Design of an Efficient Binary Vedic Multiplier for High Speed Applications Using Vedic Mathematics with Bit Reduction Technique  

作　　者：S. K. Manikandan C. Palanisamy S. K. Manikandan;C. Palanisamy(Department of EEE, Velalar College of Engineering and Technology, Erode, India;Department of Information Technology, Bannari Amman Institute of Technology, Sathyamangalam, India)

机构地区：[1]Department of EEE, Velalar College of Engineering and Technology, Erode, India [2]Department of Information Technology, Bannari Amman Institute of Technology, Sathyamangalam, India

出　　处：《Circuits and Systems》2016年第9期2593-2602,共10页电路与系统（英文）

摘　　要：Vedic mathematics is the system of mathematics followed in ancient Indian and it is applied in various mathematical branches. The word “Vedic” represents the storehouse of all knowledge. Because using Vedic Mathematics, the arithmetical problems are solved easily. The mathematical algorithms are formed from 16 sutras and 13 up-sutras. But there are some limitations in each sutra. Here, two sutras Nikhilam sutra and Karatsuba algorithm are considered. In this research paper, a novel algorithm for binary multiplication based on Vedic mathematics is designed using bit reduction technique. Though Nikhilam sutra is used for multiplication, it is not used in all applications. Because it is special in multiplication. The remainder is derived from this sutra by reducing the remainder bit size to N-2 bit. Here, the number of bits of the remainder is constantly maintained as N-2 bits. By using Karatsuba algorithm, the overall structure of the multiplier is designed. Unlike the conventional Karatsuba algorithm, the proposed algorithm requires only one multiplier with N-2 bits only. The speed of the proposed algorithm is improved with balancing the area and the power. Even though there is a deviation in lower order bits, this method shows larger difference in higher bit lengths.Vedic mathematics is the system of mathematics followed in ancient Indian and it is applied in various mathematical branches. The word “Vedic” represents the storehouse of all knowledge. Because using Vedic Mathematics, the arithmetical problems are solved easily. The mathematical algorithms are formed from 16 sutras and 13 up-sutras. But there are some limitations in each sutra. Here, two sutras Nikhilam sutra and Karatsuba algorithm are considered. In this research paper, a novel algorithm for binary multiplication based on Vedic mathematics is designed using bit reduction technique. Though Nikhilam sutra is used for multiplication, it is not used in all applications. Because it is special in multiplication. The remainder is derived from this sutra by reducing the remainder bit size to N-2 bit. Here, the number of bits of the remainder is constantly maintained as N-2 bits. By using Karatsuba algorithm, the overall structure of the multiplier is designed. Unlike the conventional Karatsuba algorithm, the proposed algorithm requires only one multiplier with N-2 bits only. The speed of the proposed algorithm is improved with balancing the area and the power. Even though there is a deviation in lower order bits, this method shows larger difference in higher bit lengths.

关 键 词：Karatsuba Nikhilam Sutra Bit Reduction REMAINDER MULTIPLIERS 

分 类 号：TN9[电子电信—信息与通信工程]