Exactly what you need:) You can choose callback version or Promise version. Note that promises will work in IE only with Promise polyfill lib.You can put this code once on a page, and this function will appear in all your files.
The loadend event is fired when progress has stopped on the loading of
  a resource (e.g. after "error", "abort", or "load" have been
  dispatched)
Callback version
        File.prototype.convertToBase64 = function(callback){
                var reader = new FileReader();
                reader.onloadend = function (e) {
                    callback(e.target.result, e.target.error);
                };   
                reader.readAsDataURL(this);
        };
        $("#asd").on('change',function(){
          var selectedFile = this.files[0];
          selectedFile.convertToBase64(function(base64){
               alert(base64);
          }) 
        });
Promise version
    File.prototype.convertToBase64 = function(){
         return new Promise(function(resolve, reject) {
                var reader = new FileReader();
                reader.onloadend = function (e) {
                    resolve({
                      fileName: this.name,
                      result: e.target.result, 
                      error: e.target.error
                    });
                };   
                reader.readAsDataURL(this);
        }.bind(this)); 
    };
    FileList.prototype.convertAllToBase64 = function(regexp){
      // empty regexp if not set
      regexp = regexp || /.*/;
      //making array from FileList
      var filesArray = Array.prototype.slice.call(this);
      var base64PromisesArray = filesArray.
           filter(function(file){
             return (regexp).test(file.name)
           }).map(function(file){
             return file.convertToBase64();
           });
      return Promise.all(base64PromisesArray);
    };
    $("#asd").on('change',function(){
      //for one file
      var selectedFile = this.files[0];
      selectedFile.convertToBase64().
          then(function(obj){
            alert(obj.result);
          });
      });
      //for all files that have file extention png, jpeg, jpg, gif
      this.files.convertAllToBase64(/\.(png|jpeg|jpg|gif)$/i).then(function(objArray){
            objArray.forEach(function(obj, i){
                  console.log("result[" + obj.fileName + "][" + i + "] = " + obj.result);
            });
      });
    })
html
<input type="file" id="asd" multiple/>