The main objective of the book is to bring out broad outlines of different types of Signed digit number system. It presents the information about the basics principles and performance of various Signed digit number system. The concept of redundant arithmetic is introduced, with the help of which we can eliminate the carry propagation chain and due to which the speed of addition operation can be increased. Also various digital adders have been designed and comparative study between them is done. With the help of adders we can realize any digital circuits. In Adder, the carry propagation causes a delay that result in the increase of execution time. The delay can be reduced either by reducing the length of carry propagation chain or by removing it. In this book we have provide a technique so that we can increase the speed of addition by using hybrid signed digit adders. Hybrid signed digit number representation perform addition in such a way that the carry propagation chain is limited to single digit position and hence are used to speed up arithmetic operation. Using the hybrid signed digit adder we have analysis the performance of the Bi- quad filter.