Description
For radix in 2..36 and positive decimal-integer exclusiveLimit repeatedly multiply an exact power from one until power>=limit.
A positional representation depends on its radix, digit range, sign convention, and treatment of leading zeros. Ordinary bases use digits from zero through radix minus one, while negative and bijective bases have different conversion rules. A single carry, borrow, or denominator step is distinct from formatting a complete number.
For radix in 2..36 and positive decimal-integer exclusiveLimit repeatedly multiply an exact power from one until power>=limit.
When to use this tool
Use Radix Power Ceiling Digit Budget when you need this digit, carry, borrow, sign, width, or denominator component for an explicit radix convention.
How to use the tool and how it works
- Enter exclusiveLimit, radix. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read digits. Use the output convention below.
For radix in 2..36 and positive decimal-integer exclusiveLimit repeatedly multiply an exact power from one until power>=limit. Return digits as the number of multiplications.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| exclusiveLimit | Positive exact decimal integer; values below it are to fit in the digit budget. | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| radix | Positional base within the explicit stated bound. | Required. Safe integer; minimum 2; maximum 36. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| digits | Minimal positional budget; zero when exclusiveLimit is one. | Required. Safe integer. |
{
"input": {
"exclusiveLimit": "256",
"radix": 2
},
"output": {
"digits": 8
}
}Limitations and assumptions
- This is the smallest fixed digit-position budget whose radix^digits covers values below the exclusive limit. Limit one returns zero positions, unlike ordinary printed notation for the number zero, which usually uses one digit.
- 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
Choose the full conversion or formatting workflow for the intended representation. Keep radix, digit alphabet, leading-zero width, signed-zero handling, and terminating/repeating-fraction assumptions explicit.
References
Similar or alternative tools
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