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I cannot understand the calculation "66 ⊕ fa = 9c". The sum is clearly over "ff", so I am confused. The topic is simple encryption algorithm.
What does a circled plus mean?
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Symbol. ⊕︀ (logic) exclusive or. (logic) intensional disjunction, as in some relevant logics.
In logic and CompSci, ⊕ is used to denote the "exclusive or" or "XOR": x∨y∧¬(x∧y). In set theory, ⊕ denotes the disjoint union. In linear algebra/vector analysis, it's used to denote the direct sum of two vector spaces. It's also used to denote parity: see P Parity.
People are saying that the symbol doesn't mean addition. This is true, but doesn't explain why a plus-like symbol is used for something that isn't addition.
The answer is that for modulo addition of 1-bit values, 0+0 == 1+1 == 0, and 0+1 == 1+0 == 1. Those are the same values as XOR.
So, plus in a circle in this context means "bitwise addition modulo-2". Which is, as everyone says, XOR for integers. It's common in mathematics to use plus in a circle for an operation which is a sort of addition, but isn't regular integer addition.
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