Binary to Decimal Converter
Convert a binary number to ordinary decimal — each digit is a power of two, doubling as you move left.
Binary uses only 0 and 1, and each position is worth twice the one to its right: 1, 2, 4, 8, 16 and so on.
How the binary to decimal converter works
Binary uses only 0 and 1, and each position is worth twice the one to its right: 1, 2, 4, 8, 16 and so on. To read it, add up the place values wherever there is a 1 — so 1011 is 8 + 2 + 1 = 11. Eight binary digits make a byte, which is why 11111111 is 255 and why so many limits in computing stop at 255, 65535 or 4294967295.
Formula: value = Σ digitₖ × bᵏ
Worked examples
| Inputs | Converted | Note |
|---|---|---|
| 11111111 | 255 | 255 — the largest byte |
| 1011 | 11 | 11 |
| 10000000 | 128 | 128 |
FAQFrequently asked questions
How do I read binary?
Each place is a power of two. Add the values where there is a 1: 1101 is 8 + 4 + 1 = 13.
Why is 255 significant?
It is the largest value in eight bits, one byte — which is why colour channels and many old limits stop there.
What is 1010 in decimal?
10.
Do computers really use binary?
Yes, because a transistor is reliably either on or off; two states are far easier to build than ten.
What about negative binary numbers?
They are usually stored as two's complement, where the top bit signals a negative value. This page handles positive numbers.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.