How to Convert Binary to Decimal
Convert an unsigned binary integer to decimal and see the powers-of-two expansion. The calculator uses exact integer arithmetic, so long bit strings are not silently rounded.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 19, 2026 · How we check conversion tools
Start at the right with position 0. Multiply each bit by 2 raised to its position, then add the results.
Binary to decimal converter with steps
Enter zeros and ones. Spaces, underscores, and an optional 0b prefix are accepted.
Binary to decimal conversion steps
- Write a power of 2 under each bit, beginning with 2⁰ under the rightmost bit.
- Multiply each power by the bit above it. A zero contributes nothing.
- Add the remaining powers. The sum is the decimal value.
For an n-bit unsigned number, the place values run from 2⁰ through 2n−1.
Binary to decimal examples
| Binary | Place-value sum | Decimal |
|---|---|---|
| 1111 | 8 + 4 + 2 + 1 | 15 |
| 101 | 4 + 0 + 1 | 5 |
| 1001 | 8 + 0 + 0 + 1 | 9 |
| 10101 | 16 + 0 + 4 + 0 + 1 | 21 |
A faster double-and-add method
Read the bits from left to right. Start at zero; for each bit, double the running value and add the new bit. For 1011: 0×2+1=1, 1×2+0=2, 2×2+1=5, and 5×2+1=11. This is the same positional calculation without writing every power.
To shorten a bit pattern for programming work, use the binary to hexadecimal converter.
Scope and limitations
This tool treats the input as an unsigned whole number. It does not interpret a leading bit as a two's-complement sign bit, and it does not accept a binary point. Leading zeros are allowed and do not change the numerical result. Inputs are limited to 512 binary digits to keep the displayed working readable.
Frequently asked questions
What is the easiest way to convert binary to decimal?
Add the powers of two whose positions contain a 1. For short numbers, this is usually the quickest method to check by hand.
What is 1111 binary in decimal?
It is 15: 8 + 4 + 2 + 1 = 15.
Does 0101 have a different value from 101?
No. Both equal decimal 5 when treated as unsigned integers. A fixed-width data format may preserve the leading zero for display, but it does not change the value.