What does a circled plus mean

Question

I cannot understand the calculation  66  oplus  fa   9c    The sum is clearly over  ff   so I am confused   The topic is simple encryption algorithm   What does a circled plus mean

User · Answer

Hope this layout works  take it to the binary representation with an XOR   66h   102 decimal   01100110 binary FAh   250 decimal   11111010 binary ------------------------------------                     10011100 binary  lt ------ that s 9Ch 156 decimal   XOR rules are basically  1 XOR 1   0 false 1 XOR 0   1 true 0 XOR 0   0 false   but the wiki I linked earlier will give you more details if needed   thats what it looks like they are doing in the screenshot you provided

User · Answer

This is not an plus  but the sign for the binary operator XOR  a   b   a XOR b 0   0   0 0   1   1 1   0   1 1   1   0

User · Answer

It s an exclusive or  XOR   If I remember correctly  when doing bitwise mathematics the dot     means AND and the plus     means OR  Putting a circle around the plus to mean XOR is consistent with the style used for OR

User · Answer

I used the logic in the replies by rampion and schnaader  I will summarise how I confirmed the results  I changed the numbers to binary and then used the XOR-operation  Alternatively  you can use the Hexadecimal tables  Click here

User · Answer

It is XOR  Another name for the XOR function is addition without carry  I suppose that s how the symbol might make sense

User · Answer

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

User · Answer

That s the XOR operator  not the PLUS operator  XOR works bit by bit  without carrying over like PLUS does  1 XOR 1   0 1 XOR 0   1 0 XOR 0   0 0 XOR 1   1

User · Answer

The plus-symbol in a circle does not denote addition  It is a XOR operation

User · Answer

It s not an addition  but an exclusive OR operation  At least the output confirms to the same

[math] What does a circled plus mean?

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