Hex Negative Number Calculator
Check whether a hex value represents a negative number at a given bit width, with a full reference of how negative ranges scale across widths.
Full breakdown (input at 8-bit)
How Negative Numbers Work in Hex
Hex digits are just symbols for magnitude — negativity is a separate layer, applied by interpreting the bit pattern with two's complement at a chosen bit width. Check the sign bit (the leftmost bit at that width): set means negative, clear means positive or zero.
Negative Number Ranges by Bit Width
The negative range always extends one value further from zero than the positive range at the same width.
| Bit width | Most negative value | Hex pattern |
|---|---|---|
| 8-bit | -128 | 0x80 |
| 16-bit | -32,768 | 0x8000 |
| 32-bit | -2,147,483,648 | 0x80000000 |
| 64-bit | -9,223,372,036,854,775,808 | 0x8000000000000000 |
Common Mistakes With Negative Hex Values
- Assuming a hex value is negative or positive without first checking it at a specific bit width.
- Expecting symmetric positive and negative ranges — they're not, the negative side is one wider.
- Forgetting the most negative value at a width has no positive counterpart at that same width.
Frequently Asked Questions
How can a hex value be negative — aren't hex digits just 0-9 and A-F?
The digits themselves don't carry a sign. A value only becomes negative once you interpret its bits at a fixed width using two's complement, which is how signed negative numbers are represented in memory.
What's the quickest way to check if a hex value is negative?
Look at the leftmost bit at your chosen width — the sign bit. If it's 1, the value is negative; if it's 0, it's positive or zero.
Do negative and positive ranges cover the same span?
No — the negative range is always one wider than the positive range at a given width, since zero only counts once. 8-bit covers -128 to 127, not -127 to 127.
How do I convert a negative number I already have into hex?
Use the Negative Decimal to Hex converter, which takes a signed decimal number and bit width and produces the corresponding two's-complement hex pattern.
Does the same hex value stay negative at every bit width?
No — a value like 0xF6 is negative at 8-bit but positive at 16-bit or wider, since the sign bit sits in a different position at each width.
What's the most negative number possible at each common bit width?
-128 at 8-bit, -32,768 at 16-bit, about -2.1 billion at 32-bit, and an enormous negative number at 64-bit — see the full table below.