Can Angular do two way data binding backwards between two input fields?

I can't make my two input fields update values when changing the opposite input.

What I want to do is make a basic $dollar to Gold oz calculator that takes in two input fields. Sample Preview: http://ift.tt/1DEmBoU

The first input is the dollar amount, the second an ounces amount. There is a third variable that contains the gold selling rate.

In my code I have been able to successfully changing the Dollar amount and make the oz amount update via angular two way data binding.

The problem is trying to make the opposite work; for example, changing the oz amount should also update the dollar amount.

Here is my html code:

<div class="row panel" ng-controller="ctrl">

  <!-- Dollar input -->
  <label class="small-6 columns">Dollar $:
    <input type="number" ng-model="dollar">
  </label>

  <!-- Ounces input -->
  <label class="small-6 columns">Ounces (oz):
    <input type="number" value="{{ ozCalc() | number:4 }}">
  </label>

</div>

Here is my angular code:

var app = angular.module('app', []);

app.controller('ctrl', ['$scope', function($scope) {
    $scope.dollar = 0;
    $scope.oz = 0;
    $scope.rate = 1267;

    //Dollar to Ounce Calculator
    $scope.ozCalc = function() {
        var oz = $scope.dollar / $scope.rate;
        return oz;
    };

    //Ounce to Dollar Calculator
    $scope.dollarCalc = function() {
        var dollar = $scope.oz * $scope.rate;
        return dollar;
    };

}]);

Any help would be really appreciated. Thanks