[math] What does a circled plus mean?

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?

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

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

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.

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 <------ 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

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

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!

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

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