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In Boolean algebra, the sum refers to the XOR operation. This makes sense to me because in GF(2) the sum is supposed to implement a sum modulo 2, which has the same truth table of the XOR logical operation.

However, in the context of sum of products, the sum refers to the logical OR operation, which is used to combine the logical ANDs representing the terms in a logical expression. Why is the sum used to represent different operations in different contexts, and how are these different meanings related to each other?

Giovanni Zaccaria
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    In boolean algebra, when you use the term "summing" (x+y), it is always ORing by default, never XORing. – Jean Marie Mar 06 '23 at 09:29
  • So when we're talking about the Galois Field we use addition as a XOR operation, but in the context of boolean algebra the sum is always to be interpreted as an OR, am I right? – Giovanni Zaccaria Mar 06 '23 at 09:31
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    That's right. Different contexts, different default conventions. Of course $+$ is poorer than $\oplus$... – Jean Marie Mar 06 '23 at 09:33

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