Calculator
Example Data Table
These examples show how fixed-width complements change with width.
| Bit Width | Original Mask | Original Binary | Inverse Mask | Inverse Binary |
|---|---|---|---|---|
| 8 | 29 | 0001 1101 |
226 | 1110 0010 |
| 8 | 170 | 1010 1010 |
85 | 0101 0101 |
| 10 | 341 | 0101 0101 01 |
682 | 1010 1010 10 |
| 12 | 240 | 0000 1111 0000 |
3855 | 1111 0000 1111 |
| 16 | 4095 | 0000 1111 1111 1111 |
61440 | 1111 0000 0000 0000 |
Formula Used
Inverse Mask = (~Mask) AND (2n - 1)
Equivalent Form: Inverse Mask = (2n - 1) - Mask
n is the selected bit width.
A fixed-width inverse mask flips every bit inside the chosen width.
Ones become zeros.
Zeros become ones.
The extra AND step removes unwanted bits beyond the selected width.
Example: for an 8-bit mask of 29, the full mask is 255. So the inverse is 255 - 29 = 226.
How to Use This Calculator
- Enter the mask value in decimal, binary, or hexadecimal form.
- Select the matching input base.
- Choose the bit width that defines the allowed mask range.
- Click Calculate Inverse Mask.
- Review decimal, binary, and hexadecimal outputs.
- Use the chart and bit table to verify every flipped position.
- Download CSV or PDF files for records or reports.
FAQs
1. What is an inverse mask?
An inverse mask is the bitwise complement of a mask within a fixed width. Every 1 becomes 0, and every 0 becomes 1, but only across the selected number of bits.
2. Why does bit width matter?
Bit width defines the valid mask boundary. The same decimal value can produce different inverse masks when the width changes, because the full mask changes too.
3. Can I enter binary or hexadecimal values?
Yes. Choose the proper input base first, then enter the value. The calculator accepts standard digits for decimal, 0s and 1s for binary, and hexadecimal characters for hex.
4. How is the inverse mask calculated?
The calculator uses (~Mask) AND (2^n - 1). This flips all bits, then trims the result to the selected width so only valid positions remain.
5. What happens if my value exceeds the chosen width?
The calculator shows a validation error. A mask must fit inside the selected width, otherwise the complement would no longer represent a valid fixed-width inverse.
6. Does this tool support exports?
Yes. You can export the result table, bit table, and example table as CSV or PDF files. That helps with documentation, coursework, and verification workflows.
7. What does the Plotly graph show?
The graph compares original bit states against inverse bit states across each position. It makes the complement pattern easy to inspect visually, especially for wider masks.
8. Is this calculator useful for teaching bitwise logic?
Yes. It helps learners see how complements work, how fixed-width masking behaves, and why binary representation matters in bitwise operations and digital logic.