Re: Re: Detecting transpositions

[dash2]

Very cool. Can you explain why it works? What makes the XOR come out to be like that?

A massive flamewar beneath your chosen depth has not been shown here

[Abigail-II]

Well, if you do an XOR of two strings (scalars that haven't been used as numbers), perl will do a bitwise XOR on the characters of the strings, instead of the bits on the numbers. Two characters that are the same will have all the bits the same, XORing those characters will give you the character of which all the bits are 0, aka "\x00". If two characters are not the same, there is at least one bitpositions where the bits are different - resulting in a 1 bit when XORing. Hence, the resulting character will be anything but "\x00".

Abigail

[sgifford]

It works because the xor of two bits is zero if and only if the two bits are the same:

0 ^ 0 = 0
1 ^ 1 = 0
0 ^ 1 = 1
1 ^ 0 = 1

So the xor of two characters (which are a string of 8 bits) will be 0 (8 0-bits) if and only if the two characters are the same.

Using xor on strings xors the characters from the first string with the characters in the second string, so in the places where the characters are identical the resulting character will be zero, and in all places where they differ it will be nonzero.