# What are the different types of Number Systems? (URGENT)?

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http://en.wikipedia.org/wiki/Numeral

if it's in computing you are talking about the dfifferent, number systems are Base 10(decimal), Base 2(binary), Base 8(Octal), Base 16(Hexadecimal) number system .

Source(s): wikipedia
• Anonymous
4 years ago

Different Types Of Number Systems

Thanks to archeological discoveries and studies of populations that still lives under primitive conditions, we know that our ancestors used various systems to count and order objects. They used their fingers, groupings of small stones, and marks on bones and tree trunks. The most ancient artifacts that has been found is a wolf bone containing 55 incisions: it was found in central Europe and is around 5000 years old.

Number system need of some symbols and some rules.

Actually the most known number systems are:

1) The decimal system- it has three properties:

a) ten different symbols in writing numbers

( 0,1,2,3,4,5,6,7,8,9). For that reason it is said to be a decimal or base ten system. Ten ones are grouped into a set of ten; ten tens are grouped into a set of hundred; and so on...

b) The value of each symbol depends on the position it occupies. Thus we say that the system is positional.

c) it is a complete system because it uses zero.

2) Roman numerals

the roman used seven letters in writing numbers. Their value were as follows: I = 1; V = 5; X = 10; L = 50; C = 100; D = 500; M = 1000;.

This was a nonpositional number system, and it is still used in designating the centuries.

a) If we encounter one letter located to the right of another one with a greater value, they two numbers are added together

b) When one letter is located on the left of another one of greater or equal value, the first is subtracted from the second

c) Whenever a line appears above a letter, we multiply that value by 1000.

3) The binary system

Only two symbols are used in this system: 0 and 1. In trasforming a binary number we use powers of 2.

In writing a number in binary form we must divide it successively by 2.

4) The sexagesimal system

In measuring time and angles, we use a system based on sixty inherited fron the Babylonians.

Ciao!

There are various types of number systems in use togay.

The normal number system in use in daily life has the base of 10. i.e. the number system has digits from 0 to 9 (total digits 10).

The number system used in the computers is called as BINARY. i.e. the number system has only 0 and 1 as digits(total digits 2). This is similar to the two states of a switch i.e ON (1) or OFF (0). the computer can detect these two states of the memmory points on the memmory devices (Floppy discs , Hard discs, magnetic tapes, USB drives etc.).

These binary numbers are grouped into 4 units of 4 each as

0000 0000 0000 0000. when all the units in this are ONE i.e.

1111 1111 1111 1111 this becomes 16 in decimal. This is called as 1 byte and is used as 1 unit in comutation in computers. As this is 16 in decimal format it is called as HEXADECIMAL number sustem. A smaller unit uses only 2 groups of 4 units as 0000 0000 to 1111 1111 this is called as 1 bit in computer terminology. As this is 8 in decimal it is called as OCTAL number system.

There is another number system in use called as the sexadecimal. this is the one used in measuring time

60 seconds = 1 minute and 60 minuts = 1 hour.

Source(s): This is what we had studied in our school.

Your question is vague, but here are some.

In mathematics, a number system is a set of numbers, (in the broadest sense of the word), together with one or more operations, such as addition or multiplication.

Examples of number systems include: natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers, and hyperreal numbers

Simply put, the natural numbers consist of the set of all whole numbers greater than or equal to zero. The set is denoted with a capital N. (In some books, the natural numbers omit 0 and begin with 1. There is no general agreement on this subject.)[1]

Integers

The natural numbers can be extended to the number system called the integers (denoted with Z) as follows. For every non-zero natural number a, there exists an integer denoted −a, which is not a natural number. As a special case −0 is defined as the natural number 0. The successor function can be extended to the integers by the rule S(−a) = −(a − 1).

Rational numbers

The rational numbers (denoted with Q) are the number system that extends the integers to include numbers which can be written as fractions. It allows division to be defined for all pairs of numbers except for division by zero.[3] It also allows the definition of exponents to be extended to negative integer exponents, and to some, but not all, rational exponents.

Polynomials:

Polynomials are not usually called numbers, but they share many properties with numbers. All of the axioms of operations hold for polynomials except for the axiom of multiplicative inverses. Polynomials do not, in general, have multiplicative inverses. Thus the set of polynomials, like the integers, is a commutative ring (with identity).

Algebraic numbers:

The algebraic numbers are a number system that includes all of the rational numbers, and is included in the set of real numbers. The construction of the algebraic numbers requires an understanding of the definition and properties of an extension field. Roughly speaking, one extends the rational numbers by appending all zeroes of polynomials with integer coefficents. This, however, would append complex numbers, which are usually excluded from the algebraic numbers, unless the set is called the complex algebraic numbers. It is, therefore, traditional to construct the real numbers first, and then define the algebraic numbers as a subset of the reals. The algebraic numbers form a field.

Real numbers:

There are many ways to construct the real number (denoted R) system: equivalence classes of Cauchy sequences, transcendental extension fields, and Dedekind cuts, to mention just three. But the most elementary definition is that the real numbers are all numbers that can be written as decimals.

Complex numbers:

The complex numbers are numbers which can be written in the form a + b · i, where a and b are real numbers and i is the square root of minus one -- that is, a number whose square is minus one. The complex numbers can be viewed as abstract symbols, as representing points in the Argand plane, as an extension field of the real numbers, as a two-dimensional vector space with basis {1, i}, and in many other ways. Originally thought to be a pure abstraction, they have proved enormously useful in many practical applications, particularly in electrical engineering.

The word number has no generally agreed upon mathematical meaning, nor does the word number system. Instead, we have many examples. Thus there is no rule to say what is a number and what is not. Some of the more interesting examples of abstractions that can be considered numbers include the quaternions, the octonions, and the transfinite numbers.

Source(s): References Richard Dedekind, 1888. Was sind und was sollen die Zahlen? ("What are and what should the numbers be?"). Braunschweig. Guiseppe Peano, 1889. Arithmetices principia, nova methodo exposita (The principles of arithmetic, presented by a new method). Bocca, Torino. Jean van Heijenoort, trans., 1967. A Source Book of Mathematical Logic: 1879-1931. Harvard Univ. Press: 83-97. B. A. Sethuraman (1996). Rings, Fields, Vector Spaces, and Group Theory: An Introduction to Abstract Algebra via Geometric Constructibility. Springer. ISBN 0-387-94848-1. Solomon Fefferman (1964). The Numbers Systems : Foundations of Algebra and Analysis. Addison-Wesley. Stoll, Robert R., 1979 (1963). Set Theory and Logic. Dover.

i only know the dewey decimal system and i dont even know if thats what youre looking for.

base-2 (binary)

base-3 (Ternary)

base-4