Base For Number System

Base For Number System

Base:

The base defined as:

                       

                         "The number that is going to be raised the power is called a base.

Base Formula For Power Or Position Of Number:

                    aXb³+a Xb²+aX b¹+aXb⁰+ a  X b(n-₁)+a X b(n-₂)+a X b(n-₃)-------n

There is above formula for the base

Where  a= digit of numbers

            b= base 

            n0,n1,n2,n3= power increase for integer value right side to left 

            And 
            n-1, n-2,n-3 show the power decrease for fraction value from left side to right side .

The base another name is the radix.

Characters Of Base In Number System:

1.The power of numbers started for  integers from right side and increase to left side.

2.The power of numbers started for fraction value at negative -1 and decrease from left side     to right side.

3.The base is used when another base converts  into decimal numbers.

4.The base is used when subtraction is used in different type of number system.

5.The base power of integer and fraction value is decreasing from the left side to right side.

Example:

Ex1:    1289 is the decimal integer number  when gives power to its digits  than its write as follows.

(1289)₁₀ = 1x10³+2x10²+8x10¹+9x10⁰

In this example the base of digit increase from the right side of numbers to the left side.

It started from the  right side so 

The 1st digit is 9 and their 10 base power is 0.

The 2nd digit is 8 with their 10 base power is 1.

The 3rd digit is 2 with their 10 base power is 2.

The 4th digit is 2 with their 10 base power is 3.

This base power shows the position of digits or weighted of the digits in the number.

Ex2:  0.166 is the decimal fraction number when gives power to this number than  its Write as follows:

(0.166)₁₀ = 1x10ᐨ¹+6x10ᐨ²+6x10ᐨ³

This example  fraction value we start to give base power from the left side to right side

so the first digit is 1 and its base power is -1 then

The 2nd number is 6 and its base power is -2 then 

The 3rd and last number is 6 with their base power -3.

In above two examples noted the base power is decreasing from left to right side and increase right to left side.