A Step towards an Easy Interconversion of Various Number Systems (original) (raw)
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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.
Novel Approach to the Learning of Various Number Systems
International Journal of Computer Applications, 2011
A number system is a set of rules and symbols used to represent a number, or any system used for naming or representing numbers is called a number system also known as numeral system. Almost everyone is familiar with decimal number system using ten digits. However digital devices especially computers use binary number system instead of decimal, using two digits i.e. 0 and 1 based on the fundamental concept of the decimal number system. Various other number systems also used this fundamental concept of decimal number system i.e. quaternary, senary, octal, duodecimal, quadrodecimal, hexadecimal and vigesimal number system using four, six, eight, twelve, fourteen, sixteen, and twenty digits respectively. The awareness and concept of various number systems, their number representation, arithmetic operations, compliments and the inter conversion of numbers belong different number system is essential for understanding of digital aspects. More over, the successful programming for digital devices require the understanding of various number systems and their inter conversion. Understanding all these number systems and particularly the inter conversion of numbers requires allot of time and techniques to expertise. In this paper the concepts of the most common number systems, their representation, arithmetic, compliments and interconversion is taken under the consideration in tabulated form. It will provide an easy understanding and practising of these number systems to understand as well as memorise them. Few of these number systems are binary, quaternary, senary, octal, decimal, duodecimal, quadrodecimal, hexadecimal and vigecimal.
2021
Cover image: Postage stamp commemorating 150th birth anniversary of Richard Dedekind, whose ideas are fundamental to much of the material in this book.
In today's world, computer plays a very significant role. It comes in different sizes, shapes and applications and had made our life simpler. The language used by the computers is in the form of binary numbers that is in 0 and 1 form .It is the lowest level that helps the machine to read. Computer usually works in binary but gives answer in decimals and that helps it to save the space. This is important as it simplifies the design of computer and related technologies. That's why it is considered as the perfect numbering system for computer. It is also considered easy and there is no comparison how much easier binary is than decimal. In this, we only need 2 digits, o and 1 while in decimal we need 10 digits that made the process much harder. It is a method of storing simple numbers such as 35 and 380 as pattern of 0's and 1's. Due to its digital nature, computers electronic can easily manipulate numbers stored in binary by treating as "on "and "off." Computers are having circuits that perform the arithmetical operations such as add, subtract, multiply, divide, and do many other things to numbers stored in binary.
Number Systems, Base Conversions, and Computer Data Representation
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.
A Different and Realistic Approach to Inter Base Conversion for Number System
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.
Cognitive, Affective, & Behavioral Neuroscience, 2014
Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).
Lecture Notes in Computer Science, 2010
We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit is 2 i −1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored.
Numeral Systems and Binary Arithmetic
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.