C++ Programming Tutorial #8 : Boolean logic gates : Building an adder circuit.
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Here I demonstrate how addition may be accomplished using the fundamental circuitry the most primitive processor imaginable. I take as given, and roughly explain the electronics behind, AND, OR and NOT "gates". We build an XOR gate and then design a 1 bit adder that supplies a left carry. Building upon the 1 bit adder, we create a fully functioning adding circuit taking 3 inputs (right carry, and two inputs for the bit being added) and providing two outputs (the result of the addition and a left carry).
It was good that I finally got to this as there was a bug in my circuit which has now been repaired.