Base-N Calculator Online

Convert numbers between different number bases (binary, decimal, hexadecimal, octal) with our online base-n calculator. This tool helps you understand how numbers are represented in different numeral systems and perform conversions between them.

What is Base-N?

Base-N refers to a numeral system that uses N distinct digits to represent numbers. The most common numeral systems are:

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

Each position in a number represents a power of the base. For example, in decimal (base-10), the number 123 represents:

1 × 10² + 2 × 10¹ + 3 × 10⁰ = 100 + 20 + 3 = 123

In binary (base-2), the number 101 represents:

1 × 2² + 0 × 2¹ + 1 × 2⁰ = 4 + 0 + 1 = 5

How to Use This Calculator

Enter the number you want to convert in the "Number to convert" field
Select the base of the number you're converting from 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

The calculator will display the converted number and show the conversion steps in the result panel.

Common Number Bases

Here are some common numeral systems and their uses:

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

Base Conversion Table

Here's a quick reference table for common number conversions:

Decimal	Binary	Octal	Hexadecimal
0	0	0	0
1	1	1	1
2	10	2	2
3	11	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A

FAQ

What is the difference between base-2 and base-10?

Base-2 (binary) uses only two digits (0 and 1) and is used in digital electronics. Base-10 (decimal) uses ten digits (0-9) and is our standard numbering system. Each position in a base-2 number represents a power of 2, while in base-10 each position represents a power of 10.

How do I convert a decimal number to binary?

To convert a decimal number to binary, you can use the division-remainder method. Divide the number by 2, record the remainder, then divide the quotient by 2 again, recording the remainder each time. Continue until the quotient is 0. The binary number is the remainders read in reverse order.

What is hexadecimal used for?

Hexadecimal (base-16) is commonly used in computer programming because it provides a more compact representation of binary data. Each hexadecimal digit represents exactly four binary digits (bits), making it easier to work with binary data in a more human-readable format.