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Ground may not be the same as earth ground.
Input ground, output ground, Micro-coomputer ground, etc...may not the the same or they may be at the same voltage.
Some times most of the grounds in a project are at (or about) 0 volts, but one of the grounds is at +300 volts. Ground can be relative to the componits in that area and not at all 0 volts.
Grounds are a common point of reference for voltages, plain and simple. If you have V+ and V-, they are the voltage potential when measured using GND as the common base. If you were to measure V+ to V- directly, you would get V+ + |V-|, which is a very different value.
It's just a common reference for the rest of the voltages in the schematic. +12vdc is +12vdc as compared to what?
Many circuits use the negative power lead as ground reference. There are many situations though (audio in particular) which require a negative supply voltage. For saftey you can't have the outside of the case at a voltage so a separate ground line is run for grounding the case and providing the refrence for the - supply.
If your supply is floating (meaning it's fully isolated from external grounds) using a -12 volt line as a ground and measuring voltage to a +12 volt line on the same supply will give you 24 volts. ALL connected circuits have to share ground at least at one point in the circuit or there's no refrence for the voltage.
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