Number Base Converter

Understanding Number Base Conversion

What is a Number Base?

A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. The most common bases in computing are binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).

Binary (Base 2)

Binary is the fundamental number system of computers, using only two digits: 0 and 1. Each digit represents a power of 2. For example, binary 1010 equals (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10 in decimal.

Octal (Base 8)

Octal uses eight digits (0-7) and is commonly used in Unix file permissions. Each octal digit represents three binary digits. For example, octal 755 represents the binary permissions 111 101 101.

Decimal (Base 10)

Decimal is our everyday number system using ten digits (0-9). It's the most intuitive for humans but requires conversion for computer processing since computers work in binary.

Hexadecimal (Base 16)

Hexadecimal uses sixteen symbols (0-9 and A-F). It's widely used in programming because one hex digit represents exactly four binary digits, making it a convenient shorthand for binary data. For example, hex FF equals binary 11111111 or decimal 255.

Common Applications

• Programming: Memory addresses, bitwise operations, color codes
• Web Development: CSS color values (hex colors like #FF5733)
• Networking: IP addresses, MAC addresses, subnet masks
• System Administration: File permissions (octal notation)
• Computer Science Education: Understanding how computers store data

Conversion Tips

When converting between bases, remember that each position represents a power of the base. For binary to hex conversion, group binary digits in sets of four. For hex to binary, expand each hex digit into four binary digits. Our converter handles all these conversions automatically with input validation to ensure accuracy.