Simple Solution: You forgot to use binmode again is all :)

open(FH,"file.exe");
binmode(FH);
my $binary;
while(<FH>) {
 $binary .= $_;
}
close(FH);

open(FH,">newfile");

binmode FH;    #<---- Add this and it works just fine :)

print FH $binary;
close(FH);
[download]

Cheers, James