The principle is sort of like that yeah.
Or rather it "can" be, but its doesnt "have to"
_Very_ generally speaking.
Digital information is allways communicated in a predetermined fashion. What I mean by that is that the sender of the information knows what the reciever interprets as being a "1" or a "0". So it doesn't really matter what the actual "1" is, what matters it that it is pretedermined.
If that is the case, any information not representing a "1" or a "0" can simply be discarded or ignored.
In real life a good comparison would be your standard light switch compared to a dimmer.
Digital would be the switch turning it on or off, no other setting than that. Analog would be like the dimmer where you can choose any lightintensity from off to on.
The Xbox and its digital audio output used a protocol called "SP-DIF" (SONY-Philips Digital Interface Format) and that protocol is understood by both the xbox and your sound system. It is basically a standard that describes in detail how the information is to be communicated. The upshot of having the standard (which has been around for a long time in professional equipment) is that you can plug more or less any digital audio device into any other digital device and it will understand the data being communicated to it. Logically connecting a cable from say a CD player to another CD player is not going to make anything useful happen as both are output devices, connecting a CD player to a SP/DIF input on your computer on the other hand is more useful since it knows what to do with the information it gets. The sender can send a copy protection order also, so even though your computer might understand it, it might not let you record the data because of this.
SP/DIF as a format when it comes to xbox is a very very slow communication (compared to, say, a gigabit network fibre)
And it takes a lot of interference before the information will get corrupted. The SP/DIF on the xbox will transfer any kind of audio data, everything from mono sound to multichannel audio like AC3(called Dolby Digital nowdays) or DTS(Digital Theater Systems)
Ideally a 75ohm cable of coaxial design, or a fibre cable is used to transport the SP/DIF signals. But chances are that any old cable will do the trick really...
To sum the above up. The above is very general information, it is possible to deditace a lifetime or two to details about this kind of stuff. But if you know the above, you will still know more than most "normal" people you will ever meet
And hopefully you won't be fooled into buying "exotic" cables spending all your money (that you could instead use to rent some movies or something)
Hints about ready made cables.
Expensive cables - You ARE getting ripped off.
Exotic cables - (see above, as they usually happen to be expensive, and there are still people around who thing something is better if its also more expensive)
Exotic materials in cables - basically stay away from these, they cause more harm than good, and thats a scientific fact.
Cheap cables - IF you use them for what they were designed for you probably have the best option possible
DIY cables.
Exotic materials - Don't go there, waste of money.
Copper - If its electric this is the material of choice
"100% Oxygen free copper" - (see above) This has been around for a long time and is today more or less the only type of copper you can buy world wide. Some people will say thats not the case, what that tells you is that they have no idea what they are talking about
Optical Fibre - There are two major materials here, the core is either some type of fiberglass fibre or made out of plastic. For the DIYer plastic is so easy to work with. Just cut off with a sidecutter and snap-on a connector. Takes about 1min or less to make a cable. Fiberglass fibre has better optical properties than plastic but requires special (expensive) tools to make the cut clean.
What type of cable to buy?
Visit a store that has a WIDE variety of cables, see your local tv/radio repairshop, they will probably know where to find a good store (as they likely buy their own cable from them)
Things you need to know (as a good sales person WILL ask you these question BEFORE he recommends a cable)
How long will the cable be
What kind of signal is it going to transport
Any specific color (trust me its not as stupid a question as it might seem actually
What connectors do they offer, go for one that is easy to work with, preferrably a sturdy one too.
Hope this helps