[jquery] Loop through checkboxes and count each one checked or unchecked

To build a result string exactly in the format you show, you can use this:

var sList = "";
$('input[type=checkbox]').each(function () {
    sList += "(" + $(this).val() + "-" + (this.checked ? "checked" : "not checked") + ")";
});
console.log (sList);

However, I would agree with @SLaks, I think you should re-consider the structure into which you will store this in your database.

EDIT: Sorry, I mis-read the output format you were looking for. Here is an update:

var sList = "";
$('input[type=checkbox]').each(function () {
    var sThisVal = (this.checked ? "1" : "0");
    sList += (sList=="" ? sThisVal : "," + sThisVal);
});
console.log (sList);