Converts between binary (base 2) and decimal (base 10) number representations — a computer-science fundamental.
How it works
Each binary digit is multiplied by its place value (a power of 2) and summed to get the decimal equivalent; the reverse direction repeatedly divides by 2 and tracks the remainders.
What this does not include
This does not include hexadecimal or octal conversion — this calculator specifically handles binary and decimal.
How to use this calculator
- Choose a direction and enter the value.
A worked example
Binary 1101 → decimal: reading right to left, the place values are 1s, 2s, 4s, 8s → 1 + 0 + 4 + 8 = 13.
Decimal 42 → binary: repeatedly dividing by 2 and tracking remainders gives 101010.
What the place values mean
| Binary position (right to left) | Decimal value |
|---|---|
| 1st | 1 |
| 2nd | 2 |
| 3rd | 4 |
| 4th | 8 |
Edge cases worth knowing
Each position’s value doubles moving left, the same base-10 idea where each digit position is worth 10 times the one before it — binary just uses 2 as its base instead of 10.
A leading zero in binary changes nothing — 01101 and 1101 represent the identical decimal value, 13.
Frequently asked questions
Why does computing use binary instead of decimal?
Digital circuits naturally represent two states (on/off, high/low voltage), making base 2 the most direct fit for how computer hardware physically works.
What’s an example of a binary place value?
In binary 1101, reading right to left, the digits represent 1s, 2s, 4s, and 8s place values — summing 8+4+0+1 gives the decimal value 13.
Can this handle very large decimal numbers?
Yes — the conversion works for any non-negative whole number, though very large binary strings become long to read.
