BooleanConvert[expr]
converts the Boolean expression expr to disjunctive normal form.
BooleanConvert[expr,form]
converts the Boolean expression expr to the specified form.
BooleanConvert[expr,form,cond]
finds an expression in the specified form that is equivalent to expr when cond is true.


BooleanConvert

BooleanConvert[expr]
converts the Boolean expression expr to disjunctive normal form.
BooleanConvert[expr,form]
converts the Boolean expression expr to the specified form.
BooleanConvert[expr,form,cond]
finds an expression in the specified form that is equivalent to expr when cond is true.
Details and Options

- BooleanConvert[expr,form] will produce an expression equivalent to expr.
- Available forms are:
-
"DNF","SOP" disjunctive normal form, sum of products "CNF","POS" conjunctive normal form, product of sums "ESOP" exclusive sum of products "ANF" algebraic normal form "NOR" two-level Nor and Not "NAND" two-level Nand and Not "BinaryNOR", "NOR2" two-argument Nor "BinaryNAND", "NAND2" two-argument Nand "AND" two-level And and Not "OR" two-level Or and Not "IMPLIES" Implies and Not "ITE","IF" If and constants "BFF" BooleanFunction form "BDT" Boolean decision tree - The expression expr can contain any Boolean or logical functions, including BooleanFunction, BooleanCountingFunction, etc.
- BooleanConvert[bf,form] converts the internal form of a pure BooleanFunction object.
- BooleanConvert supports a Method option that specifies the detailed method to use.
Examples
open all close allBasic Examples (3)
Scope (2)
Properties & Relations (3)
The output from BooleanConvert is equivalent to its input:
The output from BooleanConvert with condition is conditionally equivalent to its input:
The forms f and g are equivalent when cond is true:
They are not equivalent on their own:
Use BooleanMinimize to get the minimal length form:
Neat Examples (1)
See Also
BooleanMinimize LogicalExpand BooleanFunction BooleanTable
Function Repository: FindBooleanAlternative
Related Guides
Text
Wolfram Research (2008), BooleanConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanConvert.html (updated 2024).
CMS
Wolfram Language. 2008. "BooleanConvert." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/BooleanConvert.html.
APA
Wolfram Language. (2008). BooleanConvert. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanConvert.html
BibTeX
@misc{reference.wolfram_2025_booleanconvert, author="Wolfram Research", title="{BooleanConvert}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanConvert.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_booleanconvert, organization={Wolfram Research}, title={BooleanConvert}, year={2024}, url={https://reference.wolfram.com/language/ref/BooleanConvert.html}, note=[Accessed: 08-August-2025]}