Enter your number, pick a From Base and To Base, and the Number System Converter spits out your Converted Value instantly — plus a full breakdown across Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16) all at once.
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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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.
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.
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.
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.
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.
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.
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.
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.