# Computer number system

These digits (O and 1) are called bits and correspond to the off/on sections of the switches in the computer processor. With only these two digits, a computer can perform all the arithmetic that we can with ten digits. A number system defines how a number can be represented using distinct symbol. A number can be represented differently in different systems. For example, the two numbers (AAA)16 and (52)8 both refer to the same quantity, (42)10, but their representation are different.

As human being, we use the decimal number system (base-10 number system) for counting; while the computer uses binary number 2 system (base-2 number system) thus there are two numbers: o and 1 . A single computer switch can represent both computer numbers; 1 = ON and O = OFF. A single binary is called binary digit or bit. Computers perform operations on binary number groups called words. Today most computer uses 32-, 64-, or 128- bit words. Words are subdivided Into bolts groups called bytes. There are four most common number systems that are frequently used in computers.

These number systems are: ; Binary number system ; Decimal number system ; Hexadecimal number system ; Octal number system Computer number system is important as it helps the computer function. Without number system we can’t even think of computer because it stores all the data in form of binary number system (O and 1). So without binary number system computer couldn’t have originated. Decimal Number system is also very important as internet protocol (IPPP) which Is responsible for network communication between two or more computer systems needs It to work, The new Internet protocol (IPPP) uses Hexadecimal number system to work.

We use number systems when working with arrays, without a number system you would not be able to keep track of what is going on in a computer system. Number systems are highly ITIL to security codes. Number theory is tightly linked to cryptography, which uses On Internet security mainly) modulus arithmetic and prime number factorization, important parts of number theory. 1. 1 Statement of problem This project work addresses the issues related to computer number system, seeking answers to the following 0 How a number of digits can be converted from one number system to another. To study how to use complement system to represent negative numbers 1. 2 Objective of Study The objective of this study is to demonstrate how numbers can be converted from one number system to another 1. Signification of the Study This research work is aimed at instructing students, computer analyst and computer programmers towards a better and easy way of understanding the computer language (number system). This study should among other things; 0 Help students gain a better understanding of number system and its application to real life problems. Increase our ability to add and subtract two numbers having as many as three digits and involving renaming in the ones place. Increase our ability to convert from one number system to another. Improve our knowledge on how to use complement system to represent negative numbers 1. Literature review A lot of research in recent years has been directed at solving the computer language (number system), this is because of its importance in the computer filed.

A number system (or numeral system) has been defined by (Brother Froufrou and Furious Mammograms, 2008) as how a number can be represented using distinct symbols. This research work will concentrate on how to use these distinct symbols in representation of number. (O. E. Connors and C. I. Ann. 2010) said that the first digit (LASH) of a number system is referred to as the most significant digit (MS) while the last digit is the least significant digit (LSI). Number system can be classified into two groups: positional and non positional number system.

This research work will concentrate on position number system. (B. Ram, 2000) said that the number system in which the weight of each digit depends on its relative position within the number, is called positional number system. (Bob Brown, 2001) said that all modern computer systems use binary, or base two, to represent numbers internally. Consequently, this number system and the method of adding and subtracting in number system and numbers involving 5 renaming in the ones place and how numbers of digits needed in a system represents data.

Brother Froufrou and Furious Mammograms, 2008) said that arithmetic operations involve adding, subtracting and dividing. ” This research work will include how to use arithmetic operation in adding two integers number system, also how to use arithmetic operation in subtracting integer number system and how to use arithmetic operation in multiplication and dividing integer number system. (Brother Froufrou and Furious Mammograms, 2008) said that all arithmetic operations such as addition, subtraction, multiplication, and division can be applied to integers. Also (Brother Froufrou and Furious Mammograms, 2008) said that all arithmetic operations such as addition, subtraction, multiplication, and division can be applied to real stored in floating point format. ” This research will include how to use sign and magnitude representation of binary number to store integers. (Brother Froufrou and Furious Mammograms, 2008) said that in sign and magnitude representation, the leftmost bit defines the sign of the integer, if it is O, the integer is positive, but If it is 1 the integer is negative.

Finally, this work will include how to use two’s compliment representation to store a signed integer in an n-bit memory location. Brother Froufrou and Furious Mammograms, 2008) said that almost all computers uses two’s compliment representation to store a signed integer in an n-bit memory location. ” 6 Chapter Two 2. 0 Theoretical Background The study of number system started with the research of an Indian scholar Pinball (circa 5th-2nd centuries BC) who developed mathematical concepts for describing prosody, and in so doing presented the first known description of a binary numeral system.

He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. A set of eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were known in ancient China through the classic text I Chining. In the 1 lath century, scholar and philosopher Shah Young developed a method for arranging the hexagrams which corresponds to the sequence O to 63, as represented in binary, with yin as O, yang as 1 and the least significant bit on top. There is, however, no evidence that Shah understood binary computation.

The ordering is also the lexicographical order on sextuplet of elements chosen from a two-element set. In 1605 Francis Bacon issued a system whereby letters of the alphabet could be reduced to sequences in any random text. Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: 7 ” provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature”. The modern binary number system was studied by Gottfried Leibniz in 1679.

Leibniz system uses O and 1, like the modern binary numeral system. As a Shoeshine, Leibniz was aware of the I Chining and noted with fascination how its Seagram correspond to the binary numbers from O to 1 1 1 1 1 1, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. In 1854, British mathematician George Bole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry.

In 1937, Claude Shannon produced his master’s thesis at MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history. Entitled A Symbolic Analysis of Relay and Switching Circuits, Chanson’s thesis essentially founded practical digital circuit design. In November 1937, George Stylist, then working at Bell Labs, completed a released computer, he dubbed the ” Model K” (for ” Kitchen”, where he had assembled it), which calculated using binary addition. Bell Labs thus authorized a full research programmed in late 1938 with Stylist at the helm.

Their Complex Number Computer, completed January 8, 1940, was able to calculate complex numbers. In 8 a demonstration to the American Mathematical Society conference at Dartmouth College on September 1 1, 1940, Stylist was able to send the Complex Number Calculator remote commands over telephone lines by a teletype. It was the first computing machine ever used remotely over a phone line. Some participants of the conference who witnessed the demonstration were John von Neumann, John Macaulay and Norte Wiener, who wrote about it in his memoirs.

The earliest evidence of decimal numeral system appeared in 13th century B. C in Shank dynasty in China, and it was more advanced than contemporary Babylon and Egypt. In 1913, noted Japanese mathematics historian Yogis Mikado wrote that counting rods were used nice the year 542 BC. Counting rods (Y. Mikado called them ” calculating pieces”) are made of bamboo or wooden pieces of red and black colors, the red pieces representing positive numbers, and the black for negative numbers.

Archaeological evidence indicated that a full-fledged, positional decimal system of numerals, known as the rod calculus, consisting of ” hardware” (the counting rods) and ” software” (Chinese multiplication table) with the associated arithmetic operations of addition, subtraction, multiplication and division was fully developed in thespians calculating rods of 12 inch each from Human Change Shah Ouzo Gong mountain area, ND a bundle of well preserved animal bone calculating rods stored in a silk pouch, unearthed from a West Han era tomb from Shania Asian Yang county.

Most importantly, in 2002, Chinese archaeologists unearthed a wood script from a two- thousand-year-old site from the Warring 9 States period, on which is written ” four eight thirty two, five eight forty, six eight forty eight. ” This is the earliest discovered instance of a Chinese multiplication table, which is a prerequisite piece of ” software” for carrying out positional decimal calculation with counting rods. Unlike the multiplication tables of other civilizations, he Chinese multiplication table in use since the Warring States contains at most 81 terms, from ex. to XIX , consistent with a positional decimal rod calculus system.