhyam" (Vertically and Cross wise) which is one of the Sutras of Vedic mathematics Vedic mathematics is mainly based on sixteen Sutras and was rediscovered in early twentieth century In ancient India, this Sutra was traditionally used for decimal number multiplications within less time The same concept is applied for multiplication of binary numbers to make it useful in the digital hardware Here, the coding is done in VHDL and synthesis is done in Xilinx ISE series The combinational delay obtained after synthesis is compared with the performance of the "Modified Booth Wallace Multiplier" and "High speed Vedic multiplier" presented by Ramesh Pushpangadam Our proposed Vedic multiplier seems to have better performance

Vedic Mathematics Based Multiply Accumulate Unit

High speed pipelined multiplier architecture is proposed in this paper. The pipelined architecture consists of 3 stages. 1st stage consists of the 4 - bit Vedic Multiplication unit. 2nd stage consists of partial products and carry. 3rd stage consists of adders and the result of the multiplication. This paper presents the efficiency of Urdhva Triyagbhyam Vedic method for multiplication which strikes a difference in the actual process of multiplication itself. It enables parallel generation of partial products and eliminates unwanted multiplication steps. The proposed algorithm is modeled using Verilog, a hardware description language. It is found that 11 logic cells are required to build nibble multiplier. The propagation time of the proposed architecture is found to be 4.585ns. Implementation has been done for the Xilinx FPGA device, Spartan-3E. The results shows that multiplier implemented using Vedic multiplication is efficient in terms of area and speed compared to its implementation using Array and Booth multiplier architectures.

High speed and area efficient vedic multiplier

Multipliers are the key block in high speed arithmetic logic units, multiplier and accumulate units, digital signal processing units etc. With the increasing constraints on delay, more and more emphasis is being laid on design of faster multiplications. To enhance speed many modifications over the standard modified booth algorithm, Wallace tree methods for multiplier design have been made and several new techniques are being worked upon. Amongst these Vedic multipliers based on Vedic mathematics are presently under focus due to these being one of the fastest and low power multiplier. There are sixteen sutras in Vedic multiplication in which “Urdhva Tiryakbhyam” has been noticed to be the most efficient one in terms of speed. A large number of high speed Vedic multipliers have been proposed with Urdhva Tiryakbhyam sutra. Few of them are presented in this paper giving an insight into their methodology, merits and demerits. Compressor based Vedic Multipliers show considerable improvements in speed and area efficiency over the conventional ones.

High speed vedic multiplier designs-A review

In this paper, a novel multiplier architecture based on ROM approach using Vedic Mathematics is proposed. This multiplier's architecture is similar to that of a Constant Co-efficient Multiplier (KCM). However, for KCM one input is to be fixed, while the proposed multiplier can multiply two variables. The proposed multiplier is implemented on a Cyclone III FPGA, compared with Array Multiplier and Urdhava Multiplier for both 8 bit and 16 bit cases and the results are presented. The proposed multiplier is 1.5 times faster than the other multipliers for 16×16 case and consumes only 76% area for 8×8 multiplier and 42% area for 16×16 multiplier.

Design and implementation of two variable multiplier using KCM and Vedic Mathematics

The ever increasing demand in enhancing the ability of processors to handle the complex and challenging processes has resulted in the integration of a number of processor cores into one chip. Still the load on the processor is not less in generic system. This load is reduced by supplementing the main processor with Co-Processors, which are designed to work upon specific type of functions like numeric computation, Signal Processing, Graphics etc. The speed of ALU depends greatly on the multiplier. In algorithmic and structural levels, numerous multiplication techniques have been developed to enhance the efficiency of the multiplier which concentrates in reducing the partial products and the methods of their addition but the principle behind multiplication remains the same in all cases. Vedic Mathematics is the ancient system of mathematics which has a unique technique of calculations based on 16 Sutras. Employing these techniques in the computation algorithms of the coprocessor will reduce the complexity, execution time, area, power etc. Though there are many sutras employed to handle different sets of numeric, exploring each one gives new results. Our work has proved the efficiency of Urdhva Triyagbhyam-Vedic method for multiplication which strikes a difference in the actual process of multiplication itself. It enables parallel generation of intermediate products, eliminates unwanted multiplication steps with zeros and scaled to higher bit levels using Karatsuba algorithm with the compatibility to different data types. This sutra is to be used to build a high speed power efficient multiplier in the coprocessor.

High speed energy efficient ALU design using Vedic multiplication techniques

Cubing plays a vital role in secure communication systems, Signal Processing Applications, Finite Field Arithmetic etc. As the radix of the number used for cubing increases the process gets complicated which in turn increases the delay and power consumption. Vedic mathematics is an ancient mathematics concept that provides a fast and a reliable approach to perform arithmetic operations using sixteen Sutras or word- formulae. In this paper the Anurupya Vedic sutra is used for cubing operations with two different multiplier architectures - One array structured and one tree structure. The performance of these multipliers for cubing applications is compared on the basis of their delay, power consumption and area utilization and it is proved that Anurupya Sutra improves the performance tremendously

A Novel Time and Energy Efficient Cubing Circuit Using Vedic Mathematics for Finite Field Arithmetic

The liver performs many functions, which support metabolism, immunity, digestion, detoxification, vitamin storage, and so on. The liver is the storage organ for fat‐soluble vitamins, iron and copper. Six adult healthy guinea pigs of 16–32 weeks of age (Irrespective of sex) were procured from the Department of Laboratory Animal Medicine, TANUVAS as per ethical committee approval. Animals were dissected as per CPCSEA norms and liver pieces were utilized for scanning electron microscopy (SEM) and transmission electron microscopy (TEM) study. The study was performed to document the ultrastructural details of liver of guinea pigs by SEM and TEM. By SEM, the liver parenchyma appeared as lobular with anastomosed one cell thick hepatic cell plates, which appeared as continuous sheets with small to large holes representing sinusoids. The sinusoidal lumen was lined by two types of cells namely endothelial cells and Kupffer cells. Endothelial cells had numerous large and small cytoplasmic fenestrations. Presence of Kupffer cells along with Ito cells were observed in the sinusoids. By TEM, hepatocytes had angular shape with sinusoidal face and bile canalicular face. Hepatocytes had oval nucleus with peripheral heterochromatin and central electron lucent granules and a prominent nucleolus. Bile canaliculi were formed by two adjacent hepatocytes. Fenestrated endothelial cells with flat and elongated shape were found to be in the formation of hepatic sinusoidal wall. A narrow space of Disse was found between the sinusoidal endothelium and hepatocytes. Kupffer cells and pit cells were found within the sinusoidal lumen. Ito cells were found in the space of Disse.

Liver in guinea pig: Scanning and transmission electron microscopic studies

Background: Pancreatic stellate cell (PSC) is now known to play a critical role in pancreatic fibrosis in chronic pancreatitis and pancreatic cancer. In health, quiescent PSCs maintain normal tissue architecture.
Methods: The immunohistochemistry of the pancreas of guinea pig six animals each from 0-2 weeks, 2-8 weeks, 8-16 weeks and 16-32 weeks age groups irrespective of sex were conducted by procuring the animals from the Department of Laboratory Animal Medicine. Tissues were normally processed and embedded in paraffin and paraffin sections of three micron thickness were cut and immunohistochemistry staining protocol was followed with using primary antibody markers namely GFAP, alpha SMA and vimentin. Result: In guinea pigs of 0-2 weeks of age, quiescent pancreatic stellate cells surrounding the acini showed mild positive vimentin immunoreaction. Mild alpha SMA immunopositive reaction was noticed in the quiescent pancreatic stellate cells of 2-8 weeks, 8-16 weeks and 16-32 weeks of age groups within the pancreatic acini. The star shaped quiescent pancreatic stellate cells in the pancreas were located in the interacinar spaces or periacinar spaces, with elongated cytoplasmic processes. Strong vimentin positive quiescent pancreatic stellate cells were found in the pancreatic acini of 2-8 weeks, 8-16 weeks and 16-32 weeks of age groups.


P. Dharani

Papers

High speed energy efficient ALU design using Vedic multiplication techniques

A Novel Time and Energy Efficient Cubing Circuit Using Vedic Mathematics for Finite Field Arithmetic

Liver in guinea pig: Scanning and transmission electron microscopic studies

Immunohistochemical Identification of Pancreatic Stellate Cells in Developing Pancreas of Guinea Pig (Cavia porcellus)