BooleanMinterms
BooleanMinterms[k,n]
represents the k
minterm in n variables.
BooleanMinterms[{k1,k2,…},n]
represents the disjunction of the minterms ki.
BooleanMinterms[{{u1,…,un},{v1,…},…}]
represents the disjunction of minterms given by the exponent vectors ui, vi, ….
BooleanMinterms[spec,{a1,a2,…}]
gives the Boolean expression in variables ai corresponding to the minterms function specified by spec.
BooleanMinterms[spec,{a,a2,…},form]
gives the Boolean expression in the form specified by form.
Details
- BooleanMinterms[{{u1,u2,…}},{a1,a2,…}] gives b1∧b2∧… where bi==ai if ui is True and bi=¬ai if ui is False.
- The ui etc. can be either True and False or 1 and 0.
- BooleanMinterms[k,n] is equivalent to BooleanMinterms[{IntegerDigits[k,n,2]}].
- BooleanMinterms[spec] gives a Boolean function object that works like Function.
- BooleanMinterms[spec][a1,a2,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanMinterms[spec,{a1,a2,…}].
- BooleanConvert converts BooleanMinterms[spec][vars] to an explicit Boolean expression.
- In BooleanMinterms[spec,{a1,a2,…},form], the possible forms are as given for BooleanConvert.
- BooleanMinterms[spec,{a1,a2,…}] by default gives an expression in DNF.
Examples
open allclose allBasic Examples (4)
Equivalent ways of specifying the same minterm:
Specify a disjunction of minterms:
An equivalent way to specify a disjunction of minterms:
Return a BooleanFunction object representing the disjunction of minterms:
Properties & Relations (4)
The indices correspond to positions of True in the default ordering for BooleanTable:
BooleanMinterms can represent any BooleanFunction:
The mapping from minterms to index:
The mapping from index to minterms:
Use Subsets to enumerate all possible Boolean functions using BooleanMinterms:
BooleanMaxterms is related to BooleanMinterms:
Text
Wolfram Research (2008), BooleanMinterms, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMinterms.html.
CMS
Wolfram Language. 2008. "BooleanMinterms." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMinterms.html.
APA
Wolfram Language. (2008). BooleanMinterms. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMinterms.html