Digital and analog signals

Answer Key - Grade 8 Science Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari's recorder takes 2000 samples every second, and each sample is stored in 8 bits. How many bits does a 3-second recording need?

   48,000 bits
2. 2.

   Bo's phone takes 1000 samples every second, and each sample is stored in 16 bits. How many bits does a 4-second clip need?

   64,000 bits
3. 3.

   Esme's sensor takes 500 samples every second, and each sample is stored in 12 bits. How many bits does 6 seconds of readings need?

   36,000 bits
4. 4.

   Bits sent: 1, 0, 0, 1, 1. Which pulse did the receiver misread, and why, Jun?

   • The second, since 0.15 is not exactly 0
   • The third, since noise raised a 0 to 0.62
   • The fifth, since 0.85 is below a full pulse
   • No pulse, since digital signals are not misread

5. Read this first

   Lab report, Copying a recording (example data)

   [1] Ren's class compared two ways of copying one recording. [2] They copied an analog tape, then copied that copy, and kept going until they had five generations. [3] They also copied a digital file five times in a row. [4] After each copy, they measured how far the result differed from the original. [5] The tape's difference grew with every generation: 2%, 4%, 7%, 11% and 16%. [6] The digital file's difference stayed at 0% for all five copies. [7] Noise explains the tape results, because each copy added small random changes that the next copy kept as part of its shape. [8] A digital receiver only decides whether each pulse is closer to 0 or to 1, so small changes were thrown away at every step. [9] The class noted that a very noisy cable could still make a receiver misread a pulse, which would flip a bit.

6. 5.

   Which sentence gives the measurements that show the tape copies getting worse, Milo?

   • Sentence 7
   • Sentence 6
   • Sentence 5
   • Sentence 4
7. 6.

   Which sentence explains why the digital copies stayed the same, Noah?

   • Sentence 8
   • Sentence 6
   • Sentence 7
   • Sentence 3
8. 7.

   What does sentence 9 add that sentences 5 to 8 leave out, Pia?

   • Proof that digital copies get steadily worse over time
   • A limit: strong enough noise can still flip a digital bit
   • A sixth measurement of how the tape copies drifted
   • A reason to stop using digital files for recordings

9. Cable test (example data)

   cable length (m)	bits sent	bits misread
   10	10000	0
   50	10000	2
   100	10000	9
   200	10000	38

10. 8.

    Which conclusion does the cable table support best, Ren?

    • A digital signal cannot be misread on any cable
    • More misread bits on longer cables, yet most bits arrived
    • Cable length has no effect on how many errors happen
    • Each bit sent on the 200 m cable was misread

11. Bits per sample at 1000 samples per second (example data)

    bits per sample	brightness levels	bits stored per second
    2	4	2000
    4	16	4000
    8	256	8000

12. 9.

    Going from 4 bits to 8 bits per sample, what changes in the table, Tala?

    • Levels stay the same, but the storage needed doubles
    • Levels go up 16 times, but storage only doubles
    • Levels and storage both go up 16 times over
    • Levels and storage both double when the bits double
13. 10.

    Which statement does the sampling table support, Zee?

    • The copy's error stays the same, but the bits double
    • More samples track the wave better but cost more bits
    • More samples track the wave better at no extra cost
    • Fewer samples follow the wave more closely and save bits