Sony HDTV & Philips 5.1 Home Theatre System

I have recently received a 40" Sony Bravia which I have connected to my computer (see my sig for details) via my 4850 HDMI out. I have setup the HDMI out so that the audio goes thru my TV. This works perfectly.

I have just upgraded from my tv speakers to a Philips 5.1 HTS.

http://www.consumer.philips.com/co [...] TS3264D-37.

My question regards the connections between my Philips HTS, my Bravia, and my computer.

I would like to hook up everything to my HTS, so that I can get true 5.1 for everything.

Currently I have my computer hooked up to my Bravia via HDMI, my Xbox 360 via HDMI, my Philips 5.1 via HDMI.

My question is, my Sony Bravia has a Digital Out (Optical) and my Philips 5.1 has a Digital In (coaxial). I was wondering if I can simply buy this converter and plug them in.

http://www.amazon.com/Cables-Go-Co [...] 614&sr=8-1

At this point, will I be able to simply change the inputs on my HDTV and will the sound follow whichever input I change? Hopefully this makes sense, its kind of hard to explain...

Please feel free to ask any questions you may have.

Thank you all in advance, I just want to make sure I am not wasting money for nothing in return.