Novel Approach to the Learning of Various Number Systems

The number is a symbol or a word used to represent a numeral, while a system is a functionally related group of elements, so as whole, a number is set/group of symbols to represent numbers/numerals. In other words, any system that is used for naming or representing numbers is a number system, also known as numeral system. Almost everyone is familiar with decimal number system using ten digits. However digital devices and computers use binary number system instead of decimal number system, having only two digits i.e. 0 and 1. Binary number system is based on the same fundamental concept of decimal number system. Various other number systems also use the same fundamental concept of decimal number system, e.g. octal number system (using eight digits) and hexadecimal number systems (using sixteen digits). The knowledge of number systems, their limitations, data formats, arithmetic, inter conversion and other related terms is essential for understanding of computers and successful programming for digital devices. Understanding all these number systems and particularly their inter conversion (such process in which things are each converted into the other) of number system requires allot of time and a large number of techniques to expertise. In this particular paper the intercom version of four well-known number systems is taken under the consideration in tabulated as well as graphical form. It is simply a shorthand to the inter conversion of these number systems to understand as well as memorise it. The well-known number systems to be discussed are binary, octal, decimal and hexadecimal.

International Journal of Computer Applications, 2012

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.

ijens.org

Any system that is used for naming or representing numbers is a number system, also known as numeral system. The modern civilization is familiar with decimal number system using ten digits. However digital devices and computers use binary number ...

In today's information age, computers are being used in every walk of life. They are being used by people of all age and profession in their work and in their leisure. This new social revolution has changed the basic concept of 'Computing'. Computing in today's information age is no more limited to computer programmers and computer engineers. It has become an activity of a common man. Rather than knowing how to program a computer, most computer users simply need to understand how a computer functions and what all it can do. Even those who need to program a computer can do their job more effectively with a better understanding of how computers function and the capabilities and limitations of computers. As a result, almost all academic institutions have started offering regular courses on foundations of computing at all levels. These courses deal with the fundamental concepts of the organization, functions, and usage of modern computer systems. Hence we realized that a good textbook that can cover these concepts in an orderly manner would certainly be very useful for a very wide category of students and all types of computer users.

2019

The representation of numbers is essential for the digital logic design. In this chapter, positional number systems (decimal, binary, octal, hexadecimal), BCD and Gray codes are presented together with the rules for the conversion between numbers encoded in different bases and the representations of negative numbers. Then, the rules for the arithmetic operations and the circuits that execute them are presented. The addition of binary number is examined with particular attention, since it is the operation at the basis of all computational circuits. Alphanumeric codes and the concept of parity for error detection complete the chapter.

Introduction and aim: Converting numbers from one number system to another is an important skill, used commonly in millions of computers all over the world. However, even a beginner programmer should face the problem of converting numbers with the support of the programming language C++. This article shall briefly described two numeral systems, and after a short programming introduction in C++ the source code would be offered which easily converts a numbers within both systems. Material and methods: After a short introduction of programming in C++, there was proposed the program source code, which easily converts a numbers within both systems. To create the program the user will need some basic knowledge of the syntax of C++, a wide range of books and courses available in the market. Results: It is presented the program is written and compiled in Orwell Dev-C++ 5.1.1.0. Conclusion: Conversion of numbers within the two most common numerical systems is widespread, so the ability to create the source code, for example, in C++. Keywords: Decimal and the binary numeral system, programming, C++ language.

When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the number: For example: 843 = 8 x 10 2 + 4 x 10 1 + 3 x 10 0 = 8 x 100 + 4 x 10 + 3 x 1 = 800 + 40 + 3 For whole numbers, the rightmost digit position is the one's position (10 0 = 1). The numeral in that position indicates how many ones are present in the number. The next position to the left is ten's, then hundred's, thousand's, and so on. Each digit position has a weight that is ten times the weight of the position to its right.

In this paper, the Double Based Number System is shown along with its allied applications. We would like to discuss the application of this Number System in the area of digital signal processing. We would like to illustrate and emphasize the discussion with concrete examples of finite impulse response filtering. The application of Double Based Number System is mainly in the area of digital signal processing and finite impulse response filtering, which also allows us for an efficient implementation of the basic arithmetic operations and considerable hardware reductions in look-up table size. Number Systems are primarily chosen to enable a reduction of the complexity of the arithmetic operations as the computational complexity of algorithms crucially depends upon the number of zeros of the input data in the corresponding Number System. Experimentally, it has been observed and shown that the expected number of zeros in the representation of arbitrary integers in the Binary Signed-digit Number System tends to show that, on average for long word.