Binary-Decimal Converter
Free online binary converter. Convert between binary, decimal, hexadecimal and octal number systems instantly. Real-time conversion with step-by-step breakdown.
Binary Breakdown
Understanding Number Systems
Different number systems represent values using different bases. Decimal uses base 10, binary uses base 2, hexadecimal uses base 16, and octal uses base 8. Understanding these conversions is essential for programming, especially when working with memory addresses, color codes, and bitwise operations.
Number Systems Explained
- Decimal (Base 10) — Uses digits 0-9. This is the number system we use daily in arithmetic.
- Binary (Base 2) — Uses only 0 and 1. Computer systems use binary internally to process data.
- Hexadecimal (Base 16) — Uses 0-9 and A-F (where A=10, B=11...F=15). Common in web colors (#FF5733) and memory addresses.
- Octal (Base 8) — Uses digits 0-7. Less common but used in Unix file permissions (like 755).
Practical Applications
Web designers use hexadecimal for colors. Every color on a screen can be represented as a 6-digit hex number like #FF5733 where FF is red, 57 is green, and 33 is blue. Programmers use binary to understand bitwise operations and memory management. Network engineers use various bases when dealing with IP addresses and CIDR notation.
Conversion Formulas
To convert from any base to decimal, multiply each digit by the base raised to the position power and sum the results. For example, binary 1010 equals 1×2^3 + 0×2^2 + 1×2^1 + 0×2^0 = 8 + 0 + 2 + 0 = 10 in decimal. To convert from decimal to another base, repeatedly divide by the base and collect remainders in reverse order.