Change Number Base

Convert numbers between different bases (radixes) — binary, octal, decimal, hexadecimal, or any base from 2 to 36. Enter a number in one base and see its representation in another.

Input Number
Options
Old Base
Enter the input number base.Allowed bases are from -64 to 64, except -1 and 0.
New Base
Enter the output base.Allowed bases are from -64 to 64, except -1 and 0.
Output Format
Display the output numbers in the new base as a power series sum.
Display the decimal value next to each output number.These two options don't work at the same time. You must choose one or the other.
Output (Converted Base)

What It Does

Convert numbers between different bases (radixes) — binary, octal, decimal, hexadecimal, or any base from 2 to 36. Enter a number in one base and see its representation in another.

How It Works

Change Number Base swaps one pattern, character set, or representation for another. The interesting part is not just what appears in the output, but how consistently the replacement is applied across mixed input.

Replacement logic usually follows the exact match rule the tool expects. Small differences in case, punctuation, or surrounding whitespace can explain why one segment changes and another does not.

All processing happens in your browser, so your input stays on your device during the transformation.

Common Use Cases

  • Convert between binary, octal, decimal, and hex for programming
  • Translate memory addresses from hex to decimal
  • Convert color codes between hex and decimal RGB values
  • Debug binary flag values by converting to decimal
  • Solve computer science homework involving base conversions

How to Use

  1. Enter the number you want to convert.
  2. Select the base of your input number (e.g., 16 for hex).
  3. Select the target base (e.g., 2 for binary).
  4. View the converted result.

Features

  • Supports any base from 2 to 36
  • Common presets: binary (2), octal (8), decimal (10), hex (16)
  • Handles large numbers
  • Shows conversion steps for educational use
  • Bidirectional conversion

Examples

Below is a representative input and output so you can see the transformation clearly.

Input
Value: 255
From: 10
To: 16
Output
FF

Edge Cases

  • Very large inputs can still stress the browser, especially when the tool is working across many numbers. Split huge jobs into smaller batches if the page becomes sluggish.
  • Overlapping patterns and global replacements can produce broader changes than expected, so preview a small sample before full input.
  • If the output looks wrong, compare the exact input and option values first, because Change Number Base should be repeatable with the same settings.

Troubleshooting

  • Unexpected output often means the input is being split or interpreted at the wrong unit. For Change Number Base, that unit is usually numbers.
  • If a previous run looked different, check for hidden whitespace, changed separators, or a setting that was toggled accidentally.
  • If nothing changes, confirm that the input actually contains the pattern or structure this tool operates on.
  • If the page feels slow, reduce the input size and test a smaller sample first.

Tips

Hex digits use letters A-F for values 10-15. Bases above 16 continue with G-Z. Base 36 uses the full alphabet (0-9, A-Z).

Number Base Systems

A number base (or radix) determines how many unique digits are used to represent numbers. Decimal (base 10) uses 0-9. Binary (base 2) uses 0-1. Hexadecimal (base 16) uses 0-9 and A-F. Each base is a different way of writing the same numeric value — 255 in decimal is FF in hex and 11111111 in binary.

Why Different Bases Matter

Computers operate in binary, but binary numbers are long and hard to read. Hexadecimal is a compact representation — every hex digit maps to exactly 4 binary digits (bits). Octal maps to 3 bits. These bases make it practical to work with memory addresses, color codes, file permissions, and binary data without writing out long strings of zeros and ones.

Conversion Algorithm

To convert from base A to base B, the tool first converts the input to a base-10 integer (by multiplying each digit by its positional value), then converts from base 10 to the target base (by repeatedly dividing and collecting remainders). For direct base-to-base conversion (like hex to binary), the tool can use shortcut mappings for efficiency.

Common Conversions

Hex to binary: each hex digit maps to 4 binary digits (F = 1111, A = 1010). Octal to binary: each octal digit maps to 3 binary digits (7 = 111). Decimal to hex: used constantly for color codes (#FF0000 = rgb(255, 0, 0)). Binary to decimal: essential for understanding bitwise operations and flag values.

Frequently Asked Questions

What is the maximum base supported?

Base 36, which uses digits 0-9 and letters A-Z. This is the highest base representable with standard alphanumeric characters.

Can I convert fractional numbers?

This tool converts integer values. Fractional base conversion is a separate, more complex operation.

How do I enter a hexadecimal number?

Select base 16 as the input base, then type the hex digits. You can use uppercase or lowercase letters (FF or ff).

What about negative numbers?

The tool handles negative numbers by converting the absolute value and preserving the negative sign.

How large can the numbers be?

The tool handles numbers up to standard integer limits. For very large numbers, precision depends on the browser's arithmetic capabilities.

Is base 1 (unary) supported?

No. Base 1 is not a standard positional numeral system and is not supported. The minimum base is 2 (binary).