Number Bases Converter
This number bases converter allows you to easily convert numbers between different numeral systems. Whether you need to convert between common bases like binary, decimal, and hexadecimal, or work with more obscure bases, this tool provides accurate conversions for a wide range of number systems. Understanding different number bases is essential for computer programming, digital electronics, mathematics, and various scientific fields.
Common Number Systems
Binary (Base-2)
The binary numeral system uses two symbols, typically 0 and 1. It's fundamental to computing since digital electronic circuitry uses binary logic.
- Valid digits: 0, 1
- Example: 1011₂ = 11 in decimal
- Used in: Computer science, digital electronics, programming
Octal (Base-8)
The octal numeral system uses eight symbols (0-7) and is convenient for representing binary numbers in a more compact form.
- Valid digits: 0-7
- Example: 17₈ = 15 in decimal
- Used in: Unix file permissions, some programming contexts
Decimal (Base-10)
The decimal numeral system uses ten symbols (0-9) and is the most commonly used number system in daily life.
- Valid digits: 0-9
- Example: 42₁₀ = 42
- Used in: Everyday counting, most human activities
Hexadecimal (Base-16)
The hexadecimal numeral system uses sixteen symbols: 0-9 and A-F (or a-f). It provides a convenient way to represent binary-coded values.
- Valid digits: 0-9, A-F (case-insensitive)
- Example: 2A₁₆ = 42 in decimal
- Used in: Computer programming, memory addresses, color codes, debugging
Duodecimal (Base-12)
The duodecimal (or dozenal) system uses twelve symbols, typically 0-9 followed by A-B or other symbols for 10 and 11.
- Valid digits: 0-9, A-B (or other symbols)
- Example: 34₁₂ = 40 in decimal
- Used in: Measurements (inches in a foot), time (hours on a clock)
Sexagesimal (Base-60)
The sexagesimal system uses 60 as its base and dates back to ancient Mesopotamia.
- Modern usage is mixed with decimal (minutes, seconds)
- Used in: Time measurement (60 seconds in a minute, 60 minutes in an hour), geographic coordinates
Common Number Base Conversions
| Decimal (Base-10) | Binary (Base-2) | Octal (Base-8) | Hexadecimal (Base-16) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
| 256 | 100000000 | 400 | 100 |
Number Base Conversion Methods
Converting from Decimal to Other Bases
To convert from decimal to another base, divide repeatedly by the target base and collect the remainders in reverse order.
Converting from Any Base to Decimal
To convert from any base to decimal, multiply each digit by its place value and sum the results.
Example: 101₂ = 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 = 5₁₀
Converting Between Non-Decimal Bases
To convert between two non-decimal bases, first convert to decimal as an intermediate step, then convert to the target base.