You don't have to read only one byte at a time:

open my $FILE, '<:raw', 'i:/lenova_2008-03-28.zip' or die "Cannot open
+ 'i:/lenova_2008-03-28.zip' $!";
open my $OUT, '>', 'i:/fullhexdump.txt' or die "Cannot open 'i:/fullhe
+xdump.txt' $!";

$/ = \2048;
my $count;
while ( <$FILE> ) {
    $count += length;
    print $OUT unpack 'H*', $_;
}
close $FILE;
close $OUT;

print "\n\n$count\n\n";
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