Base Converter
Convert numbers between binary, octal, decimal, hexadecimal and more
#Understanding Number Systems
Number systems are methods of representing numbers using a set of symbols. The most common systems in computing are binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).
Each system uses a different number of unique digits. Binary uses 0-1, octal uses 0-7, decimal uses 0-9, and hexadecimal uses 0-9 and A-F. Understanding these systems is essential for programming, networking, and digital electronics.
Common Number Systems
Binary (Base 2)
Uses only 0 and 1. The fundamental language of computers. Each digit is called a "bit".
Octal (Base 8)
Uses digits 0-7. Historically used in computing, still used for Unix file permissions.
Decimal (Base 10)
Uses digits 0-9. The standard number system used in everyday life.
Hexadecimal (Base 16)
Uses 0-9 and A-F. Widely used in programming for colors, memory addresses, and more.
Common Use Cases
Programming
Memory addresses, bitwise operations, color codes, debugging
Networking
IP addresses, MAC addresses, subnet masks, port numbers
Electronics
Digital circuits, microcontrollers, embedded systems, registers
Conversion Examples
Understanding how to convert between number systems is a fundamental skill in computer science. Here's how the decimal number 255 is represented in different bases:
Notice that 255 in binary is 8 ones (11111111), which represents the maximum value of an unsigned 8-bit integer. This is why 255 is commonly seen in color values (RGB), where each color channel uses 8 bits.
Why Programmers Love Hexadecimal
Hexadecimal is the preferred number system for programmers because it provides a compact way to represent binary data. Each hexadecimal digit represents exactly 4 binary bits, making conversion between hex and binary trivial.
For example, the hex value 0xFF instantly tells a programmer this is 8 bits all set to 1. In contrast, writing 255 or 11111111 is less intuitive for understanding bit patterns.
Common uses include: CSS color codes (#FF5733), memory addresses (0x7FFF0000), Unicode characters (U+1F600), and byte sequences in network protocols.
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