Logic operations and binary operations

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  • Thread starter Thread starter Bruno Tolentino
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    Binary Logic Operations
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Discussion Overview

The discussion explores the relationships between binary operations (addition, subtraction, multiplication, division) and logical operations (AND, OR, XOR). Participants examine whether there are theoretical connections between these operations and seek to identify any corresponding logical operations for subtraction and division.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant proposes that addition is connected to XOR, multiplication to AND, and questions what binary operation corresponds to OR.
  • Another participant suggests that subtraction may be viewed as A XOR (Not B), but notes a lack of full correspondence and mentions Boolean algebras.
  • Some participants assert that OR can be seen as addition without carry, while XOR is viewed as subtraction without carry, and AND as multiplication without carry.
  • There is a mention of database operations that mimic logical and arithmetic operations, including division on data tables.
  • Disagreement arises regarding the interpretation of a referenced website, with participants asserting differing views on the connections made between operations.

Areas of Agreement / Disagreement

Participants express differing views on the connections between binary and logical operations, with no consensus reached on the correspondence of subtraction and division to logical operations. The discussion remains unresolved regarding the exact relationships.

Contextual Notes

Some claims depend on specific interpretations of operations, and there are unresolved questions about the completeness of the proposed relationships. The discussion also touches on the applicability of these concepts in Boolean algebras and database operations.

Bruno Tolentino
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If the binary operation of addition is theoretically connected with logic operation XOR, and if the binary operation of multiplication is theoretically connected with logic operation AND, so, the logic operation OR is connected with what binary operation? Exist some relationship?

Another question: the binary operation of subtraction and division are connected with some elementary logic operation or don't exist correspondent?
 
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Subtraction A-B may be seen as A XOR (NotB), I think. But there is no full correspondence that I am aware of. This seems like it may be dealt with in the area of Boolean algebras. Maybe you can use the correspondence to figure out the answer.
 
OR is an add with no carry, XOR is subtraction, AND is multiply with no carry.
 
There are some database operations that mimic some of the logical and arithmetic operations, including, to my surprise, an operation of division on data tables.
 

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