Vedic Mathematics.ppt
Download as PPTX, PDF9 likes13,423 views
The document discusses different methods for multiplication and their associated delays. It introduces the concept of Vedic mathematics as an ancient methodology for calculations based on 16 formulas. It then describes the Urdhva Tiryakbhyam multiplier technique, which reduces complexity, memory usage, and propagation delay for multiplication by calculating partial products in parallel rather than sequentially. This technique can be implemented in hardware to create an efficient complex multiplier with improved speed and lower power consumption compared to other architectures.
Vedic Mathematics.ppt
- 1. Presented by.. S.Noor Mohammad
- 5. The delay associated with the array multiplier is the Array time taken by the signals to propagate through the Multiplier gates that form the multiplication array. Large booth arrays are required for high speed multiplication and exponential operations which in turn require large partial sum and partial carry Booth registers. Multiplier Multiplication of two n-bit operands using a radix-4 booth recording multiplier requires approximately n / (2m) clock cycles to generate the least significant half of the final product, where m is the number of Booth recorder adder stages. Thus, a large propagation delay is associated with this case.
- 6. What is Vedic Mathematics..? The word „Vedic‟ is derived from the word „veda‟ which means the store-house of all knowledge. Jagadguru Shankaracharya Bharati Krishna Teerthaji Maharaja (1884-1960) Vedic Mathematics is the ancient methodology of Indian mathematics which has a unique technique of calculations based on 16 Sutras (Formulae). It covers explanation of several modern mathematical terms including arithmetic, geometry (plane, co- ordinate), trigonometry, quadratic equations, factorization and even calculus.
- 7. 16 Suthras(Formules) in Vedic Mathematics 1) (Anurupye) Shunyamanyat 2) Chalana-Kalanabyham 3) Ekadhikina Purvena 4) Ekanyunena Purvena 5) Gunakasamuchyah 16) Yaavadunam 6) Gunitasamuchyah 15) Vyashtisamanstih 7)Nikhilam Navatashcaramam 14) Urdhva-tiryakbhyam Dashatah 13) Sopaantyadvayamantyam 8) Paraavartya Yojayet 12) Shunyam Saamyasamuccaye 9) Puranapuranabyham 11) Shesanyankena Charamena 10) Sankalana- vyavakalanabhyam
- 9. Conventional method for 4-bit multiplication. 3256*7384 3256 *7384 13024 Memory usage is high for each stage 26048+ and causes delay in 9768++ execution 22792+++ 24042304
- 10. How to reduce memory usage capability and propogation delay for a complex multiplication. 3256 Here it is *7384 24042304 Reduces Complexity levels Decrese memory usage capacity Less Propagation delay HOW.. ….?
- 11. 1. CP X0 = X0 * Y0 = A Y0 2. CP X1 X0 = X1 * Y0+X0 * Y1 = B Y1 Y0 3. CP X2 X1 X0 = X2 * Y0 +X0 * Y2 +X1 * Y1 = C Y2 Y1 Y0 4. CP X3 X2 X1 X0 = X3 * Y0 +X0 * Y3+X2 * Y1 +X1 *Y2 = D Y3 Y2 Y1 Y0 5. CP X3 X2 X1 = X3 * Y1+X1 * Y3+X2 * Y2 = E Y3 Y2 Y1 6. CP X3 X2 = X3 * Y2+X2 * Y3 = F Y3 Y2 7 CP X3 = X3 * Y3 = G Y3
- 12. Hardware architecture of the Urdhva tiryakbhyam multiplier
- 13. Where it can be used Basic Applications: Vedic Mathematics is a branch of Mathematics which teaches pattern-observation and faster calculations. Vedic Mathematics covers Arithmatics Decimal operations in all decimal work, Ratios, Proportions, Trigonometry, Percentages, Averages, Interest, Annuities, Discount, the Centre of Gravity of Hemispheres, Transformation of Equations, Dynamics, Statistics, Hydro Statistics, Pneumatics, Applied Mechanics, Solid Geometry, Plane Spherical Trigonometry, Astronomy, etc. ASCI Application: The propagation delay of the resulting (16, 16)x(16, 16) complex multiplier is only 4ns and consume 6.5 mW power. We achieved almost 25% improvement in speed from earlier reported complex multipliers, e.g. parallel adder and DA based architectures.