What does a circled plus mean?

StackOverflow https://stackoverflow.com/questions/839479

  •  22-07-2019
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Question

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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Solution

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.

OTHER TIPS

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

enter image description here

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

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.

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.

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!

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

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