Description
Determine exact maximum unsigned word value and required decimal display digits for a supplied bit width.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
Determine exact maximum unsigned word value and required decimal display digits for a supplied bit width.
When to use this tool
Use Number: Unsigned Word Maximum Decimal Digits when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter bits. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
For integer bits from one through 128 compute maximumValue=2^bits-1 using exact integers, return it as decimal text, and decimalDigits as its string length inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| bits | Supplied unsigned word width in bits. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.maximumValue | Exact unsigned word maximum as decimal text. | Calculated result member: string. |
| result.decimalDigits | Decimal Digits | Calculated result member: number. |
{
"input": {
"bits": 8
},
"output": {
"result": {
"maximumValue": "255",
"decimalDigits": 3
}
}
}Limitations and assumptions
- This is an unsigned word maximum, not a signed range or a floating-point precision budget. Exact value text avoids loss of large integers, and bits is a supplied storage model rather than detected machine width.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Radix Power Ceiling Digit Budget
For radix in 2..36 and positive decimal-integer exclusiveLimit repeatedly multiply an exact power from one until power>=limit.
- Number: Integer Digit Place Value
Extract an exact base-ten digit and unsigned place-value contribution from a signed integer, counting places from zero at units.