Decode dependent picklist validFor mapping in Javascript

To process them, you can use the same type of code you see in the documentation. Here's how I'd write this in ES5:

function testBit(bitmap, index) {
  // Given an 8-bit binary string, get the index / 8 character,
  // And convert the index % 8 bit to true or false
  return !!(bitmap.charCodeAt(index >> 3) & (128 >> (index % 8)));
}
function getValidPicklistValues(controlValue, dependentListValues, controllingValues) {
  // Figure out the index of the controlValue
  var index = controllingValues.indexOf(controllingValues.find(
      function(item) { return controlValue === item.value; }
    ));
  // Return a list of matching options given the control value
  return dependentListValues.filter(function(item) {
        // atob is base64-decoding.
        return testBit(atob(item.validFor), index);
    });
}

Note that atob is a built-in for web browsers; if you're using a version of JavaScript that doesn't have a Window object, you'll need to base-64 decode the data yourself.