The Antikythera mechanism is more like a mechanical clock or calendar than an arithmetic machine.
Imagine building a simple mechanical clock that tells the hours and minutes. You could even add a second hand. And an AM/PM display. And a day of the week display. Maybe even a dial that does the days and months, and that dial does a cycle of several years to keep track of leap years. Keep adding features in that fashion until it can tell you if there are summer or winter Olympic games this year and if Jupiter is in Pisces in August of 2077 and you’ll eventually have the Antikythera mechanism.
It had a single knob on the side that the user would turn, and this would drive an impressively sophisticated set of gears which would move a set of dials on the front and back of the device. One of these dials displays an ancient Greek month/year calendar which includes a complicated un-leap day system, a dial for predicting solar and lunar eclipses, and a big display on the front that shows the position of the planets in the night sky, along with the moon and its phases. It even kept up with the cycle of the Pan-Hellenic games.
Check out a Youtube channel called Clickspring to watch a very talented Australian guy named Chris build a replica of the machine and/or receive a brain massage. Both his metalwork and his videography are sumptuous.