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Octal Number System
Octal Number System is a type of number system that has a base of eight and uses digits from 0 to 7. A number system is a system of naming, representing, or expressing numbers in different types of forms. The basic ways of representing numbers are done in four ways i.e. Octal Number System, Binary Number System, Decimal Number System, and Hexadecimal Number System.
Definition of Octal Number System
A number system with its base as eight and uses digits from 0 to 7 is called Octal Number System. The word octal is used to represent the numbers that have eight as the base. The octal numbers have many applications and importance such as it is used in computers and digital numbering systems. In the number system, octal numbers can be converted to binary numbers, binary numbers to octal numbers by first converting a binary number to decimal number then decimal number to octal number.
Similar to the octal number system, the binary number system is represented by the base 2, the decimal number system is represented by the base 10 and the hexadecimal number system is represented by the base 16. A few of the examples of these number systems are:
 \((10)_{2}\) is a binary number
 \((119)_{10}\) is a decimal number
 \((51)_{6}\) is a hexadecimal number
While solving an octal number, each place is a power of eight. For example: \((347)_{8}\) = 3 x 8^{2} + 4 x 8^{1} + 7 x 8^{0}
Conversion from Octal to Binary Numbers
For the process of conversion, we need to convert each number from the octal number to the binary number. Every digit has to be converted to a 3bit binary number and hence arriving at the binary equivalent of the octal number. Below is a table representation of the binary numbers to the octal numbers and vice versa.
Example 1  Convert \((14)_{8}\) into a binary number
Solution  Given \((14)_{8}\) is an octal number, with the help of the above table we can write \((14)_{8}\)_{ }= \((001 100)_{2}\). Zeros on the left do not have any significance. Hence, \((14)_{8}\)_{ }= \((001 100)_{2}\).
Example 2  Convert \((11100101)_{2}\)_{ }into an octal number.
Solution  Given \((11100101)_{2}\) is a binary number, with the help of the above table we first write the number into its 3bit binary number as a zero needs to be added before digits to form the 3bit binary number. So, the number can be written as \((011100101)_{2}\). Hence, the 3bit binary number is 011, 100, 101. Looking at the same table above we can convert these binary numbers to their octal numbers to derive the final number. Hence, the numbers are 3, 4, 5
Therefore, \((11100101)_{2}\) = \((345)_{8}\)
Conversion from Octal to Decimal number
The conversion of octal numbers to decimals numbers is done in a simple way. The number is expanded with the base of eight where each number is multiplied with the reducing power of 8. The decimal number system has a base of 10 after the conversion.
For example  Convert octal number \((121)_{8}\) to its decimal form.
Solution  \((121)_{8}\)_{ }= 1 x 8^{2} + 2 x 8^{1} + 1 x 8^{0}
= 1 x 64 + 2 x 8 + 1 x 1
= 64 + 16 + 1
Therefore, \((121)_{8}\) = \((81)_{10}\)
Conversion from Decimal to Octal Number
To convert decimal to octal number, a different method is used. In this method, the decimal number is divided by 8 each time a reminder is obtained from the previous digit. The first remainder obtained is the least significant digit(LSD) and the last remainder is the most significant digit(MSD). Let us understand the conversion with the help of an example.
For example  Convert the decimal number 321 to its octal form.
Solution  We need to start dividing the number 321 by 8
321/8 gives quotient 40 and the remainder is 1
40/8 gives quotient 5 and the remainder is 0
So, here quotient is 5 and the remainder is 0. The octal number starts from MSD to LSD, i.e 501
Therefore, \((321)_{10}\) = \((501)_{8}\)
Conversion from Octal to Hexadecimal Numbers
Hexadecimal is represented with base 16 and consists of both numbers and alphabets. The numbers from 09 are represented in the usual form, but from 10 to 15, it is denoted as A, B, C, D, E, F. Conversion of Octal to Hexadecimal is done in two steps i.e. first convert the octal number to decimal number and then convert it to a hexadecimal number. Let us look at an example to understand this method better.
For example  \((121)_{8}\) = \((81)_{10}\)
Solution  We already have the decimal number 81_{10}, so we only need to convert this to a hexadecimal number. To determine the hexadecimal number we need to divide the number 81 by 16 until the remainder is less than 16. It is completely divisible with the answer as 5 and the remainder as 1.
Therefore, \((121)_{8}\) = \((51)_{16}\)
Octal Number System Related Topics
Check out these interesting articles to know more about the octal number system and its related topics.
Important Points
 Conversion from octal numbers to binary numbers and vice versa is very simple.
 For converting Octal Numbers to Hexadecimal Numbers, the octal number needs to be converted to a decimal and then to hexadecimal.
 The base of each of the four number systems is very important.
Solved Examples

Example 1  Convert binary number \((001100101101110)_{2}\) to the octal number
Solution  First write the 3bit binary number for the mentioned binary number according to the table i.e 1, 4, 5, 0, 5, 6
Therefore, \((001100101101110)_{2}\)_{ }= \((145056)_{8}\)

Example 2  Convert the octal number \((456)_{8}\) to a hexadecimal number.
Solution  To convert a hexadecimal number we need to first convert the octal number to a decimal number and then convert it to a hexadecimal number.
\((456)_{8}\)_{ }= 4 x 8^{2 }+ 5 x 8^{1} + 6 x 8^{0}
= 4 x 64 + 5 x 8 + 6 x 1
= 256 + 40 + 6
\((456)_{8}\) = \((302)_{10}\)
Hence, the decimal number is \((302)_{10}\)_{. }Now we can find out the hexadecimal number by dividing 302 by 16 until the remainder is less than 16. A simple division method is applied to find out the remainder and the quotient. After dividing the number we obtain 18 as the quotient and 14 as the remainder.
Therefore, \((456)_{8}\) = \((18D)_{16}\)
FAQs on Octal Number System
What is an Octal Number System?
A number system with its base as eight and uses digits from 0 to 7 is called Octal Number System. The word octal is used to represent the numbers that have eight as the base. The octal numbers have many applications and importance such as it is used in computers and digital numbering systems. The word Octal is a short form of the Latin word 'Oct' which means short.
What are the Uses of Octal Numbers?
The Octal Number system is widely used in computer application sectors and digital numbering systems. The computing systems use 16bit, 32bit or 64bit word which is further divided into 8bits words. The octal number is also used in the aviation sector in the form of a code.
What is the Importance of the Octal Number System?
The octal number system uses digits from 0 to 7 which can be made from binary numbers by grouping binary digits in its 3bit representation. Octal numbers use a lesser number of digits as compared to decimal and hexadecimal which makes it easy to compute in fewer steps.
What are the Four Types of Number System?
The four main types of the number system are:
 Binary Number System
 Octal Number System
 Decimal Number System
 Hexadecimal Number System
Which Symbols are Used in the Octal Number System?
The octal number system is a number system of base 8 which means that 8 different symbols are needed to represent any number in the octal system. The symbols are 0, 1, 2, 3, 4, 5, 6, and 7. The smallest twodigit number in this system is \((10)_{8}\) which is equivalent to decimal 8.
What are the Advantages and Disadvantages of the Octal Number System?
The advantages of the octal number system are that it is onethird of the binary number system, the conversion process of octal to binary and vice versa is very simple, and in the octal form, it is simple to handle input and output. The disadvantages of the octal number system are that there is an additional requirement of a system within the computer that provides easier conversion of octal numbers to binary numbers before it is actually applied to a digital platform.
How Do you Convert Octal to Decimal?
To convert octal to decimal, we need to expand the number with the base of eight where each number is multiplied with the reducing power of 8. Once the product is obtained, we add the numbers to arrive at the decimal number. The decimal number system has a base of 10 after the conversion.
How Do you Convert Decimal to Octal?
To convert decimal to octal, the decimal number is divided by 8 each time a reminder is obtained from the previous digit. The first remainder obtained is the least significant digit(LSD) and the last remainder is the most significant digit(MSD).
How Do you Convert Octal to Hexadecimal?
Hexadecimal is represented with base 16 and consists of both numbers and alphabets. The numbers from 09 are represented in the usual form, but from 10 to 15, it is denoted as A, B, C, D, E, F. Conversion of Octal to Hexadecimal is done in two steps i.e. first convert the octal number to decimal number and then convert it to a hexadecimal number.
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