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- 1. PRESENTED BY NAVYASHREE S (1VK09TE018) Dept of TCE, VKIT UNDER THE GUIDANCE OF RAJANI NASSISTANT PROFESSOR,TCE DEPT
- 2. CONTENTS• INTRODUCTION• GENERAL CONSTRUCTION OF MAC UNIT• THE MULTIPLIER ARCHITECTURE• VEDIC MULTIPLIER• ADVANTAGES• DISADVANTAGES• CONCLUSION• REFERENCE
- 3. INTRODUCTION• Vedic mathematics is the name given to the ancient system of mathematics which was rediscovered from the vedas.• It gives explanation of several mathematical terms including arithematics, geometry, trignometry and even calculus.• It was constructed by Shri Bharati krsna theertaji (1884-1960), after his eight years of research on Vedas.• He constructed 16 main sutras and 16 sub sutras.• The beauty of vedic mathematics is to reduce complex calculations into simple one.
- 4. CONTINUED…• Vedic mathematics sutras are powerful and useful even for astrological calculations.• In most of the digital signal processing applications, the critical operations are multiplication and accumulation.• The DSP functions extensively make use of the multiply-accumulate (MAC) operation, for high performance digital signal processing system.• The main motivation behind this work is to achieve high speed through VLSI design and implementation of MAC unit architecture using multipliers based on Vedic mathematics.
- 5. Example: vertical and cross wise
- 6. GENERAL CONSTRUCTION OF MAC UNIT• A basic MAC architecture consist of a mulitplier and a accumulate adder .• The MAC unit computes the product of two numbers and adds the product to an accumulator register.• It provides high speed multiplication, saturation and clear –to-zero function.• Here the multiplier used is a vedic multiplier based on Urdhva Tiryagbhyam sutra.
- 7. Fig 2:MAC Architecture
- 8. THE MULTIPLIER ARCHITECTURE• The multiplier is based on an algorithm Urdhva Tiryagbhyam(Vertical and crosswise ).• This sutras shows how to handle multiplication of larger number (N X N bits) by breaking it into smaller sizes.• For multiplier, first the basic blocks, that 2x2 multiplier are made and then, 4x4 block , 8x8 block and 16x16 block have been made.• The device selected for synthesis is Device family spartan 3E, device is xc3s500, package of fg320.
- 9. VEDIC MULTIPLIER•The 2x2 Vedic multiplier modules has been implemented using twohalf-adder modules as shown in Fig. 4. The total delay is 2-half adderdelays, once the bit products are generated.• The Implementation Equations of 2x2 Vedic multiplier modules are:• R0(1-bit)=b0a0• R1(1-bit)=b0a1+b1a0• R2(1-bit)=b1a1+c1•Product=R2 & R1 & R0
- 10. Fig 4:BLOCK DIAGRAM OF 2x2 MULTIPLIER MODULE
- 11. Eg :Multiplication of 2 decimal numbers : 43*68• Consider the multiplication of two decimal numbers (43*68).•The digits on both sides of the line are multiplied and added withthe carry digit.•This carry is added in the next step and hence the process goes on. Ifmore than one line are there in one step, all the results are added toprevious carry.•In each step, unit’s place digit acts as the result bit while the higherdigits act as carry for the next step.•Initially, the carry is taken to be zero..
- 12. STEP 1 STEP 2 STEP 3 4 3 4 3 4 3 6 8 6 8 6 8 2 4 Multiplicands 3 2 carry 1 8 partial product 5 2 final product 2 4 2 9 2 4Fig 3: Multiplication of 2 digit decimal numbers using Urdhva Tiryagbhyam sutra.
- 13. Fig 4:Using Urdhva Tiryagbhyam for Binary numbersSTEP 1 STEP 2 STEP 3 STEP 41101 1101 1101 11011010 1010 1010 1010 STEP 5 STEP 6 STEP 7 1101 1101 1101 1010 1010 1010
- 14. CONTINUED…• LSB are multiplied which gives the LSB of the product (vertical).• The LSB of the multiplicand is multiplied with the next higher bit of the multiplier and added with the product of LSB and next higher bit of the multiplicand (crosswise).• The sum gives the second bit of the product and the carry is added to the next stage sum obtained by crosswise and vertical multiplication.• All four bits , are processed with crosswise multiplication and addition to give sum and carry.• The sum is corresponding bit of the product and carry is again added to the next stage addition and multiplication of three bits except the LSB.• The same operation continues until the multiplication of two MSBs to give the MSB of the product.
- 15. Fig 5:Better implementation of Urdhva Tiryagbhyam sutra for binary numbers
- 16. Continued..• A 4x4 multiplication is simplified into 4, 2x2 multiplication that can be performed in parallel.• This reduces the number of stages of logic and thus reduces the delay of the multiplier.• This example illustrates a better and parallel implementation style of Urdhva Tiryagbhyam sutra.
- 17. ADVANTAGES• Vedic multiplier is faster than the array multiplier and booth multiplier.• The area needed for vedic multiplier is very small as compared to other multiplier architecture.• MAC is used in modern digital signal processing.• MAC always lie in the critical path that determines the speed of the overall hardware systems.
- 18. DISADVANTAGES• For complex multiplications, even the system becomes complex.
- 19. CONCLUSION• The proposed vedic mathematics based MAC unit proves to be highly efficient in terms of speed. Due to its regular and parallel structure ,it can be realised easily on silicon as well.
- 20. REFERENCE• Maharaja, J.S.S.B.K.T ., “VEDIC MATHEMATICS”, Motilal banarasidass Publishers Pvt. Ltd, Delhi, 2009.• Amandeep singh , “Design and hardware realisation of a 16-bit Arithematic unit”,THAPAR UNIVERSITY(2010).• B. Parhami, "Computer Arithmetic Algorithms and Hardware Architectures", 2n d ed, Oxford University Press, New York, 2010.
- 21. THANK YOU

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