Base N Converter Calculator

Convert numbers between different bases (binary, decimal, hexadecimal, octal) with our Base N Converter Calculator. This tool helps you understand how numbers are represented in different numeral systems and how to convert between them.

What is a Base N Converter?

A Base N Converter is a tool that allows you to convert numbers between different numeral systems. The most common numeral systems are:

Binary (Base 2) - Uses digits 0 and 1
Octal (Base 8) - Uses digits 0 through 7
Decimal (Base 10) - Uses digits 0 through 9 (the standard numbering system)
Hexadecimal (Base 16) - Uses digits 0 through 9 and letters A through F

Understanding different bases is essential in computer science, digital electronics, and mathematics. This calculator provides a simple way to convert numbers between these systems.

How to Use the Calculator

Enter the number you want to convert in the "Number to Convert" field.
Select the base of the number you entered in the "From Base" dropdown.
Select the base you want to convert to in the "To Base" dropdown.
Click the "Convert" button to see the result.
Use the "Reset" button to clear all fields and start over.

Note: The number you enter must be valid for the selected base. For example, if you select Base 2, the number can only contain 0s and 1s.

Formula

The conversion between different bases is performed using the following steps:

Conversion Steps

Convert the input number from its original base to decimal (Base 10).
Convert the decimal number to the target base.

For example, to convert the binary number 1010 from Base 2 to Base 16:

First, convert 1010 (Base 2) to decimal: 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10 (Base 10)
Then, convert 10 (Base 10) to hexadecimal: 10 ÷ 16 = 0 with a remainder of 10, which is 'A' in hexadecimal. So, 10 (Base 10) = A (Base 16).

Examples

Example 1: Binary to Decimal

Convert 1101 (Base 2) to decimal:

1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13 (Base 10)

Example 2: Decimal to Hexadecimal

Convert 255 (Base 10) to hexadecimal:

255 ÷ 16 = 15 with a remainder of 15 (F in hexadecimal). 15 ÷ 16 = 0 with a remainder of 15 (F in hexadecimal). So, 255 (Base 10) = FF (Base 16).

FAQ

What is the difference between binary, octal, decimal, and hexadecimal?

Binary uses base 2, octal uses base 8, decimal uses base 10, and hexadecimal uses base 16. Each base represents numbers using a different set of digits.

Can I convert numbers between any two bases?

Yes, this calculator can convert numbers between any two bases from 2 to 36. Just select the appropriate "From Base" and "To Base" values.

What happens if I enter an invalid number for the selected base?

The calculator will display an error message if the number contains digits that are not valid for the selected base. For example, entering '8' in a Base 8 field is invalid.