Calculator
Bit Visualization Graph
This chart compares the bit states of Input A, Input B, and the calculated result from bit 7 down to bit 0.
Example Data Table
| Operation | Input A | Input B | Shift | Bit Position | Binary Result | Decimal Result |
|---|---|---|---|---|---|---|
| XOR | 170 | 204 | 1 | 2 | 01100110 | 102 |
| Left Shift A | 25 | - | 2 | - | 01100100 | 100 |
| Set Bit in A | 32 | - | - | 0 | 00100001 | 33 |
| Addition Modulo 256 | 250 | 20 | - | - | 00001110 | 14 |
Formula Used
- AND: Result = A ∧ B
- OR: Result = A ∨ B
- XOR: Result = A ⊕ B
- NOT: Result = ¬A = 255 − A
- Left Shift: Result = (A << n) mod 256
- Right Shift: Result = floor(A / 2n)
- Rotate Left: Result = ((A << n) | (A >> (8 − n))) mod 256
- Rotate Right: Result = ((A >> n) | (A << (8 − n))) mod 256
- Set Bit: Result = A ∨ (1 << p)
- Clear Bit: Result = A ∧ ¬(1 << p)
- Toggle Bit: Result = A ⊕ (1 << p)
- Test Bit: Result = (A >> p) ∧ 1
- Addition Modulo 256: Result = (A + B) mod 256
- Subtraction Modulo 256: Result = (A − B) mod 256
In discrete maths and computer arithmetic, every 8-bit result is reduced to the range 0 through 255. Signed output is then interpreted using two’s complement.
How to Use This Calculator
- Enter Input A using decimal, binary, or hexadecimal format.
- Enter Input B if your chosen operation needs a second value.
- Select the required operation from the list.
- Provide a shift amount for shift or rotate tasks.
- Provide a bit position for set, clear, toggle, or test tasks.
- Press the calculate button to display the result above the form.
- Review the decimal, signed, hexadecimal, binary, and flag outputs.
- Use the CSV and PDF buttons to export the result table.
FAQs
1. What is an 8-bit number?
An 8-bit number uses eight binary digits, so it can store 256 distinct patterns. Its unsigned range is 0 to 255, while signed two’s complement range is -128 to 127.
2. Why do bitwise operations matter in maths?
They connect Boolean algebra, modular arithmetic, and binary representation. They are useful for masks, state encoding, parity checks, compact storage, and fast arithmetic transformations.
3. What is the difference between shift and rotate?
A shift moves bits and discards some positions, often inserting zeros. A rotate moves bits circularly, wrapping the discarded part back into the opposite side.
4. How is signed decimal found from an 8-bit result?
If the most significant bit is 0, the value stays positive. If it is 1, subtract 256 from the unsigned value to get the signed two’s complement result.
5. What does XOR show?
XOR returns 1 only where the two compared bits differ. It is useful for detecting changes, toggling values, parity logic, and simple mask comparisons.
6. Why does addition wrap around at 256?
An 8-bit system can store only eight bits. Any sum above 255 loses higher bits, leaving the remainder modulo 256 as the stored result.
7. How do set, clear, and toggle bit operations work?
Set bit uses OR with a mask. Clear bit uses AND with an inverted mask. Toggle bit uses XOR with a mask targeting one chosen position.
8. What is parity in bit manipulation?
Parity tells whether the count of 1 bits is even or odd. It is used in error checking, communication protocols, and binary pattern analysis.