JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
 <div class='form-group'>
   <input type='checkbox' name='check[]' value='1' checked />aaa
   <input type='checkbox' name='check[]' value='1' />bbb
   <input type='checkbox' name='check[]' value='1' />ccc
   <input type='checkbox' name='check[]' value='1' />ddd
   <input type='checkbox' name='check[]' value='1' checked />eee
   <input type='checkbox' name='check[]' value='1' />fff

   <div id='show' class='col-sm-4'></div>
 </div>
 <div class='form-group'>
   <label class='control-label col-sm-2' for='livello'>Livello:</label>
   <div class='col-sm-4'>
     <input type='text' class='form-control' id='livello' name='livello'>
   </div>
 </div>

JavaScript

updates_(); // call on load
$("input[type=checkbox]").change(function() {
  updates_(); //call update fn
})

function updates_() {
  var str = '';
  //loop through checkboxes
  $(".form-group > input[type=checkbox]").each(function() {
    str += $(this).is(':checked') ? 1 : 0; //append 0 or 1 depending on if checked or not
  })
  $("#livello").val(str) //addd value to input box
}