You would be helped by a code indentation convention. I've made some corrections and rigged it to pass strictures.

use warnings;
use strict;

my $file = pop @ARGV;
chomp $file;

my (@letters, @bin); # added

open MESG, '+<' , $file or die $file, ' unavailable: ', $!;

while (<MESG>) { # changed to read from the open handle
    my @characters = split //;
    push @letters, @characters;
    push @bin, map {
        my $c = unpack 'b*', $_
    } @characters;
#    foreach my $letter (@letters) {
#        my ($ascii) = unpack ("C" ,$letter);
#        my ($bin) = unpack ("b*",$letter);
#        my $ordinal = ord $letter;
#        print "\n1)$letter\n";
#        print "2)$ordinal\n";
#        print "3)$ascii\n";
#        print "4)$bin\n";
#        # push is moved above
#    }
}

my %letnet;
@letnet{@letters} = @bin; # slice replaces the double foreach

while (my ($key,$value) = each (%letnet)) {
    print "$key-->$value\n";
}
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Your doubly nested hash populating loop was wrong. For each letter, it churns through all the binary representations, assigning each in turn to the $letter key's value. Eventually each key gets the value $bin[-1]. I replaced it with the efficient hash slice mechanism.

Why do you use the '+<' signature in open? It is unnecessary to have the file open to write in what you show. If you later write to the file you should call flock after open.