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The natural numbers are 1, 2, 3, 4, 5, etc. There are infinitely many natural numbers. The set of natural numbers is sometimes written N.
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Decimal Number System

Note how the set of values 0 to 9 is repeated, and for each repeat, the column to the left is incremented from 0 to 1, then 2. Each increase in value occurs, till the value of the largest number in the set is reached 9 , at which stage the next value is the smallest in the set 0 and a new value is generated in the left column ie, the next value after 9 is Base Values The base value of a number system is the number of different values the set has before repeating itself.

For example, decimal has a base of ten values, 0 to 9. Weighting Factor The weighting factor is the multiplier value applied to each column position of the number. For instance, decimal has a weighting factor of TEN, in that each column to the left indicates a multiplication value increase of 10 over the previous column on the right, ie; each column move to the left increases in a multiply factor of The set values used in decimal are.

The digit or column on the left has the greatest value, whilst the digit on the right has the least value. When doing a calculation, if the highest digit 9 is exceeded, a carry occurs which is transferred to the next column to the left. Positional Values [Units, Tens, Hundreds, Thousands etc Columns] We probably got taught at school about positional values, in that columns represent powers of This is expressed to us as columns of ones 0 - 9 , tens groups of 10 , hundreds groups of and so on.

The values are,. Columns are used in the same way as in the decimal system, in that the left most column is used to represent the greatest value. As we have seen in the decimal system, the values in the set 0 and 1 repeat, in both the vertical and horizontal directions. In a computer, a binary variable capable of storing a binary value 0 or 1 is called a BIT. In the decimal system, columns represented multiplication values of That was because there were 10 values 0 - 9 in the set.

In this binary system, there are only two values 0 - 1 in the set, so columns represent multiplication values of 2. Converting Decimal to Binary There are a number of ways to convert between decimal and binary. Lets start with converting the decimal value to binary. Method 1: Divide the number by 2, then divide what's left by 2, and so on until there is nothing left 0. Write down the remainder which is either 0 or 1 at each division stage. Once there are no more divisions, list the remainder values in reverse order. This is the binary equivalent. Method 2: Each column represents a power of 2, so use this as a basis of calculating the number.

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It is sometimes referred to as the approach. Write down the binary number. For example, the Mayans used base, possibly from counting both fingers and toes.

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  8. The Yuki language of California uses base-8 octal , by counting the spaces between fingers rather than the digits. Basic computing is based on a binary or base-2 number system where there are only two digits: 0 and 1. Programmers and mathematicians also use the base or hexadecimal system, which as you can probably guess has 16 distinct numeral symbols. Computers also use base to perform arithmetic. This is important because it allows exact computation, which is not possible using binary fractional representations.

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    Numbers and the Number System :: :

    Deb Russell is a school principal who has taught mathematics at all levels. She is also a freelance writer with more than 14 years of experience. Updated January 20, Rational numbers are either terminating or recurring in nature. Terminating Numbers : Terminating numbers are those numbers which stop after the decimal point.

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    4. Natural Numbers: It is the set of positive numbers. If a number x divides y perfectly, then x is considered as a factor of y and y becomes the multiple of x. Prime Numbers: Prime numbers are the numbers which have no factor other than 1 and itself.

      A fraction denotes a part or parts of a unit. It is majorly classified into following types- 1.

      Octal number system

      Proper Fractions: In a proper fraction the numerator is always less than the denominator. Proper Fractions are always less than 1. Mixed Fraction: A mixed fraction consists of two parts i. The fractions which consist of two parts i. All mixed fractions are improper fractions. Share this Share List.

      Introduction to number systems and binary

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