Number Base Converter
Convert between decimal, binary, hexadecimal, octal, and other number systems
Number Base Converter
Recent Conversions:
Common Conversions:
Understanding Number Systems
Number systems represent values using different bases. Our everyday decimal system is base 10, but computers often work with binary (base 2), octal (base 8), and hexadecimal (base 16) systems.
Key Concepts:
- Base: The number of unique digits used in the system
- Position Value: Each digit's place in a number represents a power of the base
- Digit Value: The actual value of each symbol (0-9, A-Z)
- Decimal Equivalent: The value in our common base-10 system
- Bit: A single binary digit (0 or 1)
Important Number Systems:
- Binary (Base 2): Used directly by computers; consists of 0's and 1's
- Octal (Base 8): Historically used as shorthand for binary
- Decimal (Base 10): Our standard everyday counting system
- Hexadecimal (Base 16): Common in programming for memory addresses, colors, etc.
- Base64: Used in computing to encode binary data as ASCII text
Number System Applications:
Binary (Base 2)
- Computer memory and processors
- Digital logic (true/false states)
- Network protocols and data transmission
Hexadecimal (Base 16)
- Memory addresses and debugging
- Color codes in HTML/CSS
- MAC addresses and IP addresses
- File formats and binary data representation
Number system conversions are essential in computer science, programming, and digital electronics, allowing efficient representation and manipulation of data.
Number System Conversion Reference
| From | To | Method |
|---|---|---|
| Decimal | Binary | Divide by 2 repeatedly, read remainders in reverse order |
| Binary | Decimal | Sum the powers of 2 where bits are 1 |
| Decimal | Hexadecimal | Divide by 16 repeatedly, convert remainders (10-15 to A-F) |
| Hexadecimal | Decimal | Convert each digit (A-F to 10-15), multiply by powers of 16 |
| Binary | Hexadecimal | Group bits in sets of 4, convert each group |
| Hexadecimal | Binary | Convert each hex digit to 4 bits |
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Number Base Visualization
Common Number Formats
Quick Conversion Tips
Binary to Hexadecimal:
Group binary digits in sets of 4, convert each group
Example: 1010 1100 = AC (hex)
Hexadecimal to Binary:
Convert each hex digit to 4 binary digits
Example: A5 = 1010 0101 (binary)
Binary to Octal:
Group binary digits in sets of 3, convert each group
Example: 001 010 111 = 127 (octal)
Mobile tip: Swipe left or right on the base dropdown to quickly change number systems
About the Number Base Converter
Convert between decimal, binary, hexadecimal, octal, and other number systems All conversions run instantly in your browser and nothing you enter is sent to a server.
Common Conversion Formulas
| From | To | Formula |
|---|---|---|
| Decimal (Base 10) | Binary (Base 2) | Divide by 2 repeatedly, read remainders bottom-up |
| Decimal (Base 10) | Hexadecimal (Base 16) | Divide by 16 repeatedly, read remainders bottom-up |
| Binary (Base 2) | Decimal (Base 10) | Sum of (bit × 2^position) from right to left |
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