Source: https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/

instrument / verified-clean

# Bit Depth Dynamic Range Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/bit-depth-dynamic-range-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Audio, Music, Photography & Color

**Tranche**: tranche-4

**Evidence ID**: t4-013

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formula is standard and appropriate for the stated theoretical PCM bit-depth calculation. The existing honest label correctly warns that real converters have lower effective dynamic range.

### Formula and scope findings

No additional record

### Unit assumptions

- bit_depth is a positive integer number of PCM bits per sample, not bytes or storage size

- The formula DR(dB) ≈ 6.02 × bits + 1.76 is the ideal quantization SNR for a full-scale sine wave with uniformly distributed quantization error

- dynamic_range_db is expressed in decibels relative to the quantization-noise floor; this is not a guarantee of real converter performance

- The 1.76 dB constant assumes the standard ideal sine-wave quantization model

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

An extreme positive bit-depth input overflows JavaScript arithmetic to Infinity, and the zero boundary produces a numerical result even though zero-bit PCM should be rejected or flagged as physically invalid.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "bit_depth": 1
  },
  "expected_outputs": {
    "dynamic_range_db": 7.78
  },
  "working": "DR ≈ 6.02 × bits + 1.76\n= 6.02 × 1 + 1.76\n= 6.02 + 1.76\n= 7.78 dB"
}
````

## Related workflows

[Audio Engineer's Racknoise floor](<https://guthlabs.ai/docs/instrument-workflows/audio-rack/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`