Calculator
Example Data Table
| Input | Width | Mode | Expected Result |
|---|---|---|---|
| FF | 8 bits | Hex to signed | -1 |
| 80 | 8 bits | Hex to signed | -128 |
| FFF6 | 16 bits | Hex to signed | -10 |
| -42 | 16 bits | Decimal to hex | FFD6 |
| 7FFFFFFF | 32 bits | Hex to signed | 2147483647 |
Formula Used
Let n be the selected bit width. The modulus is 2n. The sign limit is 2n-1.
If the sign bit is 0, signed value = unsigned value.
If the sign bit is 1, signed value = unsigned value - 2n.
For a negative decimal input, stored unsigned value = 2n - absolute value.
The valid signed range is -2n-1 to 2n-1 - 1.
How to Use This Calculator
- Select the conversion mode.
- Enter a bit width from 4 to 128.
- Enter a hexadecimal value or signed decimal value.
- Choose byte order if your hex input comes from memory bytes.
- Choose binary grouping for easier reading.
- Submit the form and review the result panel.
- Download the result as CSV or PDF if needed.
Understanding Signed Hexadecimal Values
Two's complement is a compact way to store negative and positive integers in the same fixed width field. A hexadecimal value is first expanded into binary. The selected bit width then decides which bit is the sign bit. When that leading bit is zero, the value is already a non-negative unsigned number. When that leading bit is one, the stored pattern represents a negative number. The calculator subtracts the full modulus from the unsigned value to reveal the signed result.
Why Bit Width Matters
The same hexadecimal pattern can mean different numbers under different widths. For example, FF is negative one in eight bits, but it is positive two hundred fifty five in sixteen bits. Width controls padding, overflow checks, the valid signed range, and the final hexadecimal length. That is why the form asks for bits before it evaluates any input.
Practical Uses
Programmers use this conversion when reading memory dumps, device registers, embedded logs, packet fields, and assembly output. Hardware students use it to check arithmetic circuits and instruction formats. Data analysts may use it when a sensor exports raw hexadecimal values instead of decimal readings. This page also helps when a spreadsheet or database stores signed data as unsigned hexadecimal text.
Reading the Result
The result panel shows the normalized hexadecimal pattern, grouped binary bits, unsigned decimal value, signed decimal value, sign bit, range, inverted bits, and add-one step. These details make the process easier to audit. They also help catch mistakes caused by missing leading zeroes, wrong width choices, or copied values that contain prefixes and spaces.
Good Checking Habits
Always match the bit width used by the source system. Keep leading zeroes when they are meaningful. Review the range warning before trusting a decimal input. Export the CSV when you need a compact record. Export the PDF when you need a readable report for notes, support tickets, or class work.
For best results, enter values exactly as the source displays them. Prefixes such as 0x are accepted. Separators are ignored. The calculator still reports a normalized value, so you can compare the original pattern with the fixed width form used in the final calculation and audit it later easily.
FAQs
What is two's complement?
Two's complement is a fixed width binary method for representing signed integers. It uses the highest bit as the sign bit and keeps addition logic simple.
Why does FF equal -1 in 8 bits?
In 8 bits, FF is 255 unsigned. The sign bit is 1, so subtract 256. The signed result is -1.
Can the same hex value have different meanings?
Yes. Width changes the sign bit and range. FF is -1 in 8 bits, but 255 in 16 bits.
What does trim to selected width mean?
It keeps only the lowest selected number of bits. This helps when copied values contain extra leading bits, but it can hide overflow.
What is little-endian byte order?
Little-endian order stores the least significant byte first. The calculator reverses byte pairs before applying the selected bit width.
What width should I choose?
Use the width from your source system. Common choices are 8, 16, 32, and 64 bits.
Can I convert negative decimal numbers to hex?
Yes. Select decimal to hex mode. The calculator checks the signed range and builds the stored two's complement pattern.
Why is the valid range important?
Each width has a limited signed range. Values outside that range cannot be stored correctly without changing width or losing data.