Logic Circuits That Add and Remember
The half adder and full adder that turn gates into binary arithmetic with a carry, and the flip-flop that holds one bit after its input has gone. Feedback is what turns a circuit into storage.
What a learner can do afterwards
- Give the sum and carry a full adder produces for each combination of its three inputs
- Chain full adders to add two four-bit numbers and show where overflow appears
- Explain what a flip-flop holds and why feedback is needed to hold it
1 · Read
Gates alone only decide, but wired together they can calculate. A half adder adds two bits and reports two answers: the sum bit and the carry bit. Adding 1 and 1 gives sum 0 with carry 1, exactly like carrying into the next column on paper.
A full adder handles one column completely: it adds the two column bits plus the carry in from the column before. Feeding 1, 1 and carry in 1 gives sum 1 with carry out 1, since three ones make binary 11. Chain four full adders and each carry out becomes the next carry in, rippling left.
A carry out of the leftmost column has nowhere to go, and that is overflow. Adding 1011 and 0110 gives sum bits 0001 with a final carry of 1, so the true answer needs five bits and a four bit box overflows. No final carry means the answer fits.
A flip-flop is the part that remembers: it holds one bit by feeding its output back to its input. Without that feedback loop, a circuit output only mirrors its present input, so the bit vanishes the moment the input changes.
Adders total each column with carries, overflow is the homeless final carry, and feedback is what holds a bit.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.