Thank you for your post and welcome to the Community!
In regards to your post, I would recommend using an AUX cable (3.5mm to 3.5mm) into your headphone jack on the TV into the SoundTouch 20. Make sure you have the Aux setting selected for your audio. You will not need to purchase a Digital to analog converter for this.
I hope this helps! If you have any further questions or queries, you know where to find us!