Reading multiple files with Javascript FileReader API one at a time

I came up with a solution myself which works.

function readmultifiles(files) {
  var reader = new FileReader();  
  function readFile(index) {
    if( index >= files.length ) return;
    var file = files[index];
    reader.onload = function(e) {  
      // get file content  
      var bin = e.target.result;
      // do sth with bin
      readFile(index+1)
    }
    reader.readAsBinaryString(file);
  }
  readFile(0);
}

This should read the files one by one:

function readmultifiles(files) {
    var ul = document.querySelector("#bag>ul");
    while (ul.hasChildNodes()) {
        ul.removeChild(ul.firstChild);
    }
    // Read first file
    setup_reader(files, 0);
}

// Don't define functions in functions in functions, when possible.

function setup_reader(files, i) {
    var file = files[i];
    var name = file.name;
    var reader = new FileReader();
    reader.onload = function(e){
                        readerLoaded(e, files, i, name);
                    };
    reader.readAsBinaryString(file);
    // After reading, read the next file.
}

function readerLoaded(e, files, i, name) {
    // get file content  
    var bin = e.target.result;
    // do sth with text

    var li = document.createElement("li");
    li.innerHTML = name;
    ul.appendChild(li);

    // If there's a file left to load
    if (i < files.length - 1) {
        // Load the next file
        setup_reader(files, i+1);
    }
}