Number Base Converter
Convert numbers between decimal, binary, octal, and hexadecimal. Supports large numbers with grouped digit display.
Additional Info
About Number Base Converter
Number base conversion is a fundamental skill in computer science and programming. Every piece of digital data is ultimately stored as binary (base 2), but developers work with decimal (base 10) for human-readable values, hexadecimal (base 16) for memory addresses and color codes, and octal (base 8) for Unix file permissions. Understanding number base conversion is essential for low-level programming, network engineering, cryptography, and any work involving bitwise operations, memory addressing, or binary protocols.
Number Bases Quick Reference
Binary (Base 2) uses only 0 and 1. Each digit (bit) represents a power of 2. Eight bits make one byte, which can represent values 0-255. Binary is essential for understanding bitwise operations (&, |, ^, ~, <<, >>) and subnet masks in networking. Octal (Base 8) uses digits 0-7. Each octal digit maps to exactly 3 binary digits, making it convenient for Unix file permissions (e.g., 755 = rwxr-xr-x). Hexadecimal (Base 16) uses 0-9 and A-F. Each hex digit maps to exactly 4 binary digits (one nibble), making it the most compact way to represent binary data.
Common hex values every developer should recognize: 0xFF = 255 (maximum byte value), 0xFFFF = 65,535 (maximum 16-bit unsigned integer), 0x7FFFFFFF = 2,147,483,647 (maximum 32-bit signed integer). In CSS, hex color codes like #FF5733 represent RGB values where FF=255 red, 57=87 green, 33=51 blue. In programming, hex prefixes vary by language: 0x (C, Java, JavaScript, Python), &H (Visual Basic), and $ (Pascal, Delphi). This converter supports underscore and space separators in input for readability (e.g., 1111_0000 or FF 00 FF).
Frequently Asked Questions
What are number bases?
A number base (or radix) determines how many digits are used to represent numbers. Decimal uses 10 digits (0-9), binary uses 2 (0-1), octal uses 8 (0-7), and hexadecimal uses 16 (0-9, A-F).
Why is hexadecimal used in programming?
Hexadecimal is compact — each hex digit represents exactly 4 binary digits (bits). This makes it ideal for representing memory addresses, colors (e.g., #FF0000), and byte values.
How do I read binary numbers?
Each binary digit (bit) represents a power of 2, from right to left. For example, 1010 in binary = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal.