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Multiplication Of Urdhva Tiryabhyam Sutra

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Urdhva Tiryakbhyam Sutra is a general multiplication formula applicable to all cases of multiplication. It literally means “Vertically and crosswise”. It is based on a novel concept through which the generation of all partial products can be done with the concurrent addition of these partial products. Power dissipation which results in higher device operating temperatures. Therefore it is time, space and power efficient. It is demonstrated that this architecture is quite efficient in terms of silicon area/speed. Now let us take two three digit decimal numbers and understand the Urdhva technique. Let the first number be “123” and the second the number be “456”.
Step 1: Initially the unit’s digit numbers are multiplied and the unit’s digit of the product that is 8 is kept as the unit’s digit of the result, the …show more content…

2. Let us consider the multiplication of two decimal numbers (5498 × 2314). The conventional methods already know to us will require 16 multiplications and 15 additions. The numbers to be multiplied are written on two consecutive sides of the square as shown in the figure. The square is divided into rows and columns where each row/column corresponds to one of the digit of either a multiplier or a multiplicand. Thus, each digit of the multiplier has a small box common to a digit of the multiplicand. These small boxes are partitioned into two halves by the crosswise lines. Each digit of the multiplier is then independently multiplied with every digit of the multiplicand and the two-digit product is written in the common box. All the digits lying on a crosswise dotted line are added to the previous carry. The least significant digit of the obtained number acts as the result digit and the rest as the carry for the next step. Carry for the first step (i.e., the dotted line on the extreme right side) is taken to be

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