The octal number system uses eight digits: 0,1,2,3,4,5,6 and 7 with the base of 8. The advantage of this system is that it has lesser digits when compared to several other systems, hence, there would be fewer computational errors. Digits like 8 and 9 are not included in the octal number system. Just as the binary, the octal number system is used in minicomputers but with digits from 0 to 7.

For example: 35₈, 23₈, 141₈ are some examples of numbers in the octal number system.

Conversion from Octal Number System to Other Number Systems

Octal Numbers are represented with digits 0-7 and with base 8. Conversion of a number system means conversion from one base to another. Following are the conversions of the Octal Number System to other Number Systems:

Steps for Conversion of Octal to Decimal Conversion:

Octal numbers are represented in base 8, but the decimal numbers are of base 10. Hence, to convert an octal number to a decimal number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Multiply each digit of the Octal number with the place value of that digit, starting from right to left i.e. from LSB to MSB.
• Step 2: Add the result of this multiplication and the decimal number will be formed.

Example: 

Steps for Conversion of Octal to Binary Conversion:

Octal numbers are represented in base 8, but the binary numbers are of base 2. Hence, to convert an octal number to a binary number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Write each digit of the octal number separately.
• Step 2: Convert each digit into an equivalent group of three binary digits.
• Step 3: Combine these groups to form the whole binary number.

Example: (247)₈ is to be converted to binary

Steps for Conversion of Octal to Hexadecimal Conversion:

Octal numbers are represented in base 8, but the hexadecimal numbers are of base 16. Hence, to convert an octal number to a hex number, the base of that number is to be changed. Follow the steps given below:

• Step 1: We need to convert the Octal number to Binary first. For that, follow the steps given in the above conversion.
• Step 2: Now to convert the binary number to Hex number, divide the binary digits into groups of four digits starting from right to left i.e. from LSB to MSB.
• Step 3: Add zeros prior to MSB to make it a proper group of four digits(if required)
• Step 4: Now convert these groups into their relevant decimal values.
• Step 5: For values from 10-15, convert it into Hex symbols i.e from A-F

Example: (5456)₈ is to be converted to hex