Number Base Converter
Convert numbers between binary, decimal, hexadecimal, octal and other bases. Perfect for programming and computer science.
Conversion Results
Number Bases Explained
Binary (Base 2)
Binary is the fundamental number system in computing, using only two digits: 0 and 1. Each digit is called a bit. Computers use binary because digital circuits have two states (on/off, high/low voltage). It's the foundation of all digital electronics and computer programming.
Common uses: Computer hardware, digital circuits, low-level programming, boolean logic
Example: Binary 1010₂ = Decimal 10; Binary 11111111₂ = Decimal 255
Decimal (Base 10)
Decimal is the standard number system used by humans, with ten digits from 0 to 9. It's based on our ten fingers and is the most intuitive system for everyday counting and mathematics. Each position represents a power of 10.
Common uses: Everyday mathematics, finance, measurements, general counting
Example: 365 = 3×10² + 6×10¹ + 5×10⁰
Hexadecimal (Base 16)
Hexadecimal uses sixteen digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It's widely used in computing because each hex digit represents exactly 4 bits. Essential for color codes, memory addresses, and machine code.
Common uses: Color codes (CSS), memory addresses, MAC addresses, debugging, assembly language
Example: Hex FF₁₆ = Decimal 255 = Binary 11111111₂; Color #FF0000 = Red
Octal (Base 8)
Octal uses eight digits from 0 to 7. Each octal digit represents exactly 3 bits, making it useful for representing binary data in a more compact form. Still used in Unix file permissions and some programming contexts.
Common uses: Unix/Linux file permissions (chmod), legacy computing systems, digital electronics
Example: Unix permission 755₈ = rwxr-xr-x; Octal 10₈ = Decimal 8
Base 36
Base 36 uses digits 0-9 and letters A-Z, providing 36 possible values per digit. It's the largest base that can be represented using standard alphanumeric characters. Commonly used for compact representations, URL shorteners, and database IDs.
Common uses: Short URLs, compact identifiers, license keys, tracking numbers
Example: YouTube video IDs, shortened URLs, product serial numbers
Other Bases (3-20)
Various other number bases serve specific purposes. Base 3 (ternary) uses 0, 1, 2 and has applications in balanced ternary computing. Base 12 (duodecimal) is more divisible than decimal. Base 20 (vigesimal) was used by ancient Mayan and Celtic cultures.
Historical/Special uses: Ancient calendars, theoretical computing, mathematical research
Example: Base 12: dozen (12), gross (144); Base 20: Mayan calendar system
Quick Conversion Reference
Decimal to Binary:
Repeatedly divide by 2, read remainders bottom-up
Example: 13 → 1101₂
Binary to Decimal:
Sum (digit × 2^position) for each digit
Example: 1101₂ → 8+4+0+1 = 13
Hex to Binary:
Each hex digit = 4 binary digits
Example: F₁₆ = 1111₂
Common Values:
10₁₀ = A₁₆ = 1010₂ = 12₈
255₁₀ = FF₁₆ = 11111111₂