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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, y_{0} is subtracted from 2
and the remaining bits of Y that is y_{i} (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 2^{n} 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.

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