To get the property value checkedon the checkbox tab, use the method .prop()or get the value directly from the DOM element. [0]returns the first selected DOM element.
var a;
if ($("#add_desc")[0].checked){
a= "true";
}else{
a= "false";
}
or
var a;
if ($("#add_desc").prop("checked")){
a= "true";
}else{
a= "false";
}
Edit
For versions of jQuery older than 1.6, .propdoes not exist, use .attras a direct replacement.