Binary conversion settings
Recent conversion history
Completed conversions will appear here during this session.
Formula used
How to use this calculator
- Select the conversion mode that matches your source value.
- Enter a number, fraction, text string, or batch list.
- Choose bit width, signed format, precision, encoding, and grouping.
- Select Convert now to view the result and working steps.
- Copy the output or export the result as CSV or PDF.
Example conversions
| Input | Input type | Binary result |
|---|---|---|
| 10 | Decimal | 1010 |
| 25 | Decimal | 11001 |
| 7.5 | Decimal fraction | 111.1 |
| 2F | Hexadecimal | 0010 1111 |
| 17 | Octal | 001 111 |
| A | ASCII text | 0100 0001 |
Understanding binary conversion
Binary uses only zero and one. Each position represents a power of two. Computers use these states for reliable digital storage and processing.
Decimal integers convert through repeated division by two. Every remainder becomes one binary digit. Reading remainders upward produces the final binary number.
Decimal fractions use repeated multiplication instead. Each integer part becomes the next fractional bit. Some decimal fractions repeat forever in binary form.
Octal and hexadecimal convert efficiently because their digits align with bits. One octal digit maps to three binary digits. One hexadecimal digit maps to four binary digits.
Negative integers need a chosen signed representation. Two's complement is common in modern computer systems. Fixed widths determine valid ranges and overflow boundaries.
Text conversion depends on character encoding. ASCII uses simple seven-bit character values. UTF encodings may use several bytes per character.
Floating-point values follow the IEEE 754 structure. Their fields contain sign, exponent, and mantissa information. Precision changes available range and stored accuracy.
Grouping improves readability without changing the number. Prefixes identify binary values in many programming languages. Careful settings keep every binary result clear and dependable.
Frequently asked questions
What is a binary number?
A binary number uses only the digits zero and one. Each position has a power-of-two place value.
How do I convert decimal integers to binary?
Divide the number by two repeatedly. Record remainders and read them from bottom to top.
Why do some decimal fractions repeat in binary?
A fraction terminates only when its reduced denominator contains powers of two. Other denominators create repeating bit patterns.
What does the 0b prefix mean?
The prefix identifies a value as binary. It is common in source code and technical documentation.
What is two's complement?
Two's complement stores signed integers within a fixed width. Negative values are formed by inversion and addition.
Can this calculator convert very large integers?
Yes. Integer base conversion uses string arithmetic, avoiding ordinary floating-point precision limits.
How are hexadecimal digits converted?
Each hexadecimal digit maps directly to four binary digits. This makes hexadecimal compact and convenient.
How is text converted into binary?
The selected encoding converts characters into bytes. Every byte is then displayed as eight binary digits.
What is IEEE 754 binary?
IEEE 754 defines floating-point storage using sign, exponent, and mantissa fields. Different precisions use different field sizes.
What causes an overflow warning?
Overflow occurs when a value cannot fit inside the selected bit width and signed range.
Can I export multiple results?
Yes. Batch results and detailed tables can be downloaded as CSV, while printing creates a PDF.