Hex to Negative Decimal Converter
Interpret a hex bit pattern as a signed two's-complement value at a chosen bit width, and see whether it reads as positive or negative.
Full breakdown (input at 8-bit)
How to Read a Hex Value as a Negative Decimal
Plain hex digits don't carry a sign on their own — a bit pattern only becomes negative once you interpret it at a fixed bit width using two's complement, which is how virtually every modern system represents signed integers.
Check the leftmost bit at that width. If it's 0, the value is positive or zero and reads the same as its unsigned decimal value. If it's 1, the value is negative: invert every bit, add 1, and that result is the magnitude — put a minus sign in front of it.
Hex to Negative Decimal Example, Step by Step
F6 (8-bit) = -10
0xF6, interpreted as 8-bit signed = -10
F6 = 1111 0110 Sign bit (bit 7) = 1 -> negative Invert: 0000 1001 +1: 0000 1010 = 0x0A = 10 Result: -10
| Step | Description | Result |
|---|---|---|
| Check the sign bit | bit 7 of F6 is 1 | negative |
| Invert all bits | F6 (11110110) inverted is 09 (00001001) | 09 |
| Add 1 | 09 + 1 = 0A | 0A (10 decimal) |
| Apply the sign | magnitude 10, sign bit was set | -10 |
At 16-bit width instead, F6 would read as plain 246 (positive) — the sign bit only lands on the leftmost bit of whichever width you're interpreting the value at.
Common Mistakes When Reading Hex as Negative Decimal
- Forgetting to pick a bit width before checking the sign bit — the same hex digits mean different things at 8-bit versus 16-bit.
- Reading the value as unsigned by default instead of checking the sign bit first.
- Adding 1 before inverting the bits, instead of after.
- Forgetting the most negative value at a given width (like 0x80 at 8-bit) has no positive counterpart at that same width.
Frequently Asked Questions
How do I know if a hex value represents a negative number?
Check the leftmost bit at your chosen bit width — the sign bit. If it's 1, the value is negative under two's complement; if it's 0, it's positive or zero. For a single hex digit, that means the digit is 8 or higher at that width's top byte.
Why does the same hex value mean different things at different bit widths?
Because the sign bit's position depends on the width. 0xF6 is negative (-10) as an 8-bit value, but positive (246) as a 16-bit value, since the sign bit sits at bit 7 in one case and bit 15 in the other.
How do you calculate the negative decimal value by hand?
If the sign bit is set, invert all the bits, add 1, convert that to decimal, and put a minus sign in front. 0xF6 inverted is 0x09, plus 1 is 0x0A (10 decimal), so 0xF6 represents -10.
What's the most negative value a given bit width can represent?
The one with only the sign bit set — 0x80 for 8-bit (-128), 0x8000 for 16-bit (-32768), and so on. It's always one further from zero than the largest positive value at that width.
Is this the same as the Hex Two's Complement Calculator?
Related but different: this page reads an existing bit pattern as a signed number. The Two's Complement Calculator instead flips a value's sign, producing a new bit pattern.
What if the hex value doesn't fit in the selected bit width?
The calculator will flag it — pick a wider bit width (16, 32, or 64-bit) so the full value fits before interpreting its sign.