Example Data Table
| Decimal |
Binary |
Hex |
Common Use |
| 10 |
1010 |
A |
Small numeric checks |
| 15 |
1111 |
F |
One nibble |
| 255 |
11111111 |
FF |
One full byte |
| 1024 |
10000000000 |
400 |
Memory values |
Formula Used
Decimal to Binary
Divide the decimal value by 2 repeatedly. Keep each remainder. Read the remainders from bottom to top.
Decimal to Hex
Divide the decimal value by 16 repeatedly. Convert remainders 10 to 15 into A to F.
Binary to Decimal
Multiply each binary digit by 2 raised to its position. Add all weighted values.
Hex to Decimal
Multiply each hex digit by 16 raised to its position. Add the weighted values.
Two's Complement
For a negative fixed-width value, the encoded value equals 2 raised to width minus the absolute value.
How to Use This Calculator
Enter a decimal, binary, or hexadecimal value. Choose the input base. Auto mode detects 0b and 0x prefixes.
Select a fixed bit width when you need padded binary or hex output. Use signed reading for fixed-width two's complement input.
Choose grouping options to make long values easier to read. Press Calculate to show results below the header and above the form.
Use the CSV button for spreadsheet storage. Use the PDF button for a quick printable report.
Number Base Conversion Guide
Why Number Bases Matter
Decimal, binary, and hexadecimal systems describe the same quantity in different forms. Decimal is familiar because it uses ten digits. Binary is essential for machines because each digit represents an on or off state. Hexadecimal is compact. It groups binary bits into readable blocks for memory, code, device registers, and digital design.
A clear converter saves time and prevents manual mistakes. It also helps learners see how place value changes between bases. Each position has a weight. In decimal the weights are powers of ten. In binary they are powers of two. In hexadecimal they are powers of sixteen. The value stays the same, but the written form changes.
Practical Uses
This calculator supports everyday conversions and technical checks. Programmers can inspect flags, masks, addresses, and byte values. Students can verify homework steps. Electronics users can compare bit patterns and hexadecimal register values. Data workers can prepare clean values for spreadsheets or documentation.
Advanced options make the result easier to read. Fixed bit width adds leading zeros when a value needs a defined size. Signed interpretation helps with two's complement numbers. Grouping can split long binary strings into nibbles or bytes. Uppercase hex keeps exported values consistent with many manuals.
Accuracy Tips
Start by choosing the correct input base. Use decimal for ordinary numbers. Use binary for strings containing only zeros and ones. Use hexadecimal for values that may contain A through F. Prefixes like 0b and 0x are accepted for clarity.
Check the bit width before using signed results. A negative value needs enough bits to fit its range. An unsigned value also needs enough space. When the width is too small, the calculator warns you instead of hiding overflow.
Exports are useful when results must be saved. The CSV file works well for spreadsheet logs. The PDF file is useful for reports, notes, or client records. Always review the on-page result before sharing exported files.
Learning the Formula
Conversion is mainly repeated division and place value expansion. Decimal to binary divides by two. Decimal to hex divides by sixteen. Binary or hex back to decimal multiplies each digit by its positional weight. These simple rules power the whole tool.
FAQs
1. What does this calculator convert?
It converts numbers between decimal, binary, and hexadecimal forms. It also supports grouping, prefixes, fixed bit width, and signed two's complement handling.
2. Can I enter 0b or 0x prefixes?
Yes. Auto mode detects 0b as binary and 0x as hexadecimal. You can also choose the base manually.
3. Does the tool support negative decimal values?
Yes. Negative decimal values are shown with a minus sign. If fixed width is selected, the tool can show a two's complement output.
4. What is fixed bit width?
Fixed bit width pads the output with leading zeros. It is useful for byte, word, register, and memory address formatting.
5. What is signed two's complement reading?
It reads binary or hex input as a signed fixed-width value. The highest bit acts as the sign bit.
6. Why does the calculator show an overflow message?
The selected bit width is too small for the value. Choose a larger width or enter a smaller number.
7. What does binary grouping do?
Binary grouping splits long binary values into readable blocks. Groups of four match hex digits. Groups of eight match bytes.
8. What are the export buttons for?
The CSV button downloads a spreadsheet-friendly result. The PDF button downloads a simple report for records, notes, or sharing.