© 2021 JETIR July 2021, Volume 8, Issue 7 www.jetir.org (ISSN-2349-5162) JETIR2107213 Journal of Emerging Technologies and Innovative Research (JETIR) www.jetir.org b680 The FPGA Implementation for Transformation of Binary to Double Base Number System (DBNS) with Bases 2 and 5 using Parallel Comparison Method Satrughna Singha Department of Computer Science and Engineering Maulana Abul Kalam Azad University of Technology Haringhata, Nadia, West Bengal, India satrughna.singha@gmail.com Amitabha Sinha Department of Microelectronics and VLSI Technology Maulana Abul Kalam Azad University of Technology Haringhata, Nadia, West Bengal, India becas_amits83@hotmail.com Abstract—In this paper the FPGA implementation of the novel transformation method from binary to double base number system (DBNS) with bases 2 and 5 using parallel comparison method has been presented. Nowadays the DBNS is becoming popular among the other non-binary number systems for their competences of performing multiplication operation efficiently. The DBNS has the major problem which is associated with this number system is the conversion from binary data to DBNS data despite the various advantages of the DBNS. A number of schemes exist to convert the binary number to the DBNS. By observing these matters in view the FPGA implementation of a novel architecture has been proposed for the conversion of binary to DBNS with bases 2 and 5 using parallel comparison method. Keywords—Field Programmable Gate Arrays (FPGAs), Configurable Logic Block (CLB), Binary Search Tree (BST), Conversion Processing Element (CPE), Double Base Number Systems (DBNS), Multiple Index DBNS, Range Table Search (RTS). I. INTRODUCTION In recent times the non-binary number systems are getting attentions among the researchers due to their capabilities of efficient handling of arithmetic operations. Digital signal and image processing applications [1] [2] are compute intensive and demand high performance arithmetic operations in real-time [3] [4] [5]. The Double Base Number System (DBNS) with the bases 2 and 5 having the number representation: x = i, j di, j 2 i 5 j ..........(1) where di, j  {0,1} and i and j are integers and referred to as binary and quinary exponents [6] respectively. The form (1) will be denoted as a double base number system (DBNS). Obviously, the binary number system is an exceptional case of the above illustration. The double base number system is very useful in signal processing applications. The Binary Search Tree (BST) method and the Range Table Search (RTS) method have been used to transform a binary data into the DBNS data. In BST approach the major problem is the time taken for comparison in each iteration. For this reason a new method which is known as the parallel comparison technique which has been employed to reduce the time complexity of the BST approach. The parallel comparison approach reduces not only the time complexity, but also the hardware complexity that has been encountered in the Binary Search Tree (BST) approach [7] [11] despite the Binary Search Tree (BST) methodology gives a proficient architecture for binary to DBNS transformation. In the parallel comparison approach the main advantages of both the Binary Search Tree (BST) and the Range Table Search (RTS) methods have been exploited. Observing these matters in view, a novel architecture has been presented for the transformation of binary to a single index pair DBNS with bases 2 and 5 using parallel comparison method. II TRANSFORMATION OF BINARY TO MULTIPLE DIGITS DBNS WITH BASES 2 AND 5 In this portion the Binary Search Tree (BST) method and the Range Table Search (RTS) method have been used to transform a binary number into a multiple index pairs (indices) DBNS [9] [10] number with bases 2 and 5. A. Transformation Using Binary Search Tree (BST) The BST technique is a popular method to search a number among the various numbers present in an array. Using this basic idea a hardware circuit can be designed for matching a given binary data in a static array. This decreases both the hardware and time complexities. First of all the numbers of the 4*4 DBNS table have been organized in the rising sequence i.e. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 and 1000. Then the given input binary data will be matched with 40 which is nearly in the middle position of the table or array. If the number be larger than 40, then in the next step the number will be matched with 200. If the number be less than 40, then the number will be checked with 8. The procedure is going on and for a given 10-bit binary number, the procedure will face four checking operations. In fact the number of checking operations needed in BST method entirely depends on the numbers existing in the corresponding DBNS table. It is assumed that there are N numbers in the DBNS table. Then for each iteration the number of comparisons have been always = log 2 N. B. Transformation using Range Table Search (RTS) In the BST method the maximum of seven iterations have been needed for transforming a 10-bit binary data extending from 0 to 1023 into Double Base Number [15]. At this moment to decrease the time complexity further, RTS method has been presented. In this method the given input data will be checked concurrently with the reference data which have been stored in the DBNS table. The numbers of the DBNS table have been organized in downward sequence shown below: 1000 500 250 200 125 100 50 40 Range – 1 Range – 2