Number Base Converter
Convert between decimal, hexadecimal, binary, and octal instantly.
Perfect for developers, embedded engineers, and CS students.
100% client-side — works offline, no sign-up required.
Number Converter
Why Number Base Conversion Matters in Programming
Every programmer encounters number base conversion regularly — whether reading memory addresses in hexadecimal debugger output, working with binary flags in embedded systems, understanding Unix file permissions in octal, or decoding CSS hex color codes into their RGB decimal components. The four most common number systems in computing are decimal (base 10, used by humans), binary (base 2, used by computers internally), hexadecimal (base 16, used to compactly represent binary data), and octal (base 8, used in Unix permissions and some legacy systems). Understanding how these systems relate to each other is a fundamental skill in computer science and software engineering.
Decimal to Hexadecimal: The Most Common Conversion
Hexadecimal is ubiquitous in programming. CSS colors use hex (#FF5733), memory addresses appear in hex in debuggers and crash dumps, and network packet analysis tools like Wireshark display data in hex. One hex digit represents exactly 4 binary bits, making it a compact shorthand for binary data — a full byte (8 bits) is just two hex digits (00 to FF). When you see a memory address like 0x7FFF4A21 in a debugger, that's hex. This converter lets you paste any such value, select Hex, and instantly see the decimal and binary equivalents.
Binary Conversion for Embedded and Low-Level Development
Embedded engineers working with microcontrollers and digital logic frequently need to convert between decimal and binary. Register configurations, bitmasks, GPIO pin states, interrupt flags, and protocol bytes are all specified in binary in datasheets. Being able to quickly verify that decimal value 173 equals binary 10101101 — confirming which bits are set — is essential for low-level programming. This converter shows all four bases simultaneously, so you can cross-reference decimal, hex, and binary for any register value without context-switching between tools.
Octal Numbers and Unix File Permissions
Octal (base 8) may seem obscure but is essential for Unix/Linux developers. The chmod command uses octal notation — 755 means owner has read/write/execute (7=111 binary), group has read/execute (5=101), others have read/execute. Understanding that octal 7 equals binary 111 and decimal 7 makes permission calculations intuitive. This converter supports octal input and output, making it a handy reference when setting file permissions or working with legacy codebases that use octal literals.
Privacy and Performance
All conversions use JavaScript's built-in parseInt() and Number.toString() functions with the appropriate base parameter. No data leaves your browser, no external libraries are loaded, and the tool works fully offline after the initial page load. This makes it safe to use with sensitive values like API keys, encryption parameters, or internal memory addresses in production debugging sessions.
ToolsMatic Number Converter vs Alternatives
Number Base Converter — Frequently Asked Questions
What is hexadecimal and why use it?
Hexadecimal (base 16) uses digits 0–9 and letters A–F. One hex digit represents exactly 4 binary bits, making it a compact shorthand for binary. Memory addresses, color codes, and byte values are almost always shown in hex because it's far more readable than long binary strings.
How do I convert decimal to binary?
Enter your decimal number in the input field, select "Decimal (base 10)" from the dropdown, and click Convert. The binary result appears instantly in the Binary output box.
What is octal and when is it used?
Octal (base 8) uses digits 0–7. It's most commonly seen in Unix file permissions — chmod 755 uses octal notation where each digit represents three binary permission bits (read, write, execute). It also appears in some legacy computing and C language code.
Can I convert hex color codes?
Yes. Enter a hex color component (e.g. "ff" for the red channel of #FF5733), select Hex, and convert to decimal to get the value 255. For a full color like FF5733, split it into FF, 57, and 33 components and convert each separately to get R=255, G=87, B=51.
Is this accurate for large numbers?
Yes, for integers within JavaScript's safe integer range (up to 2^53 − 1, approximately 9 quadrillion). For numbers beyond this range, precision may be lost — in those cases, use a BigInt-based tool or a language like Python.
Does this tool work offline?
Yes. The conversion uses JavaScript's built-in parseInt() and .toString() methods with the base as a parameter. No network calls are made — the tool works fully offline after the initial page load.
Why does hex output show lowercase letters?
JavaScript's .toString(16) produces lowercase hex by default (e.g. "2a" instead of "2A"). Both are valid — uppercase is often preferred in memory dumps and certain APIs, but lowercase is equally correct in CSS color codes and most modern contexts.