# Number systems

This calculator shifts numbers between different number systems. In different number systems there are e.g. just two or three digits instead of 10.

## Number systems

Normally, we calculate in the decimal system, i.e. a system of ten digits 0,,9. All numbers higher than 10 are written als combination of some of those signs.

## How to transform numbers from one system into another?

You just gotta know what value a digit has if it stands on a certain place. For example, a 1 on the second right place does always mean 10 in the decimal system, but means another number in any other number system.
The value of the digits in a system with n digits is calculates as follows:
The right digit has always the value 1*its value
The second right digit has the value n*its value
The third right digit has the value n*n*its value, the fourth right digit the value n*n*n*its value and so on.
The value of the number is gotten by adding the values received.

Tu make this more understandable, here an example :
Let's calculate the value of a number written as 3142 in the 5-digit system. At right stands a 2 having the value 1*2=2.
Left to it stands a 4 having the value 5*4=20.
Left to it stands a 1 having the value 5*5*1=25.
At the left stands a 3 having the value 5*5*5*3=375.
So you get 375+25+20+2=422.

## How to transform a decimal number into another number system?

This is also easy: Take the number you want to transform and divide it by the number of digits in that number system. Note the division remainders.

Here is an example: Lets transform 347 into the system with 4 digits.
347:4=86 Remainder 3, so 3 stands on the right.
86:4=21 Remainder 2, so 2 is the next digit on the right
21:4=5 Remainder 1, so 1 is the next digit.
5:4=1 Remainder 1, so we got one more 1.
1:4 equals 0 Remainder 1, so we got one more 1 and are done.
This means 347 is written as 11123 in the 4-digit system.

## What are number systems needed for?

Other number systems have different applications. For example the dual system consisting of zeroes and ones is useful in computer science, cause computers just understand 0 (no power) and 1 (power).

## Number systems

This is a free online calculator for number systems. Just enter your number and it will be transformed.