What is a Binary/Hex/Decimal Converter?
The Binary/Hex/Decimal Converter is a powerful online tool designed to help developers, students, and IT professionals quickly convert numbers between different number systems. Whether you're working with binary code, hexadecimal color values, or need to understand how computers represent numbers, this tool makes conversions instant and accurate.
Our converter supports four essential number systems: Binary (base 2), Octal (base 8), Decimal (base 10), and Hexadecimal (base 16). These are fundamental to computer science, programming, and digital electronics. Understanding how to convert between these systems is crucial for anyone working in technology.
Key Features:
- Multi-System Support: Convert between Binary, Octal, Decimal, and Hexadecimal instantly
- Simultaneous Display: See all conversions at once for quick reference
- Copy Functionality: Easily copy individual results to clipboard
- Quick Examples: Load common conversions with one click
- Educational Tips: Learn about each number system while converting
- Privacy First: All conversions happen locally in your browser—no data sent to servers
Common Use Cases:
- Programming: Understanding memory addresses, bit manipulation, and data structures
- Web Design: Converting hexadecimal color codes (e.g., #FF5733) to RGB values
- Network Administration: Working with IP addresses and subnet masks
- Computer Science Education: Learning about number systems and computer architecture
- Embedded Systems: Programming microcontrollers and understanding register values
Perfect For: Software developers, web designers, computer science students, network engineers, embedded systems programmers, and anyone learning about digital systems.
Understanding Number Systems
Binary (Base 2)
Binary uses only two digits: 0 and 1. It's the fundamental language of computers because digital circuits can easily represent two states: on (1) and off (0). Every piece of data in a computer is ultimately stored and processed in binary.
Example: 1010₂ = 10₁₀ (ten in decimal)
Octal (Base 8)
Octal uses digits 0-7. While less common today, it's still used in Unix file permissions (e.g., chmod 755) and provides a more compact representation than binary. Each octal digit represents exactly three binary digits.
Example: 144₈ = 100₁₀ (one hundred in decimal)
Decimal (Base 10)
Decimal is the standard number system humans use daily, with digits 0-9. It's called "base 10" because it has ten unique digits. This is the most familiar number system for everyday counting and arithmetic.
Example: 255₁₀ = FF₁₆ (255 in hexadecimal)
Hexadecimal (Base 16)
Hexadecimal uses digits 0-9 and letters A-F (representing values 10-15). It's extremely popular in programming because it provides a compact way to represent binary data. Each hex digit represents exactly four binary digits (bits).
Example: FF₁₆ = 255₁₀ (commonly used for RGB color values)
Frequently Asked Questions
How do I convert binary to decimal?
To convert binary to decimal manually, multiply each digit by 2 raised to its position (counting from right, starting at 0), then sum the results. For example, 1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10₁₀. Our converter does this instantly!
What is hexadecimal used for in programming?
Hexadecimal is widely used in programming for: color codes in web design (#FF5733), memory addresses, representing byte values, MAC addresses, Unicode characters, and debugging. It's more compact than binary while being easy to convert to/from binary since each hex digit equals 4 binary digits.
Why do computers use binary?
Computers use binary because digital circuits work with two states: on (1) and off (0), corresponding to high and low voltage. This makes binary the most reliable and efficient system for electronic devices. All other number systems (octal, decimal, hex) are just convenient ways for humans to represent binary data.
How do I convert decimal 255 to hexadecimal?
To convert 255₁₀ to hex: divide 255 by 16 = 15 remainder 15. The quotient (15) and remainder (15) in hex are both "F", giving us FF₁₆. This is why 255 is such a common number in computing—it's the maximum value for one byte (8 bits), and equals FF in hexadecimal.
What is the relationship between hexadecimal and binary?
Each hexadecimal digit represents exactly 4 binary digits (bits). For example, F₁₆ = 1111₂, A₁₆ = 1010₂. This 4-to-1 relationship makes hex perfect for representing binary data compactly. Converting between them is straightforward: group binary digits in sets of four from right to left.
Can I use lowercase letters in hexadecimal?
Yes! Hexadecimal letters (A-F) can be uppercase or lowercase—both are valid. Our converter accepts both "FF" and "ff" as the same value. However, uppercase is more common in technical documentation and programming.
What are the limits of this converter?
Our converter supports numbers up to JavaScript's maximum safe integer (2⁵³ - 1, or 9,007,199,254,740,991). This is sufficient for virtually all practical programming needs. Numbers are limited to 50 characters in length for performance and usability.
How accurate is the number system converter?
The converter is 100% accurate for all integers within the supported range. It uses JavaScript's built-in parseInt() and toString() methods with different bases, which follow IEEE 754 standards. All conversions are mathematically precise with no rounding errors for integers.