Number System Converter

Computers store and process numbers in different formats — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — and the Number System Converter translates any number between these four bases. Enter your number, select the From Base and To Base, and get the Converted Value right away. Secondary outputs show the equivalent representation across all four number systems simultaneously — Binary, Octal, Decimal, and Hexadecimal.

Enter a valid number in the selected base system

Results

Converted Value

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Binary (Base 2)

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Octal (Base 8)

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Decimal (Base 10)

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Hexadecimal (Base 16)

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Frequently Asked Questions

How does number system conversion work?

Number system conversion involves converting a number from one base to another. First, convert the source number to decimal (base 10), then convert the decimal to the target base. Each digit is multiplied by the base raised to its position power.

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

Binary uses base 2 (digits 0-1), octal uses base 8 (digits 0-7), decimal uses base 10 (digits 0-9), and hexadecimal uses base 16 (digits 0-9 and A-F). Each system represents numbers using different digit sets and position values.

How do I convert from decimal to binary?

To convert decimal to binary, repeatedly divide the decimal number by 2 and record the remainders. The binary representation is the remainders read in reverse order from bottom to top.

What are the valid characters for hexadecimal numbers?

Hexadecimal numbers use digits 0-9 and letters A-F (or a-f). A=10, B=11, C=12, D=13, E=14, and F=15 in decimal. Letters can be uppercase or lowercase.

Can I convert negative numbers between number systems?

This converter works with positive integers. For negative numbers, you would typically handle the sign separately and convert the absolute value, then apply the sign to the result.

What's the maximum number I can convert?

The converter can handle large integers within JavaScript's safe integer range (up to 2^53 - 1). Very large numbers may lose precision due to floating-point limitations.

Why is binary important in computing?

Binary is fundamental to computing because digital systems use two states (on/off, high/low voltage). All data in computers is ultimately represented in binary, making it essential for programming and digital electronics.

How do I verify my conversion is correct?

You can verify conversions by converting back to the original base or by manually calculating using the positional notation formula: sum of (digit × base^position) for each digit position.