Edit in JSFiddle

  var calculateNUSMatricNumber = function (id) {
      var matches = id.toUpperCase().match(/^A\d{7}|U\d{6,7}/);
      if (matches) {
          var match = matches[0];

          // Discard 3rd digit from U-prefixed NUSNET ID
          if (match[0] === 'U' && match.length === 8) {
              match = match.slice(0, 3) + match.slice(4);
          }

          var weights = {
              U: [0, 1, 3, 1, 2, 7],
              A: [1, 1, 1, 1, 1, 1]
          }[match[0]];

          for (var i = 0, sum = 0, digits = match.slice(-6); i < 6; i++) {
              sum += weights[i] * digits[i];
          }

          return match + 'YXWURNMLJHEAB'[sum % 13];
      }
  };

  $('input').on('change keyup', function () {
      $('span').text(calculateNUSMatricNumber(this.value) || 'Invalid input!');
  });

External resources loaded into this fiddle:

<div class="container">
    <div class="panel panel-default">
        <div class="panel-heading">NUS Matriculation Number Calculator</div>
        <div class="panel-body">
            <div class="input-group input-group-lg">
                <input type="text" class="form-control" placeholder="A0012345 / A0012345A / a0012345 / a0012345@nus.edu.sg">
                <span class="input-group-addon">Output</span>
            </div>
        </div>
        <table class="table table-striped table-bordered table-hover">
            <thead>
                <tr>
                    <th>Input Format</th>
                    <th>Example</th>
                </tr>
            </thead>
            <tbody>
                <tr>
                    <td>Matriculation number with missing check digit</td>
                    <td>A0012345</td>
                </tr>
                <tr>
                    <td>Matriculation number with wrong check digit</td>
                    <td>A0012345A</td>
                </tr>
                <tr>
                    <td>NUSNET ID</td>
                    <td>a0012345</td>
                </tr>
                <tr>
                    <td>NUS email address</td>
                    <td>a0012345@nus.edu.sg</td>
                </tr>
            </tbody>
        </table>
    </div>
</div>
.container {
    padding-top: 15px;
}