Free Online Number Base Converter — Binary, Octal, Decimal & Hex

Convert numbers between Binary, Octal, Decimal, and Hexadecimal in real time. Perfect for programmers, students, system administrators, and anyone working with different number systems. This tool is completely free, runs entirely in your browser, and requires no signup or installation.

Key Features

🔢 Multi-Base Conversion

Binary (base 2) conversion
Octal (base 8) conversion
Decimal (base 10) conversion
Hexadecimal (base 16) conversion
Convert from any base to all others

⚡ Real-Time Processing

Instant conversion as you type
Automatic input validation
Error detection for invalid digits
Color-coded results per base
Prefix notation hints (0b, 0o, 0x)

📋 Easy Output Handling

One-click copy to clipboard
All four results shown simultaneously
Clear, readable output format
Compact multi-panel display
Mobile-friendly interface

🔒 Privacy & Security

100% client-side processing
No data sent to servers
No registration required
No cookies or tracking
Works offline once loaded

Why Use Our Number Base Converter?

100% Free & Unlimited: Convert unlimited numbers between bases without registration, subscriptions, or any restrictions.

Complete Privacy: All conversions happen locally in your browser using JavaScript. No data is uploaded to servers or stored anywhere.

Instant Results: Real-time conversion with automatic validation as you type — no button clicks required.

Developer Friendly: Designed for developers with prefix hints (0b, 0o, 0x), color-coded outputs, and one-click copying.

Error Detection: Automatic validation prevents invalid digits for each base with clear error feedback.

Mobile Responsive: Works perfectly on desktop, tablet, and mobile devices with a touch-optimized interface.

How to Convert Numbers Between Bases

Choose the Input Base: Select whether you want to enter a Binary, Octal, Decimal, or Hexadecimal number.
Enter Your Number: Type or paste the number into the input field. Only valid digits for the chosen base are accepted.
View All Results: The tool instantly converts and displays the number in all four bases simultaneously.
Copy the Result: Click the copy button next to any output to copy it to your clipboard.

Understanding Number Systems

A number system (or numeral system) is a writing system for expressing numbers. The most commonly used system is the decimal system (base 10), which uses digits 0–9. In computing, binary (base 2), octal (base 8), and hexadecimal (base 16) are essential for representing data, memory addresses, and machine instructions.

The Four Common Number Bases:

Binary (Base 2): Uses digits 0 and 1 only. Every digital computer uses binary internally because electronic circuits have two states: on (1) and off (0). Prefix: 0b

Octal (Base 8): Uses digits 0–7. Commonly used in Unix/Linux file permissions (e.g., chmod 755). Each octal digit represents exactly 3 binary bits. Prefix: 0o

Decimal (Base 10): Uses digits 0–9. The standard number system humans use every day for counting, math, and commerce. No prefix needed.

Hexadecimal (Base 16): Uses digits 0–9 and letters A–F. Widely used in programming for colors (#FF5733), memory addresses, and byte values. Each hex digit represents exactly 4 binary bits. Prefix: 0x

Example: Decimal 255 = Binary 11111111 = Octal 377 = Hex FF

Example: Decimal 42 = Binary 101010 = Octal 52 = Hex 2A

How Base Conversion Works

To Decimal (from any base): Multiply each digit by its base raised to its position power (starting from 0 on the right), then sum the results. For example, binary 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10.

From Decimal (to any base): Repeatedly divide the decimal number by the target base, recording the remainder at each step. The remainders read in reverse order give you the result. For example, 10 ÷ 2 = 5 r 0, 5 ÷ 2 = 2 r 1, 2 ÷ 2 = 1 r 0, 1 ÷ 2 = 0 r 1 → binary 1010.

Between Non-Decimal Bases: Convert to decimal first, then from decimal to the target base. Our tool handles this automatically and instantly.

Binary ↔ Hex Shortcut: Group binary digits in sets of 4 (from right) and convert each group to its hex equivalent. For example, 1111 1111 = FF. This works because 2⁴ = 16.

Binary ↔ Octal Shortcut: Group binary digits in sets of 3 (from right) and convert each group to its octal equivalent. For example, 111 111 111 = 777. This works because 2³ = 8.

Common Use Cases

Programming & Software Development: Convert between hex and decimal for memory addresses, color codes, ASCII values, and bitwise operations. Understanding binary is essential for flags and masks.

Unix/Linux File Permissions: File permissions in Linux use octal notation (e.g., 755 = rwxr-xr-x). Each octal digit represents read (4), write (2), and execute (1) permissions.

Web Development & Design: Hex color codes (#RRGGBB) define colors in CSS and HTML. Converting between hex and decimal helps understand RGB values.

Networking: IP addresses, subnet masks, and MAC addresses involve conversions between decimal, binary, and hexadecimal for configuration and troubleshooting.

Digital Electronics: Binary is the language of digital circuits. Engineers convert between binary, hex, and decimal when designing logic gates, microcontrollers, and embedded systems.

Computer Science Education: Learning number base conversion is fundamental to understanding how computers store and process data.

Debugging & Reverse Engineering: Hex dumps, memory inspectors, and debuggers display data in hexadecimal. Converting to decimal or binary helps interpret raw data.

Comparing Number Systems

Binary vs Decimal: Binary uses only 0 and 1, making it simple for machines but verbose for humans. Decimal 255 requires 8 binary digits (11111111).

Hexadecimal vs Binary: Hex is a compact representation of binary. One hex digit = 4 binary bits, so a byte (8 bits) is always exactly 2 hex digits. Much easier to read than long binary strings.

Octal vs Hexadecimal: Octal was popular in older computing systems (PDP-8) but hex became standard with byte-oriented architectures. Hex aligns better with 8-bit, 16-bit, 32-bit, and 64-bit word sizes.

Why Multiple Bases?: Each base serves a purpose — decimal for human readability, binary for machine operation, hex for compact binary representation, and octal for legacy systems and Unix permissions.

Quick Reference Table

Decimal	Binary	Octal	Hex
0	0000	0	0
1	0001	1	1
8	1000	10	8
10	1010	12	A
16	10000	20	10
42	101010	52	2A
100	1100100	144	64
255	11111111	377	FF
256	100000000	400	100
1024	10000000000	2000	400
65535	1111111111111111	177777	FFFF

Perfect For

Software developers & programmers
System administrators (Linux/Unix)
Computer science students
Embedded systems engineers
Network engineers & administrators
Digital electronics designers

Web developers (hex colors)
Cybersecurity professionals
Game developers
QA testers & debuggers
Math & CS teachers
Reverse engineers

Pro Tips for Number Base Conversion

Memorize Powers of 2: Knowing 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁸=256, 2¹⁰=1024, 2¹⁶=65536 makes conversions much faster.
Use Hex-Binary Shortcut: Each hex digit maps to exactly 4 binary digits. Memorize: 0=0000, 1=0001, ..., 9=1001, A=1010, ..., F=1111.
Octal-Binary Shortcut: Each octal digit maps to exactly 3 binary digits: 0=000, 1=001, ..., 7=111.
Prefix Conventions: In most programming languages: 0b = binary, 0o or 0 = octal, 0x = hex.
Unix Permissions: chmod uses octal: r=4, w=2, x=1. So 755 = rwx (7) r-x (5) r-x (5) for owner/group/others.
Hex Colors: #RRGGBB uses 2 hex digits per channel. #FF0000 = red, #00FF00 = green, #0000FF = blue.
Verify Results: Use our tool to check your manual conversions. A quick sanity check can catch arithmetic errors.
Max Byte Value: A byte (8 bits) ranges from 0–255 decimal, 00–FF hex, 00000000–11111111 binary, 0–377 octal.

Common Programming Examples

File Permissions (Octal): chmod 644 → rw-r--r-- (owner read/write, group read, others read)

CSS Colors (Hex): #1E90FF = DodgerBlue (R=30, G=144, B=255)

IP Subnet (Binary): 255.255.255.0 = 11111111.11111111.11111111.00000000

Memory Address (Hex): 0x7FFF5FBFFB38 — a typical stack address on 64-bit systems

Bit Flags (Binary): READ=0b001, WRITE=0b010, EXEC=0b100, ALL=0b111

ASCII 'A' (All Bases): Decimal 65 = Binary 1000001 = Octal 101 = Hex 41

Best Practices

Always Use Prefixes: When writing non-decimal numbers in code, use the appropriate prefix (0b, 0o, 0x) to avoid ambiguity.
Group Digits: For readability, group binary digits in sets of 4 or 8 (e.g., 1111_0000) and hex in pairs (e.g., FF 00).
Validate Input Range: Check that digits are valid for the chosen base — e.g., binary should only contain 0 and 1.
Consider Signed Values: For signed integers, the most significant bit is the sign bit. Two's complement is the standard representation.
Document Your Base: Always comment which base you're using when writing constants in code to prevent confusion.
Use Language Built-ins: Most languages have built-in functions for base conversion (parseInt, toString, format) — use them for reliability.
Watch for Overflow: Large numbers may exceed integer limits. JavaScript safely handles integers up to 2⁵³ - 1.

Troubleshooting Common Issues

"Invalid digit" Error:You entered a digit that doesn't exist in the chosen base. Binary only allows 0–1, octal only 0–7, and hex only 0–9 and A–F.

Unexpected Result:Make sure you selected the correct input base. Entering "10" in binary means 2 in decimal, not 10.

Leading Zeros:Leading zeros don't change the value (0010 = 10) but may be needed for fixed-width representations like bytes.

Very Large Numbers: Extremely large numbers may lose precision due to floating-point limits. For very large values, consider using BigInt in JavaScript.

🔒 100% Privacy Guaranteed

All number base conversions are performed entirely in your web browser using JavaScript. Your data is never uploaded to our servers, stored in databases, logged, or transmitted to any third party. Everything happens locally on your device, ensuring complete privacy and security.

Number Base Converter - Binary, Octal, Decimal & Hexadecimal

About Number Base Conversion

Complete Guide to Number Base Conversion