The best connection will be to use the optical input on the Bose if your DTV box has optical out.
If not then you can use the analog RCA stereo outputs to the Bose if the DTV box has them.
If the DTV box only has HDMI connect it to your TV with HDMI and use the audio out of the TV to the Bose.
If the TV doesn't have audio outs at all then you will need an HDMI audio extractor like this one http/www.monoprice.com/Product?p_id=5557&kpid=105557&gclid=CPPY2sLnwcYCFYIXHwodhY0FTw
The best connection will be to use the optical input on the Bose if your DTV box has optical out.
If not then you can use the analog RCA stereo outputs to the Bose if the DTV box has them.
If the DTV box only has HDMI connect it to your TV with HDMI and use the audio out of the TV to the Bose.
If the TV doesn't have audio outs at all then you will need an HDMI audio extractor like this one http/www.monoprice.com/Product?p_id=5557&kpid=105557&gclid=CPPY2sLnwcYCFYIXHwodhY0FTw