Would it be possible for the product of $f ^ $s to contain a "1" and hence pollute your $_ string?
Yes, but no. It could certainly be possible that the XORred
string contains a character "1". But this is ok, the
tr/\x00/1/c turns anything that is not
"\x00" into a "1" anyway - after
the tr, the string will only contain
"\x00" and "1" characters.
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