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AngularJS passing data to Javascript variables and opposite

I am looking for a solution on passing data from a specific input text field to AngularJS. it may be a Javascript variable too. If the variable is changed from inside a javascript code it is not updating on AngularJS side. If i take the same variable and in the text field add at least one character or modify something i see variable updating and everything working as it should.
I tried something with angular.element(document.getElementById('ControllerElementID')).scope().funct(); but still no luck. When i update at least one field from the keyboard, all text fields that are related to "ng-model="sig.sigBase6422"" are updating properly as it should. If i call this updates through a JavaScript function i see updates only on specific text field and no updates at all on ng-model happening. How to make it updating as simple as possible? Below i will post a small example. I was able to store data from variable to a external file and in AngularJS read it from file and use it. this is way too long, complicated and ridiculous. I am sure there should be a better way.
Thank you!
<script type="text/javascript">
function addtext1() {document.getElementById("myID1").value = "1111111111111111";}
function addtext2() {document.getElementById("myID2").value = "2222222222222222";}
</script>
<div>
<form action="#" name="FORM1">
<TEXTAREA NAME="sigData" ng-model="sig.sigBase6422" ROWS="10" COLS="20">String: </TEXTAREA>
</form><br>
<input type="text" name="myID1" id="myID1" ng-model="sig.sigBase6422" ><br>
<input type="text" name="myID2" id="myID2" ng-model="sig.sigBase6422" ><br>
<p>Value {{sig.sigBase6422}}!</p>
</div>
<!-- test field -->
Add text 1
Add text 2

Indeed if you want to use AngularJS for what it was created, you have to rewrite your code completely using directive or controller. You variables and functions accessible from the view should be attached to the $scope too.
var myApp = angular.module("myApp", []);
myApp.controller("myCtrl", function($scope){
$scope.addtext1 = function () {
$scope.sig.sigBase6422 += "1111111111111111";
};
$scope.addtext2 = function () {
$scope.sig.sigBase6422 += "2222222222222222";
};
$scope.sig = {
sigBase6422: ""
};
});
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.4.8/angular.min.js"></script>
<div ng-app="myApp" ng-controller="myCtrl">
<form action="#" name="FORM1">
<TEXTAREA ng-model="sig.sigBase6422" ROWS="10" COLS="20">String: </TEXTAREA>
</form><br/>
<input type="text" name="myID1" id="myID1" ng-model="sig.sigBase6422" /><br/>
<input type="text" name="myID2" id="myID2" ng-model="sig.sigBase6422" /><br/>
<p>Value {{sig.sigBase6422}}!</p>
<!-- test field -->
<button ng-click="addtext1()">Add text 1</button>
<button ng-click="addtext2()">Add text 2</button>
</div>

You seem to have misunderstood how angular works. What you're trying to do is not how angular works. What you're trying to do with native JavaScript can be done with angular. Angular can update dom and Dom updates angular as it's responsible for causing updates.... anyway without getting any deeper. You need to read more on how angular works and try sticl within the bounds of angular instead of mixing.
That being said :
Tigger change on the Dom element after you have updated its value. Or better yet get access to scope variable on the Dom and call a function in angular with the value you're and set they value from inside of a angular.

Use this code while updating the value.
pick the controller first using
var scope = angular.element(document.getElementById('yourControllerElementID')).scope();
scope.<variablename> = <your operation>;
then
scope.$apply();
the remaining thing will be taken care by Angular.

Need help adapting code from jQuery to Angular

I found some code here: Textarea limit characters for each row in javascript
I want to use it in my project, but I'm having trouble figuring out how to make it work in Angular, particularly setting the directives.
Here's the relevant fiddle: http://jsfiddle.net/aSU7x/
Do I just change
onchange="Validate(this)" onkeyup="Validate(this)"
to
ng-change="Validate(this)" ng-keyup="Validate(this)"
?
I'm still not too familiar with Angular, and I'm only slightly more familiar with jQuery. What would I have to do with the scope, controller, etc.? What would a proper Angular implementation of this code look like? Thanks for the time.

Basic idea of calling a function in angular using scope and $event
angular.module('changeExample', [])
.controller('ExampleController', ['$scope',
function($scope) {
$scope.keyupfnc = function(evt) {
console.log(evt.which);
};
}
]);
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script>
<div ng-app="changeExample">
<div ng-controller="ExampleController">
<input type="text" ng-keyup="keyupfnc($event)" />
</div>
</div>

What causes AngularJS variable change to fire html update?

I got this example from the W3Schools tutorial on AngularJS. I made a small change from binding the value of the checkbox span to using an expression. I figured that the todo list wouldn't update any more. But it still does. What causes the ng-repeat to fire just because I have added a todo item?
http://plnkr.co/edit/Kojz2ODWDS8dFDNzjYR5?p=preview
<!DOCTYPE html>
<html>
<script src= "http://ajax.googleapis.com/ajax/libs/angularjs/1.3.14/angular.min.js"></script>
<body ng-app="myApp" ng-controller="todoCtrl">
<h2>My Todo List</h2>
<form ng-submit="todoAdd()">
<input type="text" ng-model="todoInput" size="50" placeholder="Add New">
<input type="submit" value="Add New">
</form>
<br>
<div ng-repeat="x in todoList">
<input type="checkbox" ng-model="x.done"> <span>{{x.todoText}}</span>
</div>
<p><button ng-click="remove()">Remove marked</button></p>
<script>
var app = angular.module('myApp', []);
app.controller('todoCtrl', function($scope) {
$scope.todoList = [{todoText:'Clean House', done:false}];
$scope.todoAdd = function() {
$scope.todoList.push({todoText:$scope.todoInput, done:false});
$scope.todoInput = "";
};
$scope.remove = function() {
var oldList = $scope.todoList;
$scope.todoList = [];
angular.forEach(oldList, function(x) {
if (!x.done) $scope.todoList.push(x);
});
};
});
</script>
</body>
</html>

Clicking the Add New Button submits the corresponding form and by using ng-submit="todoAdd()" it will call this function. This in turn adds an entry to the todoList in your scope. As this array has been modified the angular digest cycle is triggered and the list is updated.
Some suggestions for your questions: First of all, you mean W3Schools, not the W3C (which is a standardization organization and normally is not doing tutorials, which is why I got curios - Also, you will find lots of reasons why not to use W3Schools when goolgin around or looking at meta). Also, if you compare to some other code, you should include it or at least link to it.
I found it by googling and it seems your only change is using <span>{{x.todoText}}</span> instead of <span ng-bind="x.todoText"></span>. There really is no difference in terms of the digest cycle here. The only difference is that by using {{}} it might at first be rendered as curly brackets in the browser window, before the variable is actually replaced. Thus, it is usually better to use ng-bind.

Angular JS and ng-model not displaying

I am a newbie at Angular JS and this is what I started with:
var myApp = angular.module('myApp', []);
myApp.controller('WizardController', ['$scope', function($scope){
$scope.user = {};
$scope.displayName = 'Hello';
}]);
user is used to gather the data in the input fields in my steps <input type='text' ng-model='user.name'> and when I call it like so {{user.name}} what is inside the input text appears in a next step.
My question is how do I get $scope.displayName to display on my page.
<p ng-model="displayName"></p>
<p>{{displayName}}</p>
<p><input type='text' ng-model='displayName'></p>
I have tried all of these and none seem to work. Please help.
here is a jfiddle http://jsfiddle.net/Fc7KZ/

Make sure you added the ng-app and ng-controller attributes to your html
<body ng-app="myApp" ng-controller="WizardController">
<p ng-model="displayName"></p>
<p>{{displayName}}</p>
<p><input type='text' ng-model='displayName'></p>
</body>
Update 1:
Your js fiddle did not have angular library here is the version corrected:
http://jsfiddle.net/Fc7KZ/2/

You seem to be using angular-wizard. Your Fiddle doesn't include Angular or Lodash, which are both pre-requisites of that project. I'm guess your local code doesn't either, if not then that's your problem.

AngularJS: late-binding of ng-model to dom element

I have a web page with some HTML elements which I cannot edit. I'd like to dynamically attach ng-model attributes to these and have AngularJS re-bind them to the scope. A simplified example of what I want to accomplish can be found here
<script src="//code.jquery.com/jquery-2.1.0.min.js"></script>
<script src="//ajax.googleapis.com/ajax/libs/angularjs/1.2.16/angular.min.js"></script>
<script>
function MyCtrl($scope) {
$scope.myModel1 = "Hi";
$scope.myModel2 = "there";
var myModel2 = angular.element("#myModel2");
//This won't work
myModel2.attr("ng-model", "myModel2");
}
</script>
<div ng-app ng-controller="MyCtrl">
<input type="text" ng-model="myModel1"/>
<!-- I can't touch this -->
<input type="text" id="myModel2" />
</div>

You need to use $compile (docs)
$compile(myModel2.attr("ng-model", "myModel2"))($scope);
demo
When you load your page, angular uses $compile on the HTML automatically, that's how it knows which elements to assign which directives to. If you just change the attribute like you tried, angular doesn't know. You have to use $compile.