Number Base Converter

What is Number Base Conversion

Number base conversion translates values between different numeral systems — binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16). Computers operate in binary, but developers need different bases depending on context.

Quick Conversion Reference

Common Use Cases by Base

• Binary: Bitwise operations, permission masks, network subnets (255.0.0.0 = 11111111.00000000...)
• Octal: Unix file permissions (chmod 755 = rwxr-xr-x)
• Hexadecimal: Memory addresses, color values (#FF5733), byte stream debugging

Code prefixes: 0b (binary) · 0o (octal) · 0x (hexadecimal)

Common Use Cases

• Memory/register debugging: Convert hex addresses or register values to binary to inspect individual bit states
• Network programming: Convert between binary subnet masks and decimal IP notation
• Permission configuration: Understand the binary meaning of chmod 644 (read/write/execute bits)
• Embedded development: Quickly switch between hex byte streams and binary bit manipulation

How to Use

1. Select the input base (binary, octal, decimal, or hexadecimal) and enter your value
2. The tool instantly displays the equivalent value in all other bases
3. Supports large numbers — results can be copied to clipboard with one click

FAQ

Why is hexadecimal so prevalent in programming?

Each hex digit maps exactly to 4 binary bits (1 nibble), making hex-to-binary conversion trivial. 0xFF is 1111 1111 — far more compact than writing raw binary.

Is octal used for anything besides file permissions?

In modern development, rarely. Unix file permissions are the primary use case. You may also encounter octal in legacy C code and certain protocols (e.g., MIDI).

How can I mentally convert hex to decimal quickly?

Memorize key anchors: 0xA=10, 0xF=15, 0x10=16, 0xFF=255, 0x100=256. Most conversions can be derived from these reference points.