Number Base Converter

Converted 255 from base 10 to base 16, giving FF.

How it works

• Read every digit of the input in base 10 and accumulated an exact integer.
• Repeatedly divided by the target base and read the remainders to produce the target digits.
• Rendered the result with the digits 0-9A-Z.

• Arbitrary-precision arithmetic means values larger than 2^53 are converted exactly.

Methodology

1. Validate the value as a signed integer and both bases as integers from 2 to 36.
2. Accumulate the exact value by iterating the input digits, multiplying by the source base and adding each digit.
3. Produce the target digits by repeated division with remainder, then restore the sign.

Usage

1. Enter the integer to convert.
2. Choose the source and target bases from 2 to 36.
3. Read the converted result.

Examples

These are examples, not current values: they use fixed inputs, while the interactive tool computes live results in your browser.

Decimal to hexadecimal

{
  "value": "255",
  "fromBase": 10,
  "toBase": 16
}

Binary to decimal

{
  "value": "11111111",
  "fromBase": 2,
  "toBase": 10
}

Big integer stays exact

{
  "value": "123456789012345678901234567890",
  "fromBase": 10,
  "toBase": 16
}

Limitations

Positional notation

Every positional number system expresses a value as a sum of digits times a power of the base. Converting changes only the representation, never the value, which is why the result can be converted back exactly.