Decimal (base 10) to Binary (base 2) Converter
A number base says how many distinct digits a positional system uses. Use the converter below to turn decimal (base 10) into binary (base 2) and back.
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255 decimal = 11111111 binary
Results shown are estimates for informational purposes only. Nothing on CalcFlow is financial, tax, legal, or medical advice. Always consult a qualified professional before making important decisions.
Decimal (base 10) to Binary (base 2) Conversion Table
| Decimal (base 10) | Binary (base 2) |
|---|---|
| 1 decimal | 1 binary |
| 2 decimal | 10 binary |
| 4 decimal | 100 binary |
| 8 decimal | 1000 binary |
| 10 decimal | 1010 binary |
| 16 decimal | 10000 binary |
| 64 decimal | 1000000 binary |
| 100 decimal | 1100100 binary |
| 255 decimal | 11111111 binary |
| 1,000 decimal | 1111101000 binary |
Binary (base 2) to Decimal (base 10) Conversion Table
| Binary (base 2) | Decimal (base 10) |
|---|---|
| 1 binary | 1 decimal |
| 2 binary | 2 decimal |
| 4 binary | 4 decimal |
| 8 binary | 8 decimal |
| 10 binary | 10 decimal |
| 16 binary | 16 decimal |
| 64 binary | 64 decimal |
| 100 binary | 100 decimal |
| 255 binary | 255 decimal |
| 1,000 binary | 1000 decimal |
Worked example: 255 decimal = 11111111 binary. Decimal 255 is binary 11111111, octal 377 and hexadecimal FF.
Need other units? Open the full Number Base Converter.
Popular Number Bases Conversions
Formula
value = sum of digit x base^position; hex digits 0-9 and A-F; base 36 uses 0-9 and A-ZUnderstanding Number Bases Conversion
A number base says how many distinct digits a positional system uses. Humans count in base 10. Computers store numbers in base 2 (binary) and programmers often write them in base 16 (hexadecimal) because each hex digit stands for exactly four bits. Octal (base 8) groups bits in threes and still appears in file permissions. This tool converts whole non-negative numbers up to 9,007,199,254,740,991 (2^53 - 1), the largest integer that is always exact.
Tips and Best Practices
- 1One hex digit equals four binary digits, so 0xFF is 11111111.
- 2Binary 1010 is decimal 10, hex A.
- 3Add 0x or 0b prefixes only in code; this tool wants plain digits.
Real-World Example
Decimal 255 is binary 11111111, octal 377 and hexadecimal FF.
Common Mistakes to Avoid
- Entering a digit that does not exist in the base, such as 2 in binary.
- Confusing letter O with zero in octal and hex.
- Expecting fractions or negatives; only whole non-negative numbers are supported.
How to Use
- Type a number in the Decimal (base 10) box.
- The Binary (base 2) result appears instantly; you can also edit the Binary (base 2) box to convert backwards.
- Use the swap button to reverse the direction and Copy result to copy the answer.
Frequently Asked Questions
How many binary (base 2) are in 10 decimal?
How many decimal (base 10) are in 10 binary?
What is the formula to convert decimal (base 10) to binary (base 2)?
What is 255 in hex?
Sources: Standard positional numeral systems; ECMAScript Number.MAX_SAFE_INTEGER = 2^53 - 1.