That's a good one but if you want to pump out 5.1 digital use this one.
http://kanexlive.com/products/item.aspx?id=3495
I don't think you can get 5.1 out of macbook air because it doesn't have a toslink like other macs. see this post and one very frustrated purchaser of, i believer, that very adapter:
https://forums.macrumors.com/threads/799536/
I apologize for the caps, but I feel it is required...
DO NOT BUY ANYTHING FROM THAT COMPANY!!!
I bought this adapter because at the time their product page said it supported uncompressed audio formats. After purchasing the cable, they snuck a little blog post on a subsection of the site stating that it did not. Over the weekend, they quietly changed the page to no longer reflect the uncompressed audio comments. I submitted a complaint to their site that was admittedly not worded very politely (no cursing, just complaining about being "duped" by their poor wording) and requested a swap for the USB+HDMI only model or a refund. They have refused, so I am now going through the process of filing a Better Business Bureau complaint to see if I can recoup my $78 after shipping. I'll be lucky if I see a single penny back and now I have to pay $40 to get a functional product from a reputable business (Monoprice.com is awesome and I should have known better!). Needless to say, avoid at all costs!
("THAT COMPANY" being Kanex - I didn't realize that both quotes didn't copy.)