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TABLE 2: SY NTHESIZE RESULT FOR NIKHILAM AND ANURUPY ENA

Table 2 SY NTHESIZE RESULT FOR NIKHILAM AND ANURUPY ENA

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Step-5: (1 x 1) =1. As there is no carried over number from the previous step it is retained. Thus fifth digit = 1 Urdhva 8x8 bit Vedic multiplier is structured using 4X 4 bit Urdhva blocks as shown in Fig. 2. In this fig. 2. The 8 bit multiplicand A can be decomposed into pair of 4 bits AH-AL. Similarly multiplicand B can be decomposed into BH-BL.
Step-5: (1 x 1) =1. As there is no carried over number from the previous step it is retained. Thus fifth digit = 1 Urdhva 8x8 bit Vedic multiplier is structured using 4X 4 bit Urdhva blocks as shown in Fig. 2. In this fig. 2. The 8 bit multiplicand A can be decomposed into pair of 4 bits AH-AL. Similarly multiplicand B can be decomposed into BH-BL.
Fig. 4. 8 bit Vedic Square Algorithm Square Algorithm using Dwanda yoga (Duplex-D) property of Urdhva tiryagbhyam sutra. To find the square of any number which is near the base 10,100 etc., Y avadunam Sutra is used. The Sutra is used for Squaring, is limited to number which ends with digit 5 only is “Ekadhikena Purvena sutra”. The other method “Dwandwa Yoga” or Duplex-D is used in two different senses. The first one is by squaring and the second one is by cross multiplication. [6] To calculate the square of a number, we have used “Duplex-D” property of Urdhva Tiryagbhyam. To find the Duplex, we take twice the product of the outermost pair and then add twice the product of the next outermost pair and so on till no pairs are left. When there are odd numbers of bits in the original sequence, there is one bit left by itself in the middle and this enters as its square. Thus for 7654371.
Fig. 4. 8 bit Vedic Square Algorithm Square Algorithm using Dwanda yoga (Duplex-D) property of Urdhva tiryagbhyam sutra. To find the square of any number which is near the base 10,100 etc., Y avadunam Sutra is used. The Sutra is used for Squaring, is limited to number which ends with digit 5 only is “Ekadhikena Purvena sutra”. The other method “Dwandwa Yoga” or Duplex-D is used in two different senses. The first one is by squaring and the second one is by cross multiplication. [6] To calculate the square of a number, we have used “Duplex-D” property of Urdhva Tiryagbhyam. To find the Duplex, we take twice the product of the outermost pair and then add twice the product of the next outermost pair and so on till no pairs are left. When there are odd numbers of bits in the original sequence, there is one bit left by itself in the middle and this enters as its square. Thus for 7654371.
As shown in Fig. 3, we write the multiplier and the multiplicand in two rows. For 95, the deviation can be obtained by ‘all from 9 and the last from 10” sutra i.e., the last digit 5 is from 10 and remaining digit 9 from 9 gives 05. For 97, the last digit 7 is from 10 and remaining digit 9 from 9 gives 03. We can write two columns of numbers, one (Column 1) consisting of the numbers to be multiplied and the other (Column 2) consisting of their compliments. The product also consists of two parts which are separated by a vertical line for the purpose of illustration. The RHS (right hand side) of the product can be obtained by simply multiplying the numbers of the Column 2 i.e., (5x3 = 15). The LHS (left hand side) of the product can be found by cross subtracting the second number of Column 2 from the first number of Column 1 or vice versa, i.e., 95 - 3 =92 or 97-5 = 92. The final result is obtained by concatenating RHS and LHS (Answer = 9215).[3] The upa-Sutra ‘A nurupyena' means ‘proportionality’. This Sutra is highly useful to find products of two numbers when both of them are near the Common bases i.e. powers of base 10. It is very clear that in such cases the expected ‘Simplicity ‘in doing problems is absent.[3]
As shown in Fig. 3, we write the multiplier and the multiplicand in two rows. For 95, the deviation can be obtained by ‘all from 9 and the last from 10” sutra i.e., the last digit 5 is from 10 and remaining digit 9 from 9 gives 05. For 97, the last digit 7 is from 10 and remaining digit 9 from 9 gives 03. We can write two columns of numbers, one (Column 1) consisting of the numbers to be multiplied and the other (Column 2) consisting of their compliments. The product also consists of two parts which are separated by a vertical line for the purpose of illustration. The RHS (right hand side) of the product can be obtained by simply multiplying the numbers of the Column 2 i.e., (5x3 = 15). The LHS (left hand side) of the product can be found by cross subtracting the second number of Column 2 from the first number of Column 1 or vice versa, i.e., 95 - 3 =92 or 97-5 = 92. The final result is obtained by concatenating RHS and LHS (Answer = 9215).[3] The upa-Sutra ‘A nurupyena' means ‘proportionality’. This Sutra is highly useful to find products of two numbers when both of them are near the Common bases i.e. powers of base 10. It is very clear that in such cases the expected ‘Simplicity ‘in doing problems is absent.[3]
Fig.5. Vedic Cube Algorithm In this 8-bit Anurupye Vedic cube algorithm 4x4 Vedic cube block and 4x4 bit Vedic square blocks are used to implement the algorithm. In final stage carry save adders are used to obtain the result.
Fig.5. Vedic Cube Algorithm In this 8-bit Anurupye Vedic cube algorithm 4x4 Vedic cube block and 4x4 bit Vedic square blocks are used to implement the algorithm. In final stage carry save adders are used to obtain the result.
Fig. 6. simulation result for signed multiplier (32x32) using Urdhva tiryagbhyam International J ournal of Emerging Technology in Computer Science & Electronics (IJ ETCSE ISSN: 0976-1353 Volume 14 Issue 2-APRIL 2015.
Fig. 6. simulation result for signed multiplier (32x32) using Urdhva tiryagbhyam International J ournal of Emerging Technology in Computer Science & Electronics (IJ ETCSE ISSN: 0976-1353 Volume 14 Issue 2-APRIL 2015.
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