Description
For radix in 2..256, left and right digits within zero through radix-1, and incoming zero or one return digit=(left+right+incoming) modulo radix and carry=floor(sum/radix).
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..256, left and right digits within zero through radix-1, and incoming zero or one return digit=(left+right+incoming) modulo radix and carry=floor(sum/radix).
When to use this tool
Use Positional Digit Carry Single Column 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 left, right, incoming, radix. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read digit, carry. Use the output convention below.
For radix in 2..256, left and right digits within zero through radix-1, and incoming zero or one return digit=(left+right+incoming) modulo radix and carry=floor(sum/radix).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Safe integer; minimum 0. |
| right | Right | Required. Safe integer; minimum 0. |
| incoming | Incoming | Required. Safe integer; minimum 0; maximum 1. |
| radix | Positional base within the explicit stated bound. | Required. Safe integer; minimum 2; maximum 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| digit | Numeric digit under the stated radix convention. | Required. Safe integer. |
| carry | Carry | Required. Safe integer. |
{
"input": {
"left": 8,
"right": 7,
"incoming": 1,
"radix": 10
},
"output": {
"digit": 6,
"carry": 1
}
}Limitations and assumptions
- Only one nonnegative positional addition column is evaluated. Input/output digits are numeric values, not symbols, and no full integer parsing, string formatting, or signed arithmetic is performed.
- 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
- Balanced Ternary Single Digit Carry
For a safe integer value compute digit=((value+1) modulo three)-1 and carry=(value-digit)/3.
- Balanced Ternary Single Digit Value
Map one balanced-ternary symbol T, 0, or 1 to its numeric digit value.