Binary Converter
Convert a number between binary and decimal, in either direction.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter a number and choose a direction to convert between binary and decimal.
Enter a decimal number, or a binary number using only 0s and 1s, depending on the direction chosen below.
Your result
101010
Result
AI explanation
Formula
Repeated division/multiplication by 2 to convert between decimal and binary place valuesWorked example
Decimal 42 to binary
| Field | Value |
|---|---|
| Value | 42 |
| Convert | from-decimal |
| Result | 101010 |
Assumptions
- Only non-negative whole numbers are supported.
- Binary input must contain only the digits 0 and 1.
Frequently asked questions
How does binary-to-decimal conversion work?
Each binary digit represents a power of 2, from right to left (1, 2, 4, 8, ...) — sum the powers of 2 where the binary digit is 1 to get the decimal value.
Why is binary used in computing?
Digital circuits represent data using two voltage states (on/off), which map naturally to the two binary digits 0 and 1 — all computer data is ultimately stored and processed in binary.
Can this handle very large numbers?
Yes — it uses arbitrary-precision arithmetic, so very long binary strings or large decimal numbers convert exactly without losing precision.