Logic Circuits That Add and Remember · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Circuits that add and remember

Computing · Computer Systems · ages 16-17
Name ______________________   Date ____________

  1. What three inputs does a full adder take?

    • two column bits plus the carry in
    • three bits from the same column
    • sum, carry and clock

  2. A half adder receives 1 and 1. What does it output?

    • sum 1, carry 0
    • sum 0, carry 1
    • sum 1, carry 1

  3. One flip-flop stores exactly one bit.

    Circle one:   True   False

  4. Four chained adders total 0111 and 0001. What is the result?

    • 1000 with no overflow
    • 0000 with overflow
    • 0110 with no overflow

  5. A full adder receives 1, 1 and carry in 1. What are its sum and carry out?

    • sum 0, carry 1
    • sum 1, carry 0
    • sum 1, carry 1

  6. Adding 1011 and 0110 gives sum bits 0001 with a final carry of 1. What does this mean?

    • the answer 0001 fits with room to spare
    • the true answer needs five bits, so the four bit box overflows
    • the adders were wired backwards

  7. A set signal puts 1 into a flip-flop, then the signal goes away. What keeps the stored 1?

    • the AND gate truth table
    • the feedback loop feeding output back to input
    • the carry rippling left

  8. A builder chains four adders but leaves each carry in unconnected. What goes wrong?

    • each column forgets the carry from its right neighbour
    • the circuit runs too fast to read
    • every sum bit flips twice
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Circuits that add and remember W1-mt_zPgkt6zf-i-s1

  1. two column bits plus the carry in · It totals its own column and folds in the carry from the right.
  2. sum 0, carry 1 · Two ones make binary 10, so the sum is 0 with a carry of 1.
  3. True · It holds a single 0 or 1 for as long as feedback feeds it.
  4. 1000 with no overflow · Seven plus one is eight, which fits four bits, and no carry leaves the top.
  5. sum 1, carry 1 · Three ones total binary 11, so sum 1 with carry out 1.
  6. the true answer needs five bits, so the four bit box overflows · A carry out of the top bit is the overflow signal.
  7. the feedback loop feeding output back to input · Feedback recirculates the bit, so it persists after its input has gone.
  8. each column forgets the carry from its right neighbour · The ripple is the whole design. Cut carries make every column but the first untrustworthy.
Worksheet · LightMySky