🔢 Decimal Conversion Tool

Real-time interconversion between binary, octal, decimal, and hexadecimal numbers. Bitwise operations and ASCII conversion are also supported.

(2-36)
Binary
Please enter a number
Octal
Please enter a number
Decimal
Please enter a number
Hexadecimal
Please enter a number
A AND B
-
A OR B
-
A XOR B
-
NOT A
-
A << Shift (Left Shift)
-
A >> Shift (Right Shift)
-
⇔

ASCII character table (0 to 127)

Usage and Application Examples

  • Converts color codes (hexadecimal) to RGB values (decimal)
  • Check network subnet mask in binary
  • Understanding the meaning of Unix file permissions (octal) in binary
  • Check and debug the results of bitwise operations in each decimal

What is Number Base Converter?

A real-time conversion tool enabling instant translation between binary, octal, decimal, and hexadecimal number systems. Enter any number in one base, and the tool automatically displays equivalent values in all other bases. Essential for programmers, computer science students, and anyone working with bitwise operations or digital systems, this tool eliminates manual conversion and prevents arithmetic errors.

How to Use

Enter a number into any of the four input fields (binary, octal, decimal, or hexadecimal). The tool immediately converts and displays equivalent values in the remaining bases. All fields update in real-time—change any value and others adjust automatically. For binary, enter strings of 0s and 1s; for hexadecimal, use 0-9 and A-F (case-insensitive). The tool handles both positive integers and large numbers, making it suitable for bitwise programming and hardware-level calculations.

Use Cases

Programming and debugging: Convert between bases when working with bitwise operations, file permissions, or memory addresses.
• Computer science education: Students visualize how computers represent numbers internally across different systems.
• Network configuration: Subnet masks and IP addressing calculations require hexadecimal and binary conversion.
• Hardware and embedded systems: Microcontroller programming and circuit design frequently involve register values in hexadecimal or binary notation.

Tips & Insights

Hexadecimal is preferred in programming because four binary digits map cleanly to one hex digit, making long binary numbers readable. Octal is largely historical (common in Unix file permissions like 755) but less frequently used in modern programming. Understanding base conversion builds intuition for how computers represent and manipulate data at fundamental levels. Memory addresses, color codes (RGB hex), and digital circuit designs all rely on these number systems.

Frequently Asked Questions

What are binary, octal, decimal, and hexadecimal numbers?

Binary numbers are used to represent data inside computers, octal numbers are used for Unix file permissions, decimal numbers are used for everyday numbers, and hexadecimal numbers are used for color codes and memory addresses.

How is the decimal conversion performed?

Enter a numerical value in the input field and select a radix from which to input the value, and it will be simultaneously converted to binary, octal, decimal, or hexadecimal in real time. Custom radix (2 to 36) is also supported.

What are bit operations?

Bitwise operations are operations that manipulate numbers in binary bit units, including AND, OR, XOR, NOT, shift left, and shift right, and are frequently used in programming and hardware control.

What is ASCII conversion?

ASCII (American Standard Code for Information Interchange) is a correspondence table between letter and numeric codes. For example, the letter "A" corresponds to ASCII code 65 (41 in hexadecimal). This tool allows you to interconvert between characters and codes.

Does it support custom radix (2 to 36 decimal)?

Yes, you can specify any radix from binary to hexadecimal to be converted. 36 decimal uses the characters 0-9 and A-Z, for a total of 36 characters.

Is the input data secure?

Yes. All conversion processes are completed within the browser, and input data is never sent to the server. You can use this service with peace of mind.

What is the maximum size number this tool can convert?

The converter handles very large numbers extending to hundreds or thousands of digits in most bases. For all practical applications, it works instantly with numbers well beyond standard computational limits.

Does it support floating-point decimal numbers?

This tool is currently optimized for integer conversion, which covers the majority of use cases. Floating-point conversion in different bases requires specialized tools or programming libraries.

Can I quickly copy conversion results?

Yes, click any result field to select it and use Ctrl+C (Windows) or Cmd+C (Mac) to copy. Many result fields also include dedicated copy buttons for one-click clipboard access.

What is two's complement and why is it important?

Two's complement is the standard method for representing negative numbers in binary within computer systems. Understanding it is essential for working with signed integers in programming and digital design.

Can I see step-by-step conversion instructions?

The tool provides instant conversions, but you can verify results by learning the underlying mathematical principles. Understanding division remainders and positional place values helps you manually confirm conversions.

What other bases does the tool support beyond the common ones?

Base-36 (using digits 0-9 and letters A-Z) is commonly used in computing, and the tool supports custom bases from 2 to 36. This lets you explore historical systems like base-12 (duodecimal) or specialized computing bases.