Number Base Converter (Binary, Octal, Decimal, Hexadecimal)
Convert numbers between Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16) with detailed positional notation conversion steps.
Groß- und Kleinschreibung bei Hexadezimalziffern wird automatisch unterstützt.
Mathematical Explanation
In der Mathematik und Informatik ist ein Stellenwertsystem (Positionssystem) eine Methode zur Darstellung von Zahlen, bei der der Wert einer Ziffer von ihrer relativen Position zur Basis abhängt.
Die 4 wichtigsten Zahlensysteme:
- Binärsystem (Basis 2): Nutzt ausschließlich die Ziffern
0und1. Es ist die fundamentale Sprache digitaler Computer-Hardware und Schaltkreise. - Oktalsystem (Basis 8): Nutzt die Ziffern
0 bis 7. 1 Oktalziffer entspricht genau 3 Binärstellen (Bits). - Dezimalsystem (Basis 10): Unser alltägliches Zahlensystem mit den Ziffern
0 bis 9. - Hexadezimalsystem (Basis 16): Nutzt die Ziffern
0 bis 9sowie die BuchstabenA bis F(für 10 bis 15). Eine Hex-Stelle fasst exakt 4 Bits (1 Nibble) zusammen.
Real-World Applications & Practical Use Cases
Why do we learn this? Here is how this mathematics is applied in business, engineering, science, and everyday life:
HEX Color Codes & Digital Displays
Every color displayed on screens is encoded as a 6-digit hexadecimal string (#RRGGBB), where paired hex digits represent red, green, and blue intensities from 0 to 255.
Hex code #10B981 defines the emerald green brand color (Red: 0x10 = 16, Green: 0xB9 = 185, Blue: 0x81 = 129).
IP Addressing & Subnet Masks
Network hardware routes traffic using 32-bit (IPv4) and 128-bit (IPv6) binary numbers. Subnet masks like 255.255.255.0 segment network portions from hosts.
Subnet mask 255.255.255.0 translates in binary to 24 consecutive ones followed by 8 zeros (/24 CIDR prefix).
Memory Addresses & Low-Level Code
Processors address system RAM using hexadecimal notation (such as 0x7FFF) because 1 hex digit neatly encapsulates 4 binary bits (one nibble).
Software debuggers present computer memory dumps in clean hexadecimal formatting rather than unwieldy binary bit strings.
Frequently Asked Questions (FAQ)
How do you convert decimal to binary?
Repeatedly divide the decimal number by 2 and record the remainder (0 or 1). Reading the remainders from bottom to top yields the binary representation.
Why is hexadecimal used in computing?
Hexadecimal compactly represents 4 binary bits (1 nibble) with a single character (0-9, A-F), making memory addresses and bytes much easier to read.