Number Base Converter

Convert numbers between binary, decimal, hexadecimal, and octal bases instantly. Get step-by-step explanations and learn how different number systems work.

Enter Number: Enter a valid number in the selected base format

From Base: Select the base of the input number

To Base: Select the base to convert to

Conversion Result:

All Base Conversions:

Binary (Base 2)

Octal (Base 8)

Decimal (Base 10)

Hexadecimal (Base 16)

Step-by-Step Conversion:

How to Use the Number Base Converter

Step 1: Enter Your Number

Input the number you want to convert. Make sure it's valid for the source base you've selected.

Step 2: Select Source Base

Choose the base of your input number (Binary, Octal, Decimal, or Hexadecimal).

Step 3: Select Target Base

Choose the base you want to convert to.

Step 4: Convert

Click the "Convert" button to see the result and step-by-step explanation.

About Number Base Systems

Number base systems are different ways of representing numbers. Each system uses a different base (radix) to determine the value of each digit position.

Binary (Base 2): Uses only 0 and 1. Each position represents a power of 2.
Octal (Base 8): Uses digits 0-7. Each position represents a power of 8.
Decimal (Base 10): Uses digits 0-9. The most common system we use daily.
Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Each position represents a power of 16.

Conversion Formulas

Converting from Any Base to Decimal

To convert a number from base B to decimal, use the formula:

Decimal = d₀ × B⁰ + d₁ × B¹ + d₂ × B² + ... + dₙ × Bⁿ

Where d₀, d₁, d₂, ..., dₙ are the digits of the number from right to left.

Converting from Decimal to Any Base

To convert a decimal number to base B:

Divide the decimal number by B
Record the remainder
Repeat with the quotient until it becomes 0
The remainders in reverse order form the number in base B

Use Cases and Applications

Computer Science: Understanding binary and hexadecimal systems for programming
Digital Electronics: Working with binary logic and digital circuits
Networking: IP addresses and subnet masks often use different bases
Cryptography: Many encryption algorithms work with different number bases
Education: Learning about different mathematical number systems
Software Development: Color codes in web development use hexadecimal

Examples

Example 1: Decimal to Binary

Convert 255 (decimal) to binary:

255 ÷ 2 = 127 remainder 1

127 ÷ 2 = 63 remainder 1

63 ÷ 2 = 31 remainder 1

...

Result: 11111111 (binary)

Example 2: Binary to Hexadecimal

Convert 1010 (binary) to hexadecimal:

First convert to decimal: 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10

Then convert 10 (decimal) to hexadecimal: A

Result: A (hexadecimal)

Frequently Asked Questions

What is the difference between binary and decimal?

Binary uses only two digits (0 and 1) and is base 2, while decimal uses ten digits (0-9) and is base 10. Binary is used by computers internally, while decimal is what we use in everyday life.

Why do computers use binary?

Computers use binary because it's the simplest number system that can represent information using two states: on (1) and off (0). This corresponds to the electrical states in digital circuits.

What is hexadecimal used for?

Hexadecimal is commonly used in computer programming, especially for representing colors in web design, memory addresses, and as a compact way to represent binary data.

Can I convert negative numbers?

Yes, negative numbers can be converted between bases. However, the representation depends on the system being used (like two's complement for binary).

What's the largest number I can convert?

The tool can handle very large numbers, but there are practical limits based on JavaScript's number precision. For extremely large numbers, some precision might be lost.