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The following two declarations place at the top of your forms code
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Public Delegate Sub Capture_Data(ByVal Prop_data As String)
Dim in_data As String


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The following code place in the DataReceived event handler
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 Do

 in_data = Serialport1.ReadByte

 Dim new_delegate As New Capture_Data(AddressOf Text_Out)
 Me.RichTextBox1.Invoke(new_delegate, in_data)

 Loop Until Serialport1.BytesToRead < 1


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Add the following sub routine to your code
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Public Sub Text_Out(ByVal text As Int16)

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The following line if you are receiving byte values
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Me.RichTextBox1.AppendText(Chr(text))

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or the following line if you are receiving ASCII characters
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Me.RichTextBox1.AppendText(text & " ")      

End Sub 