Source: https://guthlabs.ai/docs/instruments/number-base-converter/mechanism/

instrument mechanism / verified-clean

# Number Base Converter mechanism

The inspectable method record for Number Base Converter, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The stated formulas are adequate for nonnegative integer conversion, but the instrument also claims fractional conversion. The exact ambiguity requiring review is whether i may be negative in the positional formula and what algorithm, precision, and output notation are required for fractional and repeating results. The honest_label field is empty; the label should disclose supported signs, fractional precision, repeating-fraction behavior, and digit-case conventions.

- The positional-value formula is not explicit about fractional digits; fractions require negative powers, such as d_i·b^i for i<0, and a defined radix-point convention.

- The repeated-division algorithm converts nonnegative integers only; fractional inputs require repeated multiplication by the target base, with a termination or rounding policy.

- Digit-symbol mapping for bases above 10 is unspecified, including whether letters are uppercase, lowercase, or case-insensitive.

- Input validation rules are unspecified for invalid digits, signs, multiple radix points, empty strings, and digits greater than or equal to the source base.

- The output precision and representation policy for repeating or non-terminating fractions is unspecified.

## Units and conventions

- Inputs are dimensionless numeric strings; bases are integer radices, not physical units.

- Source and target bases are integers in the inclusive range 2 through 36.

- Integer digit positions use powers b^i with i=0 at the radix point's immediate left; fractional positions use negative powers.

- The conventional digit mapping 0-9 followed by A-Z is assumed, with A=10 through Z=35; case handling must be specified.

- The examples assume exact arithmetic and no rounding unless a fraction has a non-terminating representation.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "number_string": "101101.101",
    "source_base": 2,
    "target_base": 10
  },
  "expected_outputs": {
    "converted_representation": "45.625",
    "digit_breakdown_table": [
      {
        "digit": "1",
        "power": 5,
        "contribution": "1×2^5=32"
      },
      {
        "digit": "0",
        "power": 4,
        "contribution": "0×2^4=0"
      },
      {
        "digit": "1",
        "power": 3,
        "contribution": "1×2^3=8"
      },
      {
        "digit": "1",
        "power": 2,
        "contribution": "1×2^2=4"
      },
      {
        "digit": "0",
        "power": 1,
        "contribution": "0×2^1=0"
      },
      {
        "digit": "1",
        "power": 0,
        "contribution": "1×2^0=1"
      },
      {
        "digit": "1",
        "power": -1,
        "contribution": "1×2^-1=0.5"
      },
      {
        "digit": "0",
        "power": -2,
        "contribution": "0×2^-2=0"
      },
      {
        "digit": "1",
        "power": -3,
        "contribution": "1×2^-3=0.125"
      }
    ]
  },
  "working": "Integer part: 1×2^5 + 0×2^4 + 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 32 + 0 + 8 + 4 + 0 + 1 = 45. Fractional part: 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0 + 0.125 = 0.625. Total = 45 + 0.625 = 45.625."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The target-base-zero vector reaches an undefined division-by-zero operation and must be rejected rather than converted. The negative-number vector also exposes an unspecified signed-representation convention unless the converter explicitly chooses mathematical signed notation or a fixed-width complement format.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/number-base-converter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/number-base-converter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/number-base-converter/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche2/batch10-output.jsonl`

- `BOUNDARY_HAZARD_CATALOG.json`