There are different types of DVI connections, DVI-D (digitial only), DVI-A (analog only), and DVI-I (digital and analog in the same connector). If you are able to connect your graphics card to the monitor with a small adaptor (DVI to VGA) then you are using the analog signals. If the monitor has a DVI connector but does not support digital you are using analog. If the monitor you have is the Value Line series from Acer the site says to check with the distriutor of availability of the DVI connection. (makes be believe the monitor is analog)
A VGA to DVI adaptor does not convert a signal to digital. A DVI-D graphics card with a DVI to VGA adaptor will result in the monitor displaying a "No signal detected" message because the card is sending digital only and the monitor only understands analog. Also, any time a signal is converted from digital to analog or from analog to digital there is some lose in signal quality.
Bottom line is a DVI connector does not ensure a digital signal. You need to look at the graphics card and the monitor capabilities.
HDMI is always digital and the connector includes audio.