If I flip the values of the corners before applying the operation I get the correct results, so maybe the algorithm is missing a step or, more likely, I am completely misreading it.

I see the problem. I didn't write the article :) (It is unfortunately quite typical.)

(Perhaps the explanation is the annotation that reads: "Give every cell a number based on which corners are true/false.")

You can 'flip' the values after you've constructed them using:

@b = qw[ 1 0 0 0 ];;

$n = 0; 
$n <<= 1, $n |= $_  for @b; 
$n = ~$n & 0xf;                     ## Additional step to bitwise-not 
+and mask (flip) values.

print $n;;
7
[download]