Description
Generate complete aligned truth columns with an exact deliberate mismatch count and delegated equivalence keys under a declared valuation order.
A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.
Generate complete aligned truth columns with an exact deliberate mismatch count and delegated equivalence keys under a declared valuation order.
When to use this tool
Use this generator to create reproducible boolean equivalence quiz cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply variableCount, mismatchCount, count in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read valuationOrder, valuations, questions. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.
Enumerate all Boolean valuations in ascending false-first binary order with the first variable most significant. Draw a left truth column, flip exactly mismatchCount distinct rows for the right, and delegate equivalence checking.1
Delegated operations used for this result: equivalence biconditional match checker. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| variableCount | Variable Count | Required. Safe integer; minimum 0; maximum 8. |
| mismatchCount | Mismatch Count | Required. Safe integer; minimum 0; maximum 256. |
| count | Count | Required. Safe integer; minimum 1; maximum 64. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| valuationOrder | Valuation Order | Required. Text; exactly "ascending-binary-false-first-msb". |
| valuations | Valuations | Required. Array of Array of Boolean.; minimum items 0; maximum items 8.; minimum items 1; maximum items 256. |
| questions | Questions | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 64. |
| questions[].left | Left | Required. Array of Boolean.; minimum items 1; maximum items 256. |
| questions[].right | Right | Required. Array of Boolean.; minimum items 1; maximum items 256. |
| questions[].equivalent | Equivalent | Required. Boolean. |
| questions[].mismatchRows | Mismatch Rows | Required. Array of Safe integer.; minimum items 0; maximum items 256. |
| randomness | Replay source and normalized 32-bit seed, or null seed for an advancing context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional safe-integer replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"variableCount": 2,
"mismatchCount": 2,
"count": 1,
"seed": 42
},
"output": {
"valuationOrder": "ascending-binary-false-first-msb",
"valuations": [
[
false,
false
],
[
false,
true
],
[
true,
false
],
[
true,
true
]
],
"questions": [
{
"left": [
true,
false,
true,
true
],
"right": [
false,
true,
true,
true
],
"equivalent": false,
"mismatchRows": [
0,
1
]
}
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- These are output columns, not parsed formula expressions. Zero mismatches gives equivalence; any positive count breaks it. The complete answer table is included and should be separated from student prompts.
- A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
Similar or alternative tools
- Random Binomial Expansion Coefficient Quiz Generator
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Generate independent half/full adder cells or an explicit least-significant-first ripple-carry trace with delegated bit answers.