Number Base Systems
Binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) are the most common number systems.
Quick Reference
| Dec | Bin | Oct | Hex |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 255 | 11111111 | 377 | FF |
How to Use This Number Base Converter
Enter a number and select its current base. The calculator converts to binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16).
Formula & How It Works
To convert base-a to base-b: first convert to decimal (multiply each digit by a^position), then convert decimal to base-b (repeated division by b, collect remainders).
Calculation Example
Decimal 42 = Binary 101010 = Octal 52 = Hex 2A. Each base has its uses: binary (hardware), octal (Unix permissions), hex (memory/colors).
Expert Tips
Binary β Hex is easy: group binary digits in sets of 4 (from right). 1010 1100 = AC in hex. Unix file permissions use octal: 755 = rwxr-xr-x.
Frequently Asked Questions
Why is binary important?
Computers operate in binary (0s and 1s). Every instruction, number, and character is ultimately stored in binary.
What is hexadecimal used for?
Hex is a compact way to represent binary. 1 hex digit = 4 binary digits. Used in colors (#FF0000), memory addresses, and programming.
How to convert decimal to binary?
Divide by 2 repeatedly, read remainders bottom to top. 13 β 1101.