How to convert decimal to binary
Divide the number by 2 repeatedly and write down the remainders, then read them bottom to top. For 13: 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1, giving 1101. To go back, add up the powers of two where there's a 1: 8 + 4 + 1 = 13.
Hex and octal
Hexadecimal (base 16) uses 0–9 and A–F, and each hex digit is exactly 4 binary bits, so 1101 0110 = D6. Programmers use hex for colours (#FF8800), memory addresses and byte values. Octal (base 8) groups 3 bits per digit and still appears in Unix file permissions such as chmod 755.
This converter uses JavaScript BigInt, so 64-bit and larger values are exact. You can type prefixes such as 0x or 0b.
Frequently asked questions
What is 255 in binary?
11111111 (eight ones), which is FF in hex.
Does it handle negative numbers?
Yes, with a leading minus sign. It doesn't produce two's-complement output.
How to use the Decimal to Binary Converter
- Paste the text, number or code.
- Choose encode/decode or the target format.
- Read the result instantly.
- Copy it into your code or terminal.
Why use this Decimal to Binary Converter
100% in your browser
Nothing you enter is uploaded or stored.
Instant results
Updates as you type, no waiting.
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Works on phones, tablets and desktops.
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Explained
Formulas, tables and sources on the page.
Decimal to Binary Converter: chart and reference data
Source: exact arithmetic
| Decimal | Binary | Hex | Gray code | BCD |
|---|---|---|---|---|
| 0 | 0000 | 0 | 0000 | 0000 0000 |
| 1 | 0001 | 1 | 0001 | 0000 0001 |
| 2 | 0010 | 2 | 0011 | 0000 0010 |
| 3 | 0011 | 3 | 0010 | 0000 0011 |
| 4 | 0100 | 4 | 0110 | 0000 0100 |
| 5 | 0101 | 5 | 0111 | 0000 0101 |
| 6 | 0110 | 6 | 0101 | 0000 0110 |
| 7 | 0111 | 7 | 0100 | 0000 0111 |
| 8 | 1000 | 8 | 1100 | 0000 1000 |
| 9 | 1001 | 9 | 1101 | 0000 1001 |
| 10 | 1010 | A | 1111 | 0001 0000 |
| 11 | 1011 | B | 1110 | 0001 0001 |
| 12 | 1100 | C | 1010 | 0001 0010 |
| 13 | 1101 | D | 1011 | 0001 0011 |
| 14 | 1110 | E | 1001 | 0001 0100 |
| 15 | 1111 | F | 1000 | 0001 0101 |
Decimal to Binary Converter compared with the alternatives
| Option | Setup | Privacy | Speed |
|---|---|---|---|
| This tool | None | Local | Instant |
| Command line (base64, xxd) | Terminal | Local | Instant |
| Random online converter | None | May log input | Varies |
Who uses it in the UK
- Debugging APIs, URLs and HTML
- Embedded and electronics work
- Computer Science GCSE and A-level
- Inspecting data and encodings
More questions
Is it safe to paste API keys or tokens here?
The conversion runs entirely in your browser, so nothing is sent anywhere. Still, treat secrets carefully and never share decoded tokens in screenshots.
Is encoding the same as encryption?
No. Base64, URL and HTML encoding are reversible by anyone. They make data safe to transport or display, not secret.
Which standard does it follow?
Base64 follows RFC 4648, URL percent-encoding follows RFC 3986 and text is handled as UTF-8, matching modern browsers and servers.
Does it handle large inputs?
Yes, up to what your browser memory allows – typically several megabytes of text without problems.
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