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IMPLEMENTATION of Urdhva Triyagbhyam multiplier


8 X 8 Bit Multiplication Using Urdhva Triyakbhyam (Vertically and crosswise) for two Binary numbers

Consider two binary numbers A and B of 8 bits as respectively

                                  A =          A7A6A5A4         A3A2A1A0

                                                      (X1)                   (X0)

                                  B =           B7B6B5B4          B3B2B1B0

                                                      (Y1)                    (Y0)

Which can be viewed as two four bit numbers each, i.e. A can be viewed as X1 X0 and B can be viewed as Y1 Y0 respectively, as shown above, thus the multiplication can be written as

                                                     X1  X0

                                                *   Y1  Y0                              



Where,    CP= C = X0Y0

                     CP= A = X1Y0

             CP = B = X0Y1

             CP= D = A+B

             CP= E = X1Y1                                   here CP= Cross Product

Thus, A*B= EDC, is achieved using Urdhva Triyakbhyam (Vertically and crosswise) sutra.






Figure 4.3.

A block diagram representing 8-bit multiplication

Note: Each Multiplication operation is an embedded parallel 4x4 Multiplication modules, which again be described in as follows using Urdhva Triyakbhyam (Vertically and crosswise) sutra, where each dot represents single bit of each four bit number



Fig4.4. Line diagram for multiplication of two 4 - bit numbers.