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 248, 1098, 558, etc.
If we solve an octal number, each place is a power of eight.1
1248 = (1 × 82) + (2 × 81) + (4 × 80)
Example Octal to Decimal Conversion
Suppose 2158 is an octal number, then it’s decimal form will be,
2158 = (2 × 82) + (1 × 81) + (5 × 80)
= (2 × 64) + (1 × 8) + (5 × 1) = 128 + 8 + 5
= 14110
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.
Mathematical Mysteries 