Decimal to Binary Converter
Convert an ordinary decimal number to binary — the ones and zeros a computer actually stores.
To convert, divide repeatedly by two and collect the remainders, then read them bottom to top.
How the decimal to binary converter works
To convert, divide repeatedly by two and collect the remainders, then read them bottom to top. Equivalently, subtract the largest power of two that fits, and repeat. The result shows how many bits the number needs: anything under 256 fits in a byte, anything under 65,536 in two.
Formula: value = Σ digitₖ × bᵏ
Worked examples
| Inputs | Converted | Note |
|---|---|---|
| 255 | 11111111 | 11111111 — eight ones |
| 10 | 1010 | 1010 |
| 1000 | 1111101000 | 1111101000 |
FAQFrequently asked questions
How do I convert decimal to binary by hand?
Divide by two repeatedly and write the remainders, then read them backwards.
How many bits does my number need?
The bits row tells you — 1,000 needs 10 bits, because 2¹⁰ is 1,024.
What is 100 in binary?
1100100.
Why are powers of two easy?
Each is a single 1 followed by zeros: 64 is 1000000.
Can it do fractions?
This page converts whole numbers. Binary fractions exist but behave differently — 0.1 in decimal has no exact binary form, which is the root of most floating-point surprises.
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)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.