carlgrace
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You can do it with capacitors. Charge up two caps in parallel, then put them in series. Charge in conserved and voila! You have an adder. Flip some of the capacitors around before you put them in series and voila! You have a subtractor.
Their are lots of practical problems with this technique though. The principal issue is charge sharing with unavoidable parasitics. This means your addition will not be accurate (and will be hard to predict).
That's why op amps are used in this type of circuit. Virtual grounds are very nice things.
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