ToolHorizon

Number Base Converter

Converted result will appear here
🔢 Supported Number Bases
Convert between any of these systems
BaseNameDigits UsedExample
Base 2Binary0, 11010 = 10
Base 8Octal0–712 = 10
Base 10Decimal0–910 = 10
Base 16Hexadecimal0–9, A–FA = 10
Base 32Base32A–Z, 2–7Used in encoding
Base 64Base64A–Z, a–z, 0–9, +/Used in data transfer
🚀 How to Use
Convert numbers between bases instantly
1

Select Input Base

Choose the base your number is currently in — Binary (2), Octal (8), Decimal (10), Hexadecimal (16), or a custom base.

2

Enter the Number

Type your number into the input field. The tool validates that you've only used digits valid for the selected base.

3

Select Output Base

Choose the base you want to convert to. The result appears instantly.

4

Copy the Result

Click the copy button to grab the converted value and use it in your code, calculations, or notes.

💡 Use Cases
Who uses number base conversion and why
💻

Programming

Convert hex memory addresses, binary flags, or octal Unix permissions.

🌐

Web Development

Work with hexadecimal color codes (#FF5733) and convert them to RGB decimal values.

🔐

Cryptography

Base64 encoding is widely used to encode binary data for transmission in emails and APIs.

🎓

Computer Science

Learn and practice binary, octal, and hex number systems for exams.

⚙️

Low-Level Dev

Read binary values from hardware registers, network packets, and file formats.

🔧

Unix Permissions

Convert Unix file permission codes (e.g. 755) between octal and binary.

✨ Pro Tips
🎨

Hex for Colors

Hex color codes are base 16. #FF0000 = R:255, G:0, B:0 in decimal. Use this converter to understand CSS color values.

🔤

Hex Casing

Hexadecimal letters (A–F) can be uppercase or lowercase. Both are valid. Most compilers and tools accept either.

📐

Powers of 2

Binary numbers are base 2. Each binary digit represents a power of 2. 1111 = 8+4+2+1 = 15 in decimal.

🗂️

Unix Permissions

chmod 755 means: 7 (owner: read+write+execute), 5 (group: read+execute), 5 (others: read+execute). Convert 7 from octal to binary: 111.

❓ Frequently Asked Questions
What is a number base? +
A number base (or radix) is the number of unique digits used to represent numbers. Decimal (base 10) uses 10 digits (0–9). Binary (base 2) uses only 2 (0 and 1). Hexadecimal (base 16) uses 16 symbols (0–9 and A–F).
Why do computers use binary? +
Computer hardware is built from transistors that are either ON (1) or OFF (0). Binary maps perfectly to this two-state physical reality. All computer data — text, images, programs — is ultimately stored and processed as binary values.
Why is hexadecimal used in programming? +
Hexadecimal is a compact way to represent binary values. One hex digit represents exactly 4 binary bits. This makes hex much easier to read than long binary strings — e.g. FF in hex = 11111111 in binary.
What is Base64 used for? +
Base64 encoding converts binary data into ASCII text, making it safe to transmit over systems that only support text. It's widely used in email attachments (MIME), embedding images in HTML/CSS (data URLs), and API authentication tokens.
Can I convert negative numbers? +
Basic number base converters work with non-negative integers. Negative number representation (like two's complement) varies by system — for signed binary arithmetic, use a dedicated programming calculator.
What is the largest number I can convert? +
The tool supports large integers with no hard limit in most implementations. JavaScript's BigInt support allows converting very large numbers accurately.
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