## Definition

A number system which has its base as ‘eight’ is called an Octal number system. It uses numbers from 0 to 7. Let us take an example, to understand the concept. As we said, any number with base 8 is an octal number like 24_{8}, 109_{8}, 55_{8}, etc.

If we solve an octal number, each place is a power of eight.^{1}

124_{8 }= (1 × 8^{2}) + (2 × 8^{1}) + (4 × 8^{0})

**Example Octal to Decimal Conversion**

Suppose 215_{8 }is an octal number, then it’s decimal form will be,

215_{8} = (2 × 8^{2}) + (1 × 8^{1}) + (5 × 8^{0})

= (2 × 64) + (1 × 8) + (5 × 1) = 128 + 8 + 5

= 141_{10}

## References

^{1} “Octal Number System (Definition, Chart, Octal To Binary)”. 2022. *BYJUS*. https://byjus.com/maths/octal-number-system/.

## Additional Reading

“Octal Number System – Meaning, Conversion, Solved Examples, Practice Questions”. 2022. *CUEMATH*. https://www.cuemath.com/numbers/octal-number-system/.

⭐ “What Is Octal Number System ? – Octal To Binary, Binary To Octal & Octal To Decimal – Electronics Coach”. 2017. *Electronics Coach*. https://electronicscoach.com/octal-number-system.html.

## Videos

It is really important to understand the reason for using Hexadecimal and Octal number systems. In this video, I have explained the need, various usages of Hexadecimal and Octal number system, and also conversion between binary, hexadecimal, and octal number system.

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.