Base-N Calculator

A base-n calculator converts numbers between different numeral systems. This tool handles binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8) conversions with precision.

What is a Base-N Calculator?

A base-n calculator is a digital tool that converts numbers between different numeral systems. Each numeral system has a base that determines how many unique digits it uses to represent numbers.

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 (our standard numbering system)
Hexadecimal (base-16) - Uses digits 0-9 and letters A-F

Base-n calculators are essential in computer science, digital electronics, and programming because they help translate between different number representations used in these fields.

How to Use This Calculator

Using the base-n calculator is straightforward:

Enter the number you want to convert in the "Number to convert" field
Select the current base of your number from the "From base" dropdown
Select the target base you want to convert to from the "To base" dropdown
Click the "Convert" button
The converted number will appear in the results section

Note: The calculator accepts both uppercase and lowercase letters for hexadecimal digits (A-F).

Common Number Bases

Here's a quick reference of common numeral systems and their uses:

Base	Name	Digits Used	Common Uses
2	Binary	0, 1	Computer programming, digital electronics
8	Octal	0-7	Computer programming, some digital systems
10	Decimal	0-9	Standard counting system
16	Hexadecimal	0-9, A-F	Computer programming, color codes, memory addresses

Conversion Examples

Here are some practical examples of base conversions:

Example 1: Binary to Decimal

Convert 1010 (binary) to decimal:

1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10 (decimal)

Example 2: Decimal to Hexadecimal

Convert 255 (decimal) to hexadecimal:

255 ÷ 16 = 15 with remainder 15 (F in hex)

15 ÷ 16 = 0 with remainder 15 (F in hex)

Result: FF (hexadecimal)

Example 3: Hexadecimal to Binary

Convert 1A (hexadecimal) to binary:

1 (hex) = 0001 (binary)

A (hex) = 1010 (binary)

Result: 00011010 (binary)

FAQ

What is the difference between base-2 and base-16?

Base-2 (binary) uses only two digits (0 and 1) and is fundamental to digital computing. Base-16 (hexadecimal) uses 16 digits (0-9 and A-F) and is often used as a more compact representation of binary data in computing.

Can I convert numbers between any two bases?

Yes, this calculator can convert between any two bases from 2 to 36. Simply 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 you enter digits that are not valid for the selected base. For example, entering "8" in a base-8 field is valid, but entering "8" in a base-2 field is invalid.