Single-Digit Error Simulator

How Single-Digit Error Simulator Works?

The Single-Digit Error Simulator tests each possible digit change in a payload. It replaces each digit with every other digit and calculates the check character again. It counts the changes that produce a different result.

1. 1Enter a payload and select the algorithms to test.
2. 2Generate every single-digit substitution (9 per position).
3. 3Recompute the check character for each altered payload.
4. 4Count the substitutions that change the check character as detected.
5. 5Report the detection rate per algorithm.

Single-Digit Error Simulator Formula

The detection rate formula is Rate = detected substitutions ÷ (9 × payload length) × 100%.

Tests = { payload with position i set to d | d ≠ original digit }
Rate = |{ t ∈ Tests : f(t) ≠ f(payload) }| ÷ |Tests| × 100%

• 9 × length is the number of substitutions.

Substitutions tested = 90
Detected = 90
Rate = 100.0%

Single-Digit Error Simulator Conversion Table

The simulator table shows single-digit detection for 6 algorithms on the payload 7992739871.

The last row uses even weights with modulus 10 to show how a poor weight choice misses substitutions.

What is Single-Digit Error Simulator?

A Single-Digit Error Simulator is a tool that measures how well a check digit algorithm detects 1 mistyped digit. Single-digit errors make up about 60–95% of human transcription errors in published studies.

Every standard scheme catches 100% of single substitutions. Weights that share a factor with the modulus (such as 2 with modulus 10) do not.

What are the uses of Single-Digit Error Simulator?

There are 3 main uses of the Single-Digit Error Simulator, including scheme design, algorithm teaching, and QA evidence.

• Scheme design: Engineers prove that a new weight pattern catches all substitutions.
• Algorithm teaching: Teachers show why weights must be coprime with the modulus.
• QA evidence: Testers document detection coverage for audits.