How to Convert Number Bases
Our base converter transforms numbers between decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Essential for programming, computer science, and digital electronics.
Understanding Number Bases
Our everyday decimal system uses 10 digits (0-9). Computers use binary (0-1). Hexadecimal (0-F) is compact for representing binary. Each position represents a power of the base.
Base Conversion Method
To decimal: multiply each digit by its place value (power of base) and sum. From decimal: repeatedly divide by target base, collect remainders in reverse.
Example:
Binary 1011 to decimal: 1×8 + 0×4 + 1×2 + 1×1 = 11. Decimal 25 to binary: 25÷2=12r1, 12÷2=6r0, 6÷2=3r0, 3÷2=1r1, 1÷2=0r1 → 11001.
Common Use Cases
Real-world applications for this calculator
Programming
Work with memory addresses, bit manipulation, and color codes.
Networking
Understand IP addresses, subnet masks, and MAC addresses.
Digital Electronics
Design circuits and understand processor operations.
Tips
- Hex digits: 0-9, then A=10, B=11, C=12, D=13, E=14, F=15.
- Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256...
- Binary ↔ Hex: 4 bits = 1 hex digit.
- For large numbers, convert to decimal first, then to target base.
Frequently Asked Questions
Why do computers use binary?
Computers use electronic switches that have two states: on (1) and off (0). Binary directly represents these states, making it reliable and efficient for digital circuits.
How do I convert binary to decimal?
Multiply each bit by its place value (powers of 2 from right: 1, 2, 4, 8, 16...) and add. Binary 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Why is hexadecimal useful?
Hex is compact: each hex digit represents exactly 4 binary bits. FF in hex = 11111111 in binary = 255 in decimal. It's used for colors (#RRGGBB), memory addresses, and more.
How do I convert between binary and hex?
Group binary digits in sets of 4 (from right), then convert each group to hex: 1010 1111 = AF. Reverse: expand each hex digit to 4 bits: C3 = 1100 0011.
What is octal used for?
Octal (base 8) uses digits 0-7 and each digit represents 3 binary bits. It's used in Unix file permissions (chmod 755) and some older computer systems.