Prime Implicant Pair Adjacency Edge Counter
Count adjacency edges among supplied binary minterm indices differing in exactly one bit.
Description
Binary minterms are adjacent when their assignments differ in exactly one bit.
Binary minterms are adjacent when their assignments differ in exactly one bit. Such edges help identify combinable terms in Boolean minimization.1
The tool returns edgeCount. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Prime Implicant Pair Adjacency Edge Counter
Use this for the following task: Count adjacency edges among supplied binary minterm indices differing in exactly one bit. Prepare the specified logical encoding before running the check or transformation.
How to use Prime Implicant Pair Adjacency Edge Counter 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 variableCount, minterms according to the field table, then run the tool.
- Read edgeCount. 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 |
|---|---|---|---|
| variableCount | Variable count | integer; minimum 0; maximum 52 | Required |
| minterms | Distinct minterm indices | list of integer; minimum entries 0; maximum entries 10000; each entry: minimum 0; maximum 9007199254740991 | Required |
Supply up to 10000 distinct in-range minterm indexes and 0..52 variables. Flip each bit arithmetically, test neighbor membership in a set, and count only neighbors larger than the current index.
edge = unordered pair of supplied indexes differing in one bit The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| edgeCount | Undirected adjacency edge count | integer |
{
"input": {
"variableCount": 2,
"minterms": [
0,
1,
2,
3
]
},
"output": {
"edgeCount": 4
}
}Limitations and assumptions
The tool counts edges rather than finding prime implicants or a minimal cover. Empty input gives zero; duplicate or out-of-width indexes are rejected.
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 Minterm Index Binary Assignment Decoder when you need its operation: Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals. Choose Karnaugh Map Cell Count Grid Size Resolver for the complementary operation: Return the cell count and balanced row and column dimensions of a binary Karnaugh map for up to 52 variables.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Minterm Index Binary Assignment Decoder
Decode a minterm index into fixed-width binary bits and the corresponding conjunction of identifier literals.
- Karnaugh Map Cell Count Grid Size Resolver
Return the cell count and balanced row and column dimensions of a binary Karnaugh map for up to 52 variables.