## Description

**Existing System:**

Vedic multiplier is designed by using the concept of Vedic mathematics which uses one of the 16 sutras in it, called Urdhva-Tiryagbhyam (vertically and crosswise multiplication) sutra. By using this multiplier multiplication for all types of numbers irrespective of their size is performed. In this paper the process of 4×4 Vedic multiplier is explained and further implemented to 16bit.

**Methodology for 4×4 Vedic multiplier:**

The dot representation for 4×4 Vedic multiplier is shown below. Here the first row represents the multiplicand bits (a3a2a1a0) and the 2nd row represents the multiplier bits (b3b2b1b0). In this Vedic multiplication process addition of bits takes place which are of equal weights. In the 1st case 0 weights are added i.e., only a0b0. In 2nd case weights equal to one are added by using half adder i.e., a0b1 +a1b0. In the 3rd case Partial products of weight equal to 3 are added by using full adder i.e., a0b2+a2b0+a1b1. If any carry is generated during addition process, it will be added to the next step of addition. The maximum weight for 4 bit multiplication is 6.The same procedure is followed until we get the output as 8 bits including carry.

The design of 4×4 Vedic multiplier is used as a basic building block diagram for design of 8×8 Vedic multiplier. Further design of 16×16 is implemented by using 8×8 Vedic multiplier as basic building block. The aim of using BEC is to reduce the usage of gates compared to normal Vedic multiplier which in turn reduces the power consumption.

It has 4 groups of same size i.e. each group consists of 8*8 Vedic multiplier whose inputs are partitioned according to Urdhva-tiryagbhyam sutra. Outputs from Vedic multiplier are given as inputs to BEC adders of different sizes.

**Disadvantages**:

- Area and delay is high

**Proposed System:**

**Multiplication Using Nikhilam Sutra:**

Nikhilam Sutra factually means “all from 9 and last from 10”. Although it is valid to all cases of multiplication, it is more capable when the numbers involved are big. Since it checks out the compliment of the large number from its adjacent base to perform the multiplication operation on it, better is the original number, lesser the complexity of the multiplication.

Nikhilam Sutra stipulates subtraction of a number from the nearest power of 10 i.e. 10, 100, 1000, etc. The power of 10 from which the difference is calculated is called the Base. These numbers are considered to be references to find out whether given number is less or more than the Base. If the given number is 104, the nearest power of 10 is 100 and is the base. Hence the difference between the base and the number is 4, which is Positive and it is called NIKHILAM.

**Advantages:**

- Area is reduced
- Power is reduced

**Software implementation:**

- Modelsim
- Xilinx ISE