Source: https://guthlabs.ai/docs/instruments/base-n-number-system-converter/implementation/

instrument implementation / implementation-contract

# Base-N & Number System Converter implementation

A source-bound implementation contract for Base-N & Number System Converter; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-056

**Effect**: Computation or source lookup only

## Input and validation requirements

- Reject source or target bases outside the inclusive range 2-36, and reject digits whose numeric value is at least the base.

- Define behavior for lowercase versus uppercase digits and for signs, whitespace, malformed radix points, and multiple radix points.

- A finite fraction in one base may require a repeating expansion in another base; the implementation needs a repeating notation, precision limit, or explicit exact-fraction output policy.

- Protect against integer overflow or loss of exactness in JavaScript Number arithmetic; BigInt or rational arithmetic may be required for exact conversions.

- Roman numeral parsing must reject noncanonical or invalid subtractive forms and define behavior for zero, negative values, and values greater than 3999.

- Egyptian fractions can have multiple valid decompositions; without a stated algorithm and canonicality rule, outputs cannot be uniquely verified.

- Egyptian-fraction input must reject a zero denominator and define behavior for zero, negative, improper, or non-reduced fractions.

- Repeated division by the radix must terminate for integer conversion, but fractional conversion can fail to terminate without a stopping policy.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "mode": "positional",
    "number": "0",
    "source_base": 10,
    "target_base": 2
  },
  "expected_outputs": {
    "converted": "0",
    "value_in_source_base": 0
  },
  "working": "0 in base 10 has no nonzero place values. The same value in every positional base is 0, so 0_10 = 0_2. This is the zero-value boundary case."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/base-n-number-system-converter/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/base-n-number-system-converter/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/base-n-number-system-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-tranche6/tranche6-results.json`