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Convert between binary, decimal, hexadecimal, and octal number systems.
Number base conversion is the process of translating a number from one positional numeral system to another — such as binary (base 2), octal (base 8), decimal (base 10), or hexadecimal (base 16) — using place-value arithmetic.
Enter a value in any field to convert to all other bases. Supports integers only.
| Decimal | Binary | Hex | Octal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 8 | 1000 | 8 | 10 |
| 10 | 1010 | A | 12 |
| 16 | 10000 | 10 | 20 |
| 32 | 100000 | 20 | 40 |
| 64 | 1000000 | 40 | 100 |
| 128 | 10000000 | 80 | 200 |
| 255 | 11111111 | FF | 377 |
| 256 | 100000000 | 100 | 400 |
| 1024 | 10000000000 | 400 | 2000 |
| 65535 | 1111111111111111 | FFFF | 177777 |
Number systems use different bases to represent values. Each base determines how many unique digits are available and how place values work.
Base Systems:
Example: Decimal 42
Formula
Decimal = Σ (digit × base^position) | e.g., Binary 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10digit = the value of each digit in its own base (0–1 for binary, 0–F for hex)
base = the radix of the number system (2, 8, 10, or 16)
position = the place value exponent, starting at 0 from the right
Worked Example
Convert decimal 255 to all bases
Did you know? Hexadecimal became the dominant notation for low-level computing because each hex digit maps exactly to 4 binary bits (a nibble). This means a single byte (8 bits) is always expressed as exactly 2 hex digits — making memory dumps and color codes like #FF5733 far more readable than their 24-bit binary equivalents.
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