I bought my first console over a week back and since I didn't have a TV I got a LED Monitor (Full HD) which has an HDMI port, and also a pair of good speakers. Since XBox has the (big) analog cable and HDMI we assumed I could connect both Monitor (in full HD via HDMI) and speakers with (AV to 3.5mm convertor which I got). Only after opening box I realized at any time only either of HDMI/Analog could be connected to XBox. I have no clue how to connect Monitor+ Speakers and still get Full HD. (We tried buying an external TV tuner box, it gives only 480p). Any solutions?
It's possible to do this electrically, although mechanically the two cables interfere. Microsoft sells a special version of the AV adapter that you can use to plug both cables in at the same time, or you can break the outer casing on the AV cable so that you can fit the HDMI cable in at the same time.
Note that plugging both cables in at the same time might cause some issues if you plan on switching between inputs on the monitor while your Xbox 360 is still on, see: