I've done some searching on the internet and several forums on it but they all resort to explaining what ROM is, it retains its memory even when there there is no power to it. I know what ROM is but what I want to know is how does it actually work.
Answer
ROM typically stores data as wires that are either physically connected or physically disconnected.
In the classic diode matrix ROM, there are row wires and column wires and for each combination of row wire and column wire, there can either be a diode connecting them or not be a diode connecting them.
In the picture below, an 81316F 16K ROM from 1965 with the lid removed, you can see the row and column decoding logic around the perimeter. In the middle are two massive arrays that contain diodes at some intersections and nothing at others:
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