---
title: Format digit array as BaseN string
summary: Renders a numeric digit array into the final BaseN string representation.
status: draft
owner: SAIF DocGen
last_reviewed: 2026-07-30
library: SAIF.Framework.BaseN
reference_type: package
operation_id: OP-BASEN-003
trigger: Encode flow or direct `IConverter.FormatBaseN` invocation.
---

# Format digit array as BaseN string

This operation walks a digit array from its last position to its first and renders each position into the final output string. Most converters use the shared `ConverterBase` implementation as-is; `ExcelConverter` overrides it to enforce Excel-style bijective base-26 rollover, since base-26 column naming has no zero digit.

| Field | Value |
| --- | --- |
| **Operation ID** | OP-BASEN-003 |
| **Trigger** | Encode flow or direct formatter call |
| **Inputs** | Integer digit array |
| **Outputs** | Formatted BaseN string |
| **Primary components** | `ConverterBase.FormatBaseN`, `ExcelConverter.FormatBaseN` |
| **Entry point** | `SAIF.Framework.BaseN\ConverterBase.vb` |

## Steps

1. The numeric digit array arrives through `IConverter.FormatBaseN`.
2. An empty output string is initialized, and the array is iterated from its last index back to its first.
3. `ConverterBase.FormatBaseN` converts each digit with `ConvertNumericToAlpha(values(i))` and prepends the rendered token to the front of the output string, building the string in correct left-to-right reading order.
   - When `HexConverter` renders a digit through this shared formatter, its digit conversion still enforces the upper-bound rule ([BR-001](../business-rules.md#br-001-hexadecimal-digit-must-not-exceed-base-16)).
4. `ExcelConverter.FormatBaseN` parses the current position's value and, for every non-leading position, applies rollover handling before rendering:
   - If the current digit is `0`, it is replaced with `26`.
   - The preceding digit is then decremented by one.
   - If that preceding digit is also `0`, the borrow continues backward through the array until a non-zero digit absorbs the decrement.
   - This borrow chain removes zero digits from the rendered alphabetic form, which is what makes the output correctly bijective ([BR-003](../business-rules.md#br-003-excel-style-base-26-conversion-is-bijective-no-zero-digit)).
5. In the Excel override, a position is only rendered when its adjusted value is greater than `0`, using `ConvertNumericToAlpha(value)` to produce the emitted token.
   - This digit renderer still enforces the upper-bound rule before converting the adjusted value to a character ([BR-002](../business-rules.md#br-002-excel-base-26-digit-must-not-exceed-base-26)).
6. The completed output string is returned to the caller.

## Process flow

The following diagram visualizes this operation's control flow.

```mermaid
flowchart TD
	Start([FormatBaseN called]) --> S1[Iterate digits right to left]
	S1 --> D{ExcelConverter?}
	D -->|No| S2[Render each digit directly]
	D -->|Yes| S3[Normalize zero digits by borrowing]
	S3 --> S4[Render positive adjusted digits]
	S2 --> EndOk([Return formatted string])
	S4 --> EndOk
```

## Failure and edge-case behavior

- `ConverterBase.FormatBaseN` renders every digit it receives without exception; it does not validate array length against the converter's base or suppress zero digits.
- `ExcelConverter.FormatBaseN` mutates the incoming digit array in place while borrowing across zero digits to enforce bijective output ([BR-003](../business-rules.md#br-003-excel-style-base-26-conversion-is-bijective-no-zero-digit)).
- `ExcelConverter.FormatBaseN` skips any position whose adjusted value is `0` after rollover processing, which is how leading zero placeholders are removed from the final output.

## Related documentation
- [Operations and processes](../operations-processes.md)
- [Business rules](../business-rules.md)

## Sources
- `SAIF.Framework.BaseN\ConverterBase.vb`
- `SAIF.Framework.BaseN\HexConverter.vb`
- `SAIF.Framework.BaseN\ExcelConverter.vb`