How to Convert Binary, Octal, Decimal, and Hexadecimal Numbers
Computers speak binary, programmers use hexadecimal, and everyone else counts in decimal. Occasionally, octal still appears in legacy file permissions. Toolzo’s free Number System Converter lets you type in any of these bases and instantly see the other three — no calculation needed. This beginner‑friendly guide explains what each system means and how to read the conversions.
Why multiple number systems exist
Binary (base‑2) is the language of transistors — 0 and 1. Decimal (base‑10) is our everyday arithmetic. Hexadecimal (base‑16) uses 0‑9 and A‑F to represent bytes compactly: colour codes (#FF5733), memory addresses, and Unicode. Octal (base‑8) was used on early mainframes and still appears in Unix permissions. Understanding them opens up programming, debugging, and digital electronics.
- Read hex colour codes in web design.
- Decode binary data or machine code snippets.
- Set file permissions using octal notation (chmod 755).
Quick Reference: Number Systems
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
| 1000 | 1111101000 | 1750 | 3E8 |
Step‑by‑step: convert numbers
- Open the Number System Converter tool.
- Click inside any of the four fields (Binary, Octal, Decimal, Hex) and type a value that matches the base — e.g., type `A` in Hex.
- As you type, the other three fields update automatically. For Decimal, type `10` and you’ll see Binary `1010`, Octal `12`, Hex `A`.
- Clear a field to reset; the tool highlights invalid characters (like a digit 9 in binary).
Practical applications
If you’re studying subnet masks in networking, you’ll need to convert between decimal and binary. In CSS, RGB values are decimal, but many design tools show HEX. For an easy colour conversion, our Color Converter translates these automatically. If you’re dealing with large data units, the Data Storage Converter also uses binary/decimal toggles.
Frequently Asked Questions
What’s the highest number I can convert?
JavaScript can safely handle integers up to 2^53‑1, so the tool works for very large numbers without issue.
Can I use lowercase letters in hex?
Yes, both uppercase and lowercase A‑F are accepted.
Why are binary numbers so long?
Each binary digit (bit) holds only two values, so it takes many digits to represent even small decimal numbers.
Does it support negative numbers?
The converter works with positive integers; for signed binary, you’d need a two’s complement calculator.
Is the tool free?
Yes, completely free and all processing is client‑side.
Try the Number System Converter