$str =~ s/(\d) (\d)/frob($1, $2)/eg
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where you define a sub frob that turns two numbers into a single one, by the rules you've just described.

my %translate = (
    '0 0' => -1,
    '0 1' => -1,
    '0 2' => -1,
    '1 0' => -1,
    '1 1' => 0,
    '1 2' => 1,
    '2 0' => -1,
    '2 1' => 1,
    '2 2' => 2,
);

while (<$fh>) {
    s/(\d \d)/$translate{$1}/g;
    print "New line: $_";
}
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while (<DATA>) {
    s{(\d)\s+(\d)}{log(($1 * $2) || (1/2)) / log(2)}eg;
    print "New line: $_";
}

__DATA__
1 1 1 1 0 0 0 0 0 0 0 0
1 1 1 2 0 1 0 1 0 1 0 1
1 1 2 2 0 2 0 2 0 2 0 2
1 2 1 1 1 0 1 0 1 0 1 0
1 2 1 2 1 1 1 1 1 1 1 1
1 2 2 2 1 2 1 2 1 2 1 2
2 2 1 1 2 0 2 0 2 0 2 0
2 2 1 2 2 1 2 1 2 1 2 1
2 2 2 2 2 2 2 2 2 2 2 2
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New line: 0 0 -1 -1 -1 -1
New line: 0 1 -1 -1 -1 -1
New line: 0 2 -1 -1 -1 -1
New line: 1 0 -1 -1 -1 -1
New line: 1 1 0 0 0 0
New line: 1 2 1 1 1 1
New line: 2 0 -1 -1 -1 -1
New line: 2 1 1 1 1 1
New line: 2 2 2 2 2 2
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Assuming your input has not been mangled by lack of <code> tags (Markup in the Monastery), you can iterate over the set with a while loop and a regular expression. It might look something like:

#!/usr/bin/perl
use strict;
use warnings;

$_ = '2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2';
while (/(\d) (\d)/g) {
    my ($first, $second) = ($1, $2);
    # insert logic for output
}
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See Global matching in perlretut.