Convert numbers between binary, octal, decimal, and hex online free. Decimal to binary converter with step-by-step working shown for every conversion.
This decimal to binary converter online free instantly translates any integer between all four common number bases — binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — as well as any custom base from 2 to 36. Type a number in any base and all other representations update simultaneously. Enable Show Working to see the step-by-step division algorithm that produced the result — which makes this number system converter with working shown ideal for students learning digital electronics, computer architecture, and programming fundamentals. Working in web development and need a hex to binary converter with steps? Debugging Unix file permissions and need an octal to decimal converter? This base conversion calculator free handles all these cases in one tool. Results are instantly copyable. Custom base support means you can also work in base 3, base 5, base 12, or any other radix used in mathematical or engineering contexts.
The Number Base Converter converts integers between any two bases from binary (base-2) through hexadecimal (base-16), and to any custom base up to base-36. Conversion works by first translating the input number to its decimal (base-10) value, then converting that decimal value into the target base using repeated division. For example, converting the binary number 1011 to decimal: (1×8) + (0×4) + (1×2) + (1×1) = 11. The tool simultaneously shows the number in binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16) — the four most common bases in computing — updating all four instantly as you type.
Formula
Decimal → Base N: repeatedly divide by N; remainders in reverse order form the new number. Base N → Decimal: multiply each digit by N^position (right to left, starting at 0) and sum.
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
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