International Journal of Computer Applications (0975 – 8887) Volume 52– No.18, August 2012 37 A Different and Realistic Approach to Inter Base Conversion for Number System Saurabh Rawat Dept. of Computer Science & Engg. Graphic Era University Dehradun, India Bhaskar Nautiyal Dept. of Computer Science & Engg. Graphic Era University Dehradun, India Anushree Sah University of Greenwich, London, U.K ABSTRACT A number system (or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases. A number system is a set of rules and symbols used to represent a number. Binary ( 0 , 1 ) and other famous number systems, octal ( 0-7 ), hexadecimal ( 0-15 ) are based on same fundamental concept of decimal number system ( 0-9 ). The knowledge of number systems, their representation, limits, arithmetic compliments and inter conversion of numbers between prescribed number systems is essential for understanding of computers and successful programming for digital devices. Understanding all these number conversions ( from one base to decimal and to another base ) and related concepts requires a lot of time and large time consuming techniques to expertise. In this paper we have elaborated concepts of conversion among different bases and proposed with the help of a table to obtain simply and effectively solution from one base to another base conversion, without converting to decimal number system. This effort will also enhance the knowledge intellectuals understanding and practicing of number system conversions. General Terms Number system, binary,octal, hexadecimal,inter conversions Keywords Number system, binary,octal, hexadecimal,inter conversions 1. INTRODUCTION A number system defines a set of values to represent quantity. We talk about the number of people attending a class, the number of modules taken by each student and use numbers to represent grade.[2] Number System can be categorized in two systems:- (a) Non-Positional Number System (b) Positional Number System Non-Positional Number System- In ancient times, people used to count on fingers, when the fingers became insufficient for counting, stones, pebbles or sticks were used to indicate values. But it was very difficult to perform arithmetic with such a number system as there is no symbol for zero. Positional Number System- In this system the value of each digit is defined not by the symbol but also by the symbol position. Positional Number System is used to perform arithmetic. Existing Positional number system is decimal number system. Apart from the decimal number system, there are binary number system, octal number system and hexadecimal number system. Base (Radix)- In the number system the base or radix tells the number of symbols used in the system. In the earlier days, different civilizations were using different radixes. The Egyptian used the radix 2, the Babylonians used the radix 60 and Mayans used 18 and 20. The base of a number system is indicated by a subscript (decimal number) and this will be followed by the value of the number. For example . ) 56 ( ) 457 ( , ) 879 ( 16 8 10 A and Beside the fact that many students know the decimal (base 10) system, and are very comfortable with performing operations using this number system, it is too important for students to know and understand that the decimal system is not the only number system. By studying other number systems such as binary (base 2) quaternary (base 4), senary (base 6), octal (base 8), unodecimal ( base 11 ) , duodecimal ( base 12 ) , tridecimal ( base 13 ), quadrodecimal (base 14 ), pentadecimal (base 15 ), hexadecimal (base 16) and so forth [3], students will gain a better understanding of how number systems work in general. It is well known that the design of computers begins with the choice of number system, which determines many technical characteristics of computers. In modern computer, number system used is binary number system. All other number systems are converted to binary number system for computer to access data. 2.1 Digits and their positions Such a symbol used in a system of numeration or one of the ten Arabic number symbols, 0 through 9 is called digit. The first digit of/in any number system is always a zero. For example, a base 2 (binary) numbers have 2 digits: 0 and 1, a base 8 (octal) numbers have 8 digits: 0 through 7 and so forth. Remember that a base 10 or decimal numbers does not contain the digit 10, similarly base 8 or octal numbers does not contain a digit 8, and same is the case for the other number systems. Once the digits of a number system are understood, each and every larger numbers can be constructed using positional notation or place-value notation method. According to this method, the first right most digit (integer) has a unit’s position in decimal number. Further, to the left of the units position is the ten’s position, the position to the left of the ten’s position is the hundred’s position and so forth. Here, the units position has a weight of , or 1; the tens position has a weight of , or 10; and the hundreds position has a weight of , or 100. The exponential powers of the positions are significant for understanding numbers in other number systems. Always, the unit’s position in any number system is the position to the left of the radix point. For example the position to the left of the binary (radix) 0 10 1 10 2 10