Calculator
Formula Used
The calculator first converts each decimal value into a masked integer.
Mask formula: mask = 2bit width - 1
Masked A: A masked = A & mask
Masked B: B masked = B & mask
| Operation | Formula | Meaning |
|---|---|---|
| AND | A & B | Bit is one only when both bits are one. |
| OR | A | B | Bit is one when either bit is one. |
| XOR | A ^ B | Bit is one when both bits are different. |
| NOT | ~A & mask | Every bit is flipped inside the selected width. |
| NAND | ~(A & B) & mask | The AND result is inverted. |
| NOR | ~(A | B) & mask | The OR result is inverted. |
| XNOR | ~(A ^ B) & mask | The XOR result is inverted. |
| Shift | A << n or A >> n | Bits move left or right by the shift count. |
How to Use This Calculator
- Enter the first decimal value in the Decimal A field.
- Enter the second decimal value in the Decimal B field.
- Select the bitwise operation you want to test.
- Choose the bit width for masking.
- Enter a shift count when using a shift operation.
- Press Calculate to view the result above the form.
- Use CSV or PDF download for saving the calculation.
Example Data Table
| Decimal A | Decimal B | Operation | Width | Result | Binary Result |
|---|---|---|---|---|---|
| 25 | 14 | AND | 8 bit | 8 | 00001000 |
| 25 | 14 | OR | 8 bit | 31 | 00011111 |
| 25 | 14 | XOR | 8 bit | 23 | 00010111 |
| 25 | 0 | Left Shift A by 2 | 8 bit | 100 | 01100100 |
About the Bitwise Base 10 Calculator
Decimal Inputs With Bit Logic
A bitwise base 10 calculator helps you inspect decimal integers at the bit level. It turns ordinary base 10 inputs into binary logic results. This is useful for programming, electronics, networking, flags, permissions, and embedded control work. You can test an operation before writing code. You can also compare binary, decimal, hexadecimal, and octal forms in one place.
How Bitwise Operations Work
Bitwise math works on every bit independently. AND keeps a bit only when both matching bits are one. OR keeps a bit when either matching bit is one. XOR keeps a bit when the two matching bits are different. NOT flips every bit inside the selected width. Shift operations move bits left or right. A left shift usually multiplies an unsigned value by powers of two. A right shift usually divides it by powers of two.
Why Bit Width Matters
The width option is important. It decides how many bits are kept after every operation. An 8 bit mask keeps results from 0 to 255. A 16 bit mask keeps results from 0 to 65535. A 32 bit mask supports larger software style values. The mask also makes NOT, NAND, NOR, and XNOR easier to read, because flipped bits stay inside the chosen range.
Reading the Output
This tool accepts decimal numbers, yet it shows several output bases. The decimal answer is best for quick copying. The binary answer explains how the bits changed. The hexadecimal answer is compact and useful for developers. The octal answer is helpful for some permission and low level cases. Signed decimal output is also shown, so you can understand two's complement meaning inside the selected width.
Practical Workflow
Use the calculator by entering value A and value B. Pick an operation. Choose a bit width that matches your project. Add a shift count when you use shifting. Press calculate to see the result above the form. Review the formula and the masked input values. Then download the result as CSV or PDF for reports, lessons, code notes, or later checks.
Tips for Accurate Results
For best results, choose the same width used by your target system. Do not mix an 8 bit example with a 32 bit program unless you mean to test masking. Always check binary output when debugging flags. A small decimal change can affect many bits.
FAQs
What is a bitwise base 10 calculator?
It is a calculator that accepts decimal numbers and applies bitwise logic. It shows decimal, binary, hexadecimal, and octal results after masking values to the selected bit width.
What does AND mean in bitwise math?
AND compares matching bits from both numbers. A result bit becomes one only when both input bits are one. Otherwise, the result bit becomes zero.
What does OR do?
OR compares each matching bit. A result bit becomes one when at least one input bit is one. It is useful when combining flags.
What is XOR used for?
XOR returns one when matching bits are different. It is often used in toggling, checks, simple encodings, and logic comparisons.
Why does NOT need a bit width?
NOT flips bits. Without a selected width, the result can appear confusing. The mask keeps flipped bits inside a known range.
What is a left shift?
A left shift moves bits to the left. Empty right positions become zero. For unsigned values, it often acts like multiplication by powers of two.
What is a right shift?
A right shift moves bits to the right. Low bits are removed. For unsigned masked values, it often acts like division by powers of two.
Why export results as CSV or PDF?
CSV is useful for spreadsheets and data logs. PDF is useful for reports, lessons, and records that need a simple printable format.