How to convert between number systems?
Converting between number systems is straightforward with this tool:
- Enter a number in any of the four input fields — Binary, Octal, Decimal, or Hexadecimal.
- The tool instantly converts and fills in the values for all other systems.
- Values update in real-time as you type in any field.
- Use the swap/clear buttons to reset or swap between systems.
- Copy any converted value with a single click using the copy button.
What number systems are supported?
This tool supports four common number systems used in computing:
- Binary (Base-2): Uses digits 0 and 1. The fundamental language of computers.
- Octal (Base-8): Uses digits 0-7. Commonly used in Unix file permissions and legacy systems.
- Decimal (Base-10): Uses digits 0-9. The standard number system used in everyday life.
- Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. Widely used in programming, memory addresses, and color codes.
Frequently Asked Questions (FAQs)
What is a number system?
A number system defines how numbers are represented using a specific set of digits. The base (or radix) determines how many unique digits are used. For example, decimal uses base-10 (10 digits: 0-9), while binary uses base-2 (2 digits: 0 and 1). Each position in a number represents a power of the base.
Why do computers use binary?
Computers use binary (base-2) because it maps directly to the physical states of electronic circuits — on (1) and off (0). This two-state system is reliable, simple to implement in hardware, and resistant to noise. All modern digital computers operate on binary logic at the transistor level.
What is hexadecimal used for?
Hexadecimal is widely used in programming because it provides a compact representation of binary data. One hex digit represents exactly 4 binary bits (a nibble). Common uses include: memory addresses, color codes in CSS/HTML (#FF0000), MAC addresses, assembly language, and debugging tools.
How do I convert binary to decimal manually?
To convert binary to decimal: Write the binary number, then multiply each digit by 2 raised to its position power (starting from 0 on the right). Sum all the results. For example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀.
How do I convert decimal to hexadecimal?
To convert decimal to hexadecimal: Divide the decimal number by 16 repeatedly, recording the remainders. Read the remainders from bottom to top. Values 10-15 are represented as A-F. For example: 255₁₀ ÷ 16 = 15 remainder 15 → FF₁₆.
Why do programmers use octal sometimes?
Octal (base-8) is used in Unix/Linux file permission settings (chmod 755), some legacy systems, and certain contexts where grouping binary digits into threes is convenient. While less common than hex, it's still relevant in system administration and embedded systems programming.
