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Another way to look at XOR - it's an adder (the sum, without the carry)
Earlier quoted context omitted.
No, it's true when exactly M are true. "a1 || a2 || ... || an" is true when at least one is true. The latter is the same as "a1 + ... + an == 1 || a1 + ... + an == 2 || ... || a1 + ... + an == n".
So your + operator implicitly casts booleans to an integer type, with false=0 and true=1?
By the way, in Python, bool is a subtype of int (i.e., instanceof(True,int) == True), and True + True == 2. C is the same, and in Javascript booleans are converted to integers for arithmetic operations.
Say we have an N=4 dimensional vector space, and we use binary place values to represent units vector in a basis, like this:
w = 1000
x = 0100
y = 0010
z = 0001
Then a multivector basis could be represented e.g.:
xyz = 0111
xy = 0110
wz = 1001
Now, if ^ is the outer product:
xy^yz = xz ↔ 0110 xor 0011 = 0101.
wx^yz = wxyz ↔ 1100 xor 0011 = 1111.
and so on.
If anyone has more information about this, I'd be really interested in seeing it!
> most programming languages don’t have an explicit “logical operator” for it I guess the author never taught of != . The only thing to be careful with is that it doesn't implicitly convert arguments to boolean, so expressions like " != (flags & Flag)" will go wrong without an explicit conversion "bool(flags & Flag)" or equivalent expression like "((flags & Flag) != 0)". And let's not forget about the friend, ==. I'v…
Well, you could also use bitwise XOR in that case.
it can also be used to generate simple parity. https://en.wikipedia.org/wiki/Parity_bit#RAID
One thing I love about xor is an interesting correspondence between bitwise xor and the outer product of the exterior algebra. Say we have an N=4 dimensional vector space, and we use binary place values to represent units vector in a basis, like this: w = 1000 x = 0100 y = 0010 z = 0001 Then a multivector basis could be represented e.g.: xyz = 0111 xy = 0110 wz = 1001 Now, if ^ is the outer product: xy^yz = xz ↔ 0110…
struct Example {
int elem1;
int elem2;
...
};
Example ex1 = { 1, 2, ... };
int a = ex1.elem1;
int b = ex1.elem2;
...
I have no idea if that was the original thinking behind dot notation but it's neat and I like it.
Well, in C there's just no need. The main raison d'etre for && and || over & and | is that you can exploit their short circuiting behaviour. A hypothetical ^^ operator wouldn't bring anything extra to the table.
Earlier quoted context omitted.
So your + operator implicitly casts booleans to an integer type, with false=0 and true=1?
What you are saying is the only way I can imagine to interpret what I wrote, if one assumes I was intending to make any sense. By the way, in Python, bool is a subtype of int (i.e., instanceof(True,int) == True), and True + True == 2. C is the same, and in Javascript booleans are converted to integers for arithmetic operations.
One might imagine it (without experience, or not thinking, of any particular programming language) as being a logical OR on Booleans - which in EE at least is frequently written '+'.
"Sadly XOR doesn’t appear as an equivalent to NOT, AND and OR, as a logical operator on booleans, being relegated to just a bitewise operator in most programming languages." Well, in C there's just no need. The main raison d'etre for && and || over & and | is that you can exploit their short circuiting behaviour. A hypothetical ^^ operator wouldn't bring anything extra to the table.
One thing I love about xor is an interesting correspondence between bitwise xor and the outer product of the exterior algebra. Say we have an N=4 dimensional vector space, and we use binary place values to represent units vector in a basis, like this: w = 1000 x = 0100 y = 0010 z = 0001 Then a multivector basis could be represented e.g.: xyz = 0111 xy = 0110 wz = 1001 Now, if ^ is the outer product: xy^yz = xz ↔ 0110…