Number System Converter
Enter a positive whole number in decimal, binary, octal or hexadecimal and see its value in all four number systems, with binary in groups of four.
Result
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Examples
Decimal 255 = Binary 1111 1111 = Octal 377 = Hex FF
Decimal 42 = Binary 10 1010 = Octal 52 = Hex 2A
Decimal 100 = Binary 110 0100 = Octal 144 = Hex 64
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
What are the common number systems?
The four most common systems are: decimal (base 10, everyday use), binary (base 2, computers), octal (base 8, file permissions), and hexadecimal (base 16, colors and memory addresses).
How do I convert between number systems?
To convert to decimal: multiply each digit by its place value and add. From decimal: repeatedly divide by the target base and read remainders bottom-up. Hex digits A-F represent 10-15.
Can I enter negative numbers, decimals or prefixes such as 0x?
No. The calculator only handles whole, non-negative numbers and only the digits of the selected system: 0–1 for binary, 0–7 for octal, 0–9 for decimal, and 0–9 plus A–F (upper or lower case) for hexadecimal. Prefixes such as 0x or 0b, spaces and decimal places produce no result – so enter “ff” rather than “0xFF”, which gives decimal 255, binary 1111 1111 and octal 377. Results are exact up to 9,007,199,254,740,991 (2^53 − 1); above that the last digits may be off.
Guide
What is the Number System Converter?
The number system calculator converts numbers between decimal, binary, octal and hexadecimal and arbitrary bases from 2 to 36.
How does the Number System Converter work?
Enter a number and the source system. The calculator converts to all common number systems and shows the conversion steps. Arithmetic in different bases is possible.
Key Data and Facts
Decimal: base 10 (0-9). Binary: base 2 (0, 1). Octal: base 8 (0-7). Hexadecimal: base 16 (0-9, A-F). Example: decimal 255 = binary 11111111 = hex FF.
Step-by-Step Guide
How to use the number system converter step by step: 1. Choose the source system – decimal (base 10), binary (base 2), octal (base 8), hexadecimal (base 16) or any base from 2 to 36. 2. Enter the number – use the digits of the chosen system. In the hexadecimal system, A-F are valid for the values 10-15. 3. Read the result – the calculator displays the number in all common systems simultaneously. 4. Understand the conversion path: each digit is multiplied by the power of the base. Binary 1011 = 1*8 + 0*4 + 1*2 + 1*1 = 11 decimal. 5. Practical applications: binary for computer technology and networks (IP addresses), hexadecimal for colour codes in web design (#FF0000 = red), octal for Unix file permissions (chmod 755). Tip: Hexadecimal numbers can be easily converted to binary, since each hex digit corresponds to exactly 4 binary places (F = 1111).
Calculation Example
Decimal 200 in binary: 11001000. Decimal 200 in hex: C8. Binary 10110 in decimal: 16+4+2 = 22.
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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