If you’ve ever wondered how computers represent numbers beyond the decimal system, the octal number system is one of the easiest places to start.
In this guide, you’ll learn what the octal number system is, how it works, where it’s used, and why it’s still worth understanding—even though computers process everything in binary.
What Is the Octal Number System?
The octal number system is a base-8 numbering system that uses only eight digits:
0, 1, 2, 3, 4, 5, 6, and 7
Unlike the decimal system (base-10), which has ten digits (0–9), octal resets after 7.
For example:
| Decimal | Octal |
|---|---|
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 16 | 20 |
Just as decimal moves from 9 → 10, octal moves from 7 → 10.
Why Is It Called Base-8?
Every number system has a base, which tells you how many unique digits it contains before rolling over to the next place value.
| Number System | Base | Digits Used |
|---|---|---|
| Binary | 2 | 0–1 |
| Octal | 8 | 0–7 |
| Decimal | 10 | 0–9 |
| Hexadecimal | 16 | 0–9, A–F |
Since octal has eight unique digits, it’s called the base-8 number system.
Example of an Octal Number
Consider the octal number:
325₈
Each digit has a place value based on powers of 8.
| Digit | Place Value | Calculation |
|---|---|---|
| 3 | 8² | 3 × 64 = 192 |
| 2 | 8¹ | 2 × 8 = 16 |
| 5 | 8⁰ | 5 × 1 = 5 |
Total = 192 + 16 + 5 = 213
So,
325₈ = 213₁₀
Why Is the Octal Number System Used?
Although computers work internally using binary (0 and 1), long binary numbers can be difficult for humans to read.
Octal solves this by representing every three binary bits as one octal digit.
For example:
| Binary | Octal |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
Instead of writing:
110101111001
you can write:
6571₈
This makes binary values shorter and easier to read.
Where Is the Octal Number System Used?
Today, octal isn’t used as widely as hexadecimal, but you’ll still encounter it in some areas:
- Learning computer fundamentals
- Digital electronics
- Computer architecture
- Embedded systems
- Unix and Linux file permissions (such as 755 or 644)
- Academic computer science courses
Understanding octal also makes learning binary and hexadecimal much easier.
Advantages of the Octal Number System
- Uses fewer digits than binary, making long values easier to read.
- Every octal digit represents exactly three binary bits, making conversion straightforward.
- Helpful for understanding how different number systems relate.
- Still used in areas such as Unix/Linux permissions and computer science education.
Disadvantages of the Octal Number System
- Computers do not process octal directly; they convert it to binary first.
- Less common than hexadecimal in modern software development.
- Not suitable for everyday calculations.
- Many programming languages and hardware tools now prefer hexadecimal because it maps neatly to four binary bits.
Octal vs Binary vs Decimal vs Hexadecimal
| Feature | Binary | Octal | Decimal | Hexadecimal |
|---|---|---|---|---|
| Base | 2 | 8 | 10 | 16 |
| Digits | 0–1 | 0–7 | 0–9 | 0–9, A–F |
| Used By | Computers | Computer science | Everyday math | Programming |
| Easy for Humans | ❌ | ✅ | ✅ | ✅ |
Frequently Asked Questions
Is the octal number system still used?
Yes. While hexadecimal is more common today, octal is still used in computer science education, digital electronics, and Unix/Linux file permissions.
Why are only digits 0 to 7 allowed?
Because octal is a base-8 system. Using 8 or 9 would break the rules of the numbering system.
Why is octal easier than binary?
One octal digit represents three binary bits, making long binary numbers much shorter and easier to read.
Which is better: octal or hexadecimal?
For modern programming, hexadecimal is generally preferred because each hexadecimal digit represents four binary bits. However, octal remains useful for learning number systems and specific computing tasks.
Key Takeaways
The octal number system is a base-8 numbering system that uses digits 0 to 7. It acts as a compact way to represent binary numbers because each octal digit corresponds to three binary bits. Although hexadecimal is more common in modern computing, octal is still important for learning computer fundamentals, understanding digital systems, and working with Unix/Linux file permissions.