HexCalculator
Two's complement calculator
Enter a number — decimal, hexadecimal or binary — choose the bit width, and see its two's complement representation, how it reads as a signed and as an unsigned value, and the invert-and-add-one steps for negatives.
Step by step
Type a number to see how its two’s complement is built.
What two's complement is
Two's complement is how virtually every CPU stores signed integers. The highest bit acts as a sign: when it's set, the value is negative. To negate a number you invert every bit and add one. The trick is that addition and subtraction then work identically for positive and negative values — the hardware doesn't need special cases.
-42 in 8 bits: 42 = 00101010 → invert → 11010101 → +1 → 11010110
The same bit pattern means different things depending on interpretation:
11010110 is −42 as a signed byte but 214 as an unsigned one. That's
exactly why this calculator shows both readings — and why the HexCalculator app has
a Signed/Unsigned switch.
Ranges per bit width
| Bits | Signed range | Unsigned range |
|---|---|---|
| 8 | −128 … 127 | 0 … 255 |
| 16 | −32 768 … 32 767 | 0 … 65 535 |
| 32 | −2 147 483 648 … 2 147 483 647 | 0 … 4 294 967 295 |
| 64 | −2⁶³ … 2⁶³−1 | 0 … 2⁶⁴−1 |
Related tools and guides
- Two's complement explained — the full story, with overflow and sign extension.
- Hex calculator — signed and unsigned 64-bit arithmetic.
- Binary ↔ decimal converter — the unsigned base case.