Functional completeness | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-01-14

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Functional_completeness


00:00:49 1 Introduction
00:03:58 2 Formal definition
00:05:31 3 Characterization of functional completeness
00:05:43 4 Minimal functionally complete operator sets
00:05:51 5 Examples
00:07:51 6 In other domains
00:10:46 7 Set theory
00:11:01 8 See also
00:11:22 9 References
00:11:51 (A ↑ B);  A ∧ B
00:12:03 In other domains
00:12:49 Set theory
00:13:35 See also



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SUMMARY
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In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }, consisting of binary conjunction and negation. Each of the singleton sets { NAND } and { NOR } is functionally complete.
In a context of propositional logic, functionally complete sets of connectives are also called (expressively) adequate.From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set. In particular, all logic gates can be assembled from either only binary NAND gates, or only binary NOR gates.