How to share data between components using a service properly?

I am learning angular2 and was able to share data between sibling components using input/output.

Here is my working example.

//our root app component
import {Component, NgModule} from '@angular/core'
import {BrotherComponent} from './brother.component'
import {SisterComponent} from './sister.component'
import {BrowserModule} from '@angular/platform-browser'
import {FormsModule, ReactiveFormsModule} from '@angular/forms'

@Component({
  selector: 'my-app',
  template: `
    <div>
      <h2>Hello {{name}}</h2>
      <brother (onChange)="handleBrotherEvent($event)" [dataFromSister]="dataFromSister"></brother>
      <sister (onChange)="handleSisterEvent($event)" [dataFromBrother]="dataFromBrother"></sister>
    </div>
  `,
})
export class App {
  name:string;
  constructor() {
    this.name = 'Angular2'
  }

  handleBrotherEvent(data)
  {
    this.dataFromBrother = data;
    console.log("called from handleBrotherEvent in app", data); 
  }

  handleSisterEvent(data)
  {
    this.dataFromSister = data;
    console.log("called from sister handleSisterEvent in app", data); 
  }
}

@NgModule({
  imports: [ BrowserModule, FormsModule, ReactiveFormsModule ],
  declarations: [ App, BrotherComponent, SisterComponent ],
  bootstrap: [ App ]
})
export class AppModule {
}

Now I want to learn about services and see how I can share my data through that. I have tried to look at the angular.io documentation to understand communication between components using a service, but I am still confused on how to get this working with my example. Here is the section I have been reading:

https://angular.io/docs/ts/latest/cookbook/component-communication.html#!#bidirectional-service

I am looking for a concrete example to convert my original example to share component form data using a service. Is there somebody that can help me?

Update:

Based off the below comments, I changed my plnkr to this. Hopefully this is how its supposed to work.

http://plnkr.co/edit/zW5c8d1HJQ32qJtCHTTS?p=preview


You can always just create a binding to a variable on a service from two different components. In this example one component increments a number and the other component displays the value

enter image description here

You won't be able to detect and respond to changes with this approach. A more robust approach would be to use an observable to broadcast changes to the state in your service. e.g.

import {BehaviorSubject} from "rxjs/BehaviorSubject"

export class MyService {
    private state$ = new BehaviorSubject<any>('initialState');

    changeState(myChange) {
        this.state$.next(myChange);
    }

    getState() {
        return this.state$.asObservable();
    }
}

Then your components could subscribe to state changes and change the state by calling custom methods on the service. I have a concrete example of this approach here https://github.com/robianmcd/ng2-redux-demo/blob/redux-demo-with-service/app/user.service.ts