Tricky Circuit

Full adder: three inputs, two answers

Pass the carry to the next place

A full adder adds two bits, binary digits 0 or 1, and Cin (Carry input), the incoming carry from the previous place. It produces a sum bit here and a carry-out for the next place.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

Ideal binary logic: 0 means low and 1 means high, not a measured voltage. Supply behavior, current, output loading and response delay are omitted; diagrams show functions, not chip pinouts.

A and B are data bits; Cin means Carry input, the incoming carry; S is sum and Cout carry-out. T = A + B + Cin; T = S + 2Cout. XOR means Exclusive OR: it gives 1 for differing input bits. ⊕ and =1 label that function. Each carry is one unit of its destination place, not an extra voltage.

Difficulty

  1. Build · Build it

    Power on with A = 0, B = 0 and Cin = 1. Get S = 1 and Cout = 0.

    Need a hint?

    A = 0; B = 0; Cin = 1 → S = 1; Cout = 0

  2. Explore · Change the inputs

    Set A = 1, B = 1 and Cin = 0. Get S = 0 and Cout = 1.

    Need a hint?

    A = 1; B = 1; Cin = 0 → S = 0; Cout = 1

  3. Solve it · Solve the challenge

    Set A = 1, B = 1 and Cin = 1. Get S = 1 and Cout = 1.

    Need a hint?

    A = 1; B = 1; Cin = 1 → S = 1; Cout = 1

Extra reading and circuit recipes

Pass the carry to the next place

A calculator repeats this block across many places. Each block handles one small addition and passes its carry toward the next larger place.

T = A + B + Cin; T = S + 2Cout; S = A ⊕ B ⊕ Cin

The sum bit answers whether the total is odd. Carry-out answers whether the total reaches two or more; together they cover totals from zero to three.

A useful pattern

All three inputs high total three: binary 11. A single sum bit cannot represent it alone.

Beyond the model

Two half adders plus OR can build a full adder. OR gives 1 if at least one input is 1; AND gives 1 only if both are 1. The diagram marks them ≥1 and &. Real carries take time to propagate; this model calculates instantly.

A useful trap to avoid

Carry-in and carry-out are separate signals. Carry-in is not feedback memory, and carry-out is not always a copy of it.

A = 0, B = 0. Cin changes from 0 to 1. The result becomes…

  1. S = 1, Cout = 0
  2. S = 0, Cout = 1
  3. S = 1, Cout = 1
Read more

The total rises from zero to one. Only the units-place sum is needed.

Build it

Set A = 0, B = 0, Cin = 1. The incoming carry alone makes total 1.

T = 1; S = 1; Cout = 0

Change the inputs

Set A = 1, B = 1, Cin = 1. Total 3 splits into sum 1 and carry-out 1.

T = 3; S = 1; Cout = 1

Try another path

Keep Cin fixed and exchange A with B. Then keep A and B high and flip Cin: compare the sum change with the carry-out.

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