The Apple Support Document notes that the Intel Mac mini can be connected to digital HDTV sets via DVI, HDMI, and VGA/RGB [emphasis added]:
- A standard DVI cable can be attached from the [pre "Early 2009"] Mac mini [models] to an HDTV, supporting resolutions up to 1920x1080. [The "Early 2009" models can be connected to a DVI equipped television via DVI by using a Mini-DVI to DVI adapter].
- HDTVs with HDMI inputs can be connected to [a pre "Early 2009"] Mac mini with a DVI to HDMI adapter. A DVI to HDMI adapter will relay video but not audio from the computer. [The "Early 2009" models can be connected to an HDMI equipped television by using a Mini DisplayPort to HDMI adapter]. . . [To connect audio], the Belkin PureAV HDMI to DVI cable can be ordered from the Apple Store [and numerous other resellers].
- The DVI to VGA adapter that was included with your [pre "Early 2009] Mac mini can be used along with a VGA cable to connect [the Mac] to an HDTV with an analog PC-input (VGA/RGB), supporting resolutions 1920x1080. [The "Early 2009" models can be connected to a VGA equipped television by using a Mini-DVI to VGA adapter].
The same document provides instructions on how to connect pre "Early 2009" Intel Mac mini models to an analog television with the Apple DVI-to-Video Adapter via Composite or S-Video:
- Composite is the most widely available video input on traditional analog televisions. It delivers acceptable quality at resolutions up to 800x600 on most televisions.
- S-Video separates the analog video signal into separate channels, providing better quality than Composite. S-Video is best used with a resolution of 800x600.
For connecting the audio, Apple mentions that all Intel-based Mac mini models use "a combo mini-plug connector to output both digital audio and analog audio signals" and audio can be connected using digital and analog audio:
- Digital Audio: Use an optical mini-plug cable with the audio output on the Mac mini to connect A/V receivers and home theater audio systems with 5.1 surround sound and optical audio inputs. A mini-plug to TOSLINK adapter may be needed to connect to some receivers. The Belkin PureAV Digital Optical Cable with Mini-TOSLINK adapter is available from the Apple Store [and other resellers].
- Analog Audio: The Mac mini can be connected to most televisions, audio receivers and speakers using analog line-out. A mini-plug to stereo RCA adapter may be necessary. The Monster iCable mini-to-RCA left/right audio cable is available at the Apple Store [and elsewhere].
so it all depends which mini you got pre early 2009 or after early 2009 as for the different ports to use dvi or mini display port to connect to your tv and you need to use the appropriate resolution and adapter