Number System Converter
Convert between decimal, binary, octal and hexadecimal systems. Step-by-step explanation, free and no registration required.
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.
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.
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 den Zahlensystem-Rechner step by step: 1. Quellsystem choose -- Dezimal (Basis 10), Binaer (Basis 2), Oktal (Basis 8), Hexadezimal (Basis 16) oder eine beliebige Basis von 2 bis 36. 2. Zahl enter -- verwenden Sie die Ziffern des gewaehlten Systems. Im Hexadezimalsystem sind A-F fuer die Werte 10-15 gueltig. 3. Ergebnis ablesen -- der Rechner zeigt die Zahl in allen gaengigen Systemen gleichzeitig an. 4. Umrechnungsweg verstehen: Jede Stelle wird mit der Potenz der Basis multipliziert. Binaer 1011 = 1*8 + 0*4 + 1*2 + 1*1 = 11 dezimal. 5. Praktische Anwendungen: Binaer fuer Computertechnik und Netzwerke (IP-Adressen), Hexadezimal fuer Farbcodes im Webdesign (#FF0000 = Rot), Oktal fuer Unix-Dateiberechtigungen (chmod 755). Tipp: Hexadezimalzahlen lassen sich leicht in Binaer umwandeln, da jede Hex-Ziffer genau 4 Binaerstellen entspricht (F = 1111).
Calculation Example
Dezimal 200 in Binaer: 11001000. Dezimal 200 in Hex: C8. Binaer 10110 in Dezimal: 16+4+2 = 22.
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