# Representation of Boolean Functions Using Binary Trees

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This Demonstration shows representations of Boolean functions of two, three or four arguments using binary trees.

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Contributed by: Izidor Hafner (September 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The first use of binary trees to represent Boolean functions were Macfarlane's diagrams that he called "logical spectra" [5, p. 44]. The representation is more compact than using truth tables.

References

[1] R. Audi, ed., *The Cambridge Dictionary of Philosophy*, Cambridge: Cambridge University Press, 1995 pp. 780–782.

[2] L. Borkowski, *Elementy logiki formalnej* (*Elements of Formal Logic*, in Polish), 3rd ed., Warsaw: Wyd, 1976.

[3] L. Carroll, *Symbolic Logic and the Game of Logic*, New York: Dover, 1958.

[4] I. M. Copi and C. Cohen, *Introduction to Logic*, 9th ed., New York: Macmillan, 1994 pp. 214–218.

[5] M. Gardner, *Logic Machines, Diagrams and Boolean Algebra*, New York: Dover Publications, 1968.

## Permanent Citation

"Representation of Boolean Functions Using Binary Trees"

http://demonstrations.wolfram.com/RepresentationOfBooleanFunctionsUsingBinaryTrees/

Wolfram Demonstrations Project

Published: September 20 2016