use strict;
use warnings;

my $infile  = 'yourinputfilename';
my $outfile = 'youroutputfilename';

open(my $fhin, '<', $infile) or die "error: open '$infile': $!";
binmode($fhin);
open(my $fhout, '>', $outfile) or die "error: open '$outfile': $!";
binmode($fhout);

local $/ = \2;   # make <> operator read two bytes at a time
while (my $TileData = <$fhin>)
{
   if (length($TileData) != 2)
   {
      warn "oops, file is of uneven length, last byte='$TileData'\n";
      last;
   }
   # do your thing with bitwise stuff here...
   # my $NewTileData = ...
   print {$fhout} $NewTileData;
}