Tricky Circuit

Half adder: sum and carry

Make a tiny binary calculator

A half adder adds two bits, binary digits 0 or 1. The sum bit gives the current place; a carry bit sends an extra unit to the next place, worth twice as much.

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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 inputs, T their ordinary total, S the sum bit and C the carry. T = S + 2C. For two high inputs, T = 2 but S = 0 and C = 1: binary 10. ⊕ denotes XOR, Exclusive OR, which gives 1 for different bits.

Difficulty

  1. Build · Build it

    Power on with A = 0 and B = 1. Get sum S = 1 and carry C = 0.

    Need a hint?

    A = 0; B = 1 → S = 1; C = 0

  2. Explore · Change the inputs

    Set A = 1 and B = 1. Get sum S = 0 and carry C = 1.

    Need a hint?

    A = 1; B = 1 → S = 0; C = 1

  3. Solve it · Solve the challenge

    Set A = 0 and B = 0. Get sum S = 0 and carry C = 0.

    Need a hint?

    A = 0; B = 0 → S = 0; C = 0

Extra reading and circuit recipes

Make a tiny binary calculator

You only need two output lamps to count from zero to two. One shows the units place; the other shows the twos place.

T = A + B; T = S + 2C; S = A ⊕ B; C = A × B

The two bits together encode the whole result. Read carry first and sum second; their place values are two and one.

A useful pattern

The sum bit follows XOR, while carry is 1 only when both inputs are 1. Two different logic functions describe one addition.

Beyond the model

A half adder cannot accept a carry from a previous place. That missing third input is the reason the next circuit is called a full adder.

A useful trap to avoid

The result of 1 + 1 is not lost when the sum lamp turns off. Carry contains the twos-place part of the answer.

A = 1 and B = 1. Which two-bit result is correct?

  1. 01
  2. 10
  3. 11
Read more

The ordinary total is two. In binary, the carry is 1 and the sum bit is 0, written in that order as 10.

Build it

Set A = 0, B = 1. Read total 1, sum 1, carry 0.

T = 1; S = 1; C = 0

Change the inputs

Set A = 1, B = 1. Read total 2, sum 0, carry 1.

T = 2; S = 0; C = 1

Try another path

Swap A and B for every input pair. Addition gives the same result whichever input supplies the first 1.

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