Description
For positive integer integer and radix in 2..36 return quotient=floor((integer-1)/radix) and digit=((integer-1) modulo radix)+1.
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 positive integer integer and radix in 2..36 return quotient=floor((integer-1)/radix) and digit=((integer-1) modulo radix)+1.
When to use this tool
Use Bijective Radix One Digit Borrow 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 integer, radix. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read quotient, digit. Use the output convention below.
For positive integer integer and radix in 2..36 return quotient=floor((integer-1)/radix) and digit=((integer-1) modulo radix)+1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| integer | Safe integer number or exact signed decimal-integer text as declared below. | Required. Safe integer; minimum 1. |
| radix | Positional base within the explicit stated bound. | Required. Safe integer; minimum 2; maximum 36. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| quotient | Integer quotient under the stated division rule. | Required. Safe integer. |
| digit | Numeric digit under the stated radix convention. | Required. Safe integer. |
{
"input": {
"integer": 26,
"radix": 26
},
"output": {
"quotient": 0,
"digit": 26
}
}Limitations and assumptions
- Bijective digits range from one through radix instead of zero through radix-1. This is one least-significant-digit step, without a zero representation, symbol alphabet, or complete formatted number.
- 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
- Radix Integer Single Digit Borrow
Return the nonnegative remainder modulo radix as digit and outgoingBorrow one only when the raw subtraction is negative.
- Negative Radix One Division Step
For a signed integer and radix in -36..-2 return digit as the Euclidean remainder modulo abs(radix) and quotient=(integer-digit)/radix.