Numbers have played a pivotal role in our society since the beginning of time, yet many of us know nothing about how these numbers work. The blog article discusses different number systems like decimal, hexadecimal, octal, and binary, and their uses.

Decimal System-In the decimal system, numbers are represented using a base number (10, 12, 15, 20, etc.). This base number is combined with other numbers to create other numbers. For example, 35 can be represented as 3 plus 5 (10), or as 11 (base 10 plus 1).

How are Decimal Numbers Represented?

Decimal numbers are represented in base 10, which means that each number is divided by 10 to get its representation. The number "1" is written as "one", the number "2" is written as "two", and so on. 

Octal system-Octal numbers are a base numbering system used in computers. They are made up of the digits 0 through 7. In this system, the number 8 is not a number, but instead, it is the number 0 repeated twice.

How are Octal Numbers Represented?

Octal numbers are base 8, just like binary. To represent an octal number, you take the number and add the corresponding digit to it. For example, the number 97 is represented as 1010 in octal notation. 

Here are some examples of octal numbers:

 12345 = 0123

 12346 = 0012

 12347 = 0000

 12348 = 00002

 12349 = 00004

 1235 = 1111

Binary system-The binary system is a numbering system that uses base 2. This system is used in computers and other electronic devices, as well as in telecommunications.

In a binary system, every number is represented by a combination of two digits. The first digit represents the number's base (2 in this case), and the second digit represents its position in the number.

For example, the number 12 would be represented by the combination of 1 and 2 (1 Base 2, or 10 in decimal), the number 23 would be represented by the combination of 101 and 102 (11 Base 2, or 21 in decimal), and so on.

The advantage of using a binary system is that it's easy to convert between numbers and letters. For example, the letter A can be converted to the number 10 by adding 1 to it (10 + 1 = 11). Similarly, the letter B can be converted to the number 11 by subtracting 1 from it (11 - 1 = 10).

How are Binary Numbers Represented?

Binary number systems are made up of 0s and 1s. They're often represented using the digits 0-9, but they can also be represented in other ways. For example, in binary notation, a number that is 10,000 would be written as 1000000. In decimal notation, this would be written as 100. In hexadecimal notation, this would be written as 16. In octal notation, it would be written as 8.

In binary notation, each digit is either a 0 or a 1. So, for example, the number 11 would be written as 1010. The number 12 would be written as 1011 and so on. The number 11101 would be written as 0111110 in binary notation.

Hexadecimal system-Decimal, hexadecimal, octal and binary number systems are all base numbering systems. They all use a 10-base system. This means that each number is represented by a combination of the digits 0-9.

A hexadecimal number system is made up of 16 digits, each one representing a 0-9 number. The first six digits are used to represent the numbers 0-F, and the last six represent the numbers 10-15. For example, the number 12 would be represented as "12", "12H", "1FH", and "2FH".

How to convert the numbers?

If you are working with different number systems and need to convert these numbers to one or multiple other number systems, it can be a cumbersome task to do all the calculations.

However, with binary decimal hexadecimal converter and other similar converters available online for free, you can easily covert the decimal, binary, octal, and hexadecimal numbers into one or all of the other numbers systems.