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# Number Systems Used In Computing

What are the numbers? Are they some physical entity? Some phenomena? No, they are just objects used for measuring a quantity. You must already be aware of the decimal number system that we use. It has the digits from 0-9(0,1,2,3,4,5,6,7,8,9).

But this isn’t the only number system use in the computing world. Computers often have requirements different from us human and they may require a different number system. So let us have a look at some of the number systems used in computing.

## Decimal

We are just talking about the decimal number system. Apart from computers, it is the one we use in everyday life. The decimal system contains 10 elements, the numbers 0,1,2.3.4,5,6,7,8 and 9. Hence, it has a base or radix of 10. In the decimal number system, the numbers to the extreme left are exponentially higher in value than the ones to the right. Take the following example.

The number 126 consists of 3 different digits from the decimal system. Here, it means that the total value of 126 is 100 + 20 + 6.  Each digit in the number has a value of number * 10 positions from right-1. The decimal number system is the most widely used system for general purpose around the world.

## Binary

You must have already heard about this somewhere. Binary number system consists of only 2 numbers 1 and 0, hence the base or radix for this number system is 2. The binary system is also used in Digital Electronics to denote ON and OFF states by using 1 and 0 respectively.

he following is an example of a binary number system.

(101)2

You can see that there is a small 2 written at the bottom after the number, it is the radix of the number system and is often written to clear which number system we are talking about.

So in the number given above, we see 3 digits that are either 1 or 0. Each digit has a value of Digit * 2 position from right – 1. Hence, the value of this number in decimal systems would be 1*22 + 0*21 + 1*20 which is equal to 5 in the decimal system.

## Octal

An Octal number system consists of 8 numbers from 0 and 7, with 0 being the lowest and 7 being the highest in value. The base of this number system is 8.

Let us see an example of this number system.

(207)8

So in the number given above, we see a total of 3 digits that are between 0-7. Each digit has a value of Digit * 8 position from right – 1. So the value of this number would be 2*82 + 0*81+ 7*80 which would sum up to 135 in the decimal system.

Octal numbers are usually grouped in 3. The number (20745)8 would become 020 745since the grouping must be done from the right and you can add additional zeros to the left to complete a group of 3 numbers.

A Hexadecimal number system consists of 16 numbers from 0-F. There are 16 numbers in this system and hence it has a base of 16. Here is a table showing the decimal equivalents of characters from hexadecimal system.

​Since the base for this system is 16, it has 6 more digits than the decimal system. We obviously couldn’t have taken 10,11,12,13,14 and 15 since they are a mixture of more than 1 digit and would cause confusion. Hence, A is used for 10, B for 11 and so on till F for 15.

Let us see an example of this number system.

(0F2A)16

So in this number, we see a group of 4 digits from 0-F. Each digit has a value of Digit * 16position from right – 1. The value of this number would be 0*163 + F*162 + 2*161 + A*160which would sum up to 3882 in the decimal system.

Hexadecimal numbers are usually grouped in 4. The number (0F2A23)8 would become000F 2A23 since the grouping must be done from the right and you can add additional zeros to the left to complete a group of 4 numbers.

So these were some important number systems used in computing. I hope you understood everything. If you ever get stuck with this or need some help, just drop a comment, I’ll be there for you.

Dec 3, 2014

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Feb 1, 2017