Minterm Index Binary Assignment Decoder
Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals.
Description
A minterm is a conjunction true on exactly one binary assignment.
A minterm is a conjunction true on exactly one binary assignment. In binary counting order, the first variable is the most significant bit.1
The tool returns bits, minterm. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Minterm Index Binary Assignment Decoder
Use this for the following task: Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals. Prepare the specified logical encoding before running the check or transformation.
How to use Minterm Index Binary Assignment Decoder and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter variables, index according to the field table, then run the tool.
- Read bits, minterm. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| variables | Distinct variables in most-significant-bit order | list of string; minimum entries 0; maximum entries 52; each entry: maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| index | Minterm index | integer; minimum 0; maximum 9007199254740991 | Required |
Provide distinct ordered variable identifiers and an index below 2^variableCount. Decode the index into fixed-width bits and join the corresponding literals with &&.
bit 1 → positive literal; bit 0 → negated literal The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| bits | Binary assignment | string (binary) |
| minterm | Minterm formula | string (propositional-formula) |
{
"input": {
"variables": [
"p",
"q",
"r"
],
"index": 5
},
"output": {
"bits": "101",
"minterm": "p && !q && r"
}
}Limitations and assumptions
At most 52 variables are accepted. Zero variables permit only index zero and produce bits "" with minterm "true". No complete formula is minimized.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Maxterm Index Complement Convention Checker when you need its operation: Construct a maxterm from a binary row index and check a proposed most-significant-bit negation mask. Choose Full DNF Minterm List Builder from Truth Table for the complementary operation: Build canonical DNF minterms and their indices from true rows in binary counting order.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Maxterm Index Complement Convention Checker
Construct a maxterm from a binary row index and check a proposed most-significant-bit negation mask.
- Full DNF Minterm List Builder from Truth Table
Build canonical DNF minterms and their indices from true rows in binary counting order.