gistfile1.txt

    public class DummyViewModel : INotifyPropertyChanged
    {
        public DummyViewModel()
        {
            Values= new ObservableCollection<Reading>();
            _timer = new Timer((o) =>
                {
                    this.TextFromSerialPort = DateTime.Now.ToString();
                    App.Current.Dispatcher.Invoke(()=>this.Values.Add(new Reading(DateTime.Now,"FakeValue " + DateTime.Now.ToString())));
                }, null, TimeSpan.FromSeconds(0), TimeSpan.FromSeconds(0.1));
        }
        private Timer _timer;

        private string _textFromSerialPort;
        public string TextFromSerialPort
        {
            get { return this._textFromSerialPort; }
            set
            {
                if (value == this._textFromSerialPort) return;
                this._textFromSerialPort +=Environment.NewLine + value;
                this.OnPropertyChanged();
            }
        }

        public ObservableCollection<Reading> Values { get; private set; }

        public event PropertyChangedEventHandler PropertyChanged;

        [NotifyPropertyChangedInvocator]
        protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
        {
            var handler = PropertyChanged;
            if (handler != null) handler(this, new PropertyChangedEventArgs(propertyName));
        }
    }

    public class Reading
    {
        public Reading(DateTime time, string value)
        {
            this.Time = time;
            this.Value = value;
        }

        public DateTime Time { get; set; }
        public string Value { get; set; }
    }

gistfile2.txt

    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
            this.DataContext = new DummyViewModel();
        }
    }

gistfile3.txt

<Window x:Class="SerialPortDummy.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
                xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:serialPortDummy="clr-namespace:SerialPortDummy"
        mc:Ignorable="d"
        d:DataContext="{d:DesignInstance serialPortDummy:DummyViewModel, IsDesignTimeCreatable=True}"
        Title="MainWindow" Height="600" Width="800">
    <DockPanel>
        <DataGrid ItemsSource="{Binding Values}" DockPanel.Dock="Top" Height="400"></DataGrid>
        <TextBox Text="{Binding TextFromSerialPort}"></TextBox>
    </DockPanel>
</Window>