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A half adder circuit has one significant drawback:
since pair of bits can produce an output carry,
in addition to the inputs A and B, we need to account for a possible carry over from a bit of the lower order of magnitude.
Unfortunately, half adder has no support for such carry over input by design.
Therefore, the combination requires not two, but three inputs to make the adder circuit more useful.
The circuit that does the entire job is called a full adder.
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