The implication of not expecting a logical record size other than 1 is that you don't want to be doing fixed length I/O in the first place. There is nothing wrong with doing ordinary variable length I/O even if there is no delimiter. Just set $/ to something likely to occur and process each string of bytes read in singly, e.g. 
{ local $/ = chr(0); # if this occurs reasonably often in the file
  open (FILE, "file.binary");

  while ( <FILE> ) {
      while ( length() ) {
          my $byte;
          ( $byte, $_ ) = /^(.)(.*)$/; 
          ... Code here, processing $byte ...
      }
   }
   close FILE;
}

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In reply to Re: Reading binary file byte by byte by anonymized user 468275
in thread Reading binary file byte by byte by Anonymous Monk

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