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Subtractor based on Nikhilam Sutra:

Mathematical modeling of “Nikhilam” sutra for Binary Subtraction

The Subtraction method based on Vedic mathematics can be determined by “All from Nine and Last from Ten” sutra. This rule is applicable for decimal number system only. This rule has been little bit modified to apply in Binary arithmetic. The sutra in case of Binary mathematics can be defined as “All from one and Last from Two”. The interpretations for both the rules are same. To elucidate the rule mathematically consider the number  is subtracted from the number . So it can be written as

(11)

(12)

(13)

(14)

(15)

From equation (15) it is clear that the LSB of Y, y0 is subtracted from 2 and the remaining bits of Y that is yi (i=1 to n-1) are needed to be complemented. The output is added with X to achieve the required result.

The last term that is 2n is used to eliminate the overflow generated by the carry after the addition operation. After the elimination operation is executed if the nth position still exhibits high value then it means that the result is negative.

Fig. 4: 8 bit architecture of Binary Subtractor based on Nikhilam Sutra

From the architecture shown in Fig.-4 the first stage subtraction and addition is to determine the 2’s complement of Y and the second stage addition is nothing but the subtraction using 2’s complement methodology. The first stage 2 bit subtractor is to determine  and the MSB of the result is fed to the carry input of the first stage 7 bit parallel adder.