Logic operations and binary operations

AI Thread Summary
The discussion explores the connections between binary operations and logical operations, specifically how addition relates to XOR and multiplication to AND. It raises the question of what binary operation corresponds to the logical operation OR, suggesting it may be viewed as addition without carry. The conversation also touches on whether subtraction and division have corresponding logical operations, with a proposal that subtraction could be seen as A XOR (Not B). Participants reference Boolean algebra to further analyze these relationships and mention database operations that reflect these logical and arithmetic operations. The dialogue emphasizes the nuances in understanding these connections within mathematical frameworks.
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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