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Number Base guide

The Number Base Converter translates numbers between Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16). It supports arbitrarily large numbers using BigInt.

Worked examples

Convert Decimal to Hexadecimal

  1. Enter 255 as the number.
  2. Select "Decimal (Base 10)" as the From Base.
  3. Click Convert.
Result: FF

255 in base 10 is represented as FF in base 16 (15 × 16 + 15 = 255).

Convert Binary to Decimal

  1. Enter 1010 as the number.
  2. Select "Binary (Base 2)" as the From Base.
  3. Click Convert.
Result: 10

1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10.

Convert Hexadecimal to Decimal

  1. Enter 1A as the number.
  2. Select "Hexadecimal (Base 16)" as the From Base.
  3. Click Convert.
Result: 26

1×16¹ + 10×16⁰ = 16 + 10 = 26. The letter A represents the value 10.

Tips

  • •Hexadecimal uses the letters A-F to represent values 10-15.
  • •You can paste code prefixes like 0x, 0b, or 0o and the tool will automatically detect and strip them.
  • •Use underscores (e.g., 1_000) to make large numbers more readable; the tool ignores them.

Frequently asked questions

What is a number base?
The number of unique digits (including zero) used to represent numbers in a positional numeral system.
Why do computers use binary?
Because digital circuits have two states: on (1) and off (0). Binary maps perfectly to transistor logic.
Why do programmers use hexadecimal?
It is much shorter and more human-readable than binary. One hex digit represents exactly four binary bits (a nibble).
What are the letters A-F in hexadecimal?
They represent the numbers 10, 11, 12, 13, 14, and 15, because base 16 needs 16 unique single-character digits.
What is octal used for?
It was historically used in computing to represent binary data compactly (3 bits per digit). Today, it is mostly used for Unix file permissions (e.g., chmod 755).
What does the prefix 0x mean?
In programming languages, 0x signals that the following number is in hexadecimal format. 0b is used for binary, and 0o for octal.
Can I convert negative numbers?
The tool handles positive integers and zero. Negative numbers in computing are usually represented using two’s complement, which is a specific binary encoding.
What is the largest number I can convert?
The tool uses BigInt, so it can handle numbers with up to 200 digits without losing precision.
Why does base 10 use the digits 0-9?
Because humans have ten fingers, making base 10 the standard counting system for most cultures.
What does "base 60" mean?
It is used for measuring time and angles (60 seconds in a minute, 60 minutes in an hour). This calculator does not support base 60.
What is a nibble?
Four binary bits. It corresponds to exactly one hexadecimal digit.
What is a byte?
Eight binary bits. It is usually represented by two hexadecimal digits (e.g., FF is 11111111).
How do I convert from base 10 to base 2 manually?
Divide the number by 2 repeatedly, writing down the remainders. Read the remainders from bottom to top to get the binary number.
Why does the calculator reject certain digits?
If you select Base 2 but enter a 3, the calculator will throw an error, because the digit 3 does not exist in binary.
Can I use this for colors?
Yes! Hex color codes like #FFFFFF are just base-16 numbers. FF is 255 in decimal, which represents the maximum brightness of a color channel.
Is the conversion case-sensitive?
No, the calculator automatically converts letters to uppercase before processing (e.g., ff becomes FF).
What is the base of the English language?
It is an unweighted base-26 system (A-Z), but it doesn’t have a mathematical digit for zero.
How precise is the conversion?
It is 100% exact, up to the 200-digit limit. There is no floating-point rounding involved.
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