Worksheet

Digital and analog signals

Grade 8 Science Worksheet - Challenge Me

NameDate

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

  1. Ari's recorder takes 2000 samples a second at 8 bits each and records 6 seconds. A link sends 8000 bits each second. How many seconds to send it all?

  2. Bo's phone records 5 seconds at 1000 samples a second, 16 bits each. A weak connection sends 4000 bits each second. How many seconds to send the clip?

  3. Esme's mic takes 4000 samples a second at 8 bits each and records 3 seconds. The link sends 16000 bits each second. How many seconds to send it all?

  4. Read this first

    Use this

    Cable noise (example data). Pulses are sent as 0 or 1. The cable adds noise of up to 0.3, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  5. A cable adds noise of up to 0.3, up or down, to each pulse. Full pulse is 1, empty is 0. Can it make the receiver misread a bit, Jun?

    • No, since digital signals cannot be misread
    • Yes, since 0.3 is more than the 0 that was originally sent
    • No, since a 0 stays at most 0.3 and a 1 at least 0.7
    • Yes, since any noise changes the pulse heights

  6. Use this

    Cable noise (example data). Pulses are sent as 0 or 1. The cable adds noise of up to 0.6, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  7. A different cable adds noise of up to 0.6, up or down. Full pulse is 1, empty is 0. Can it make the receiver misread a bit, Kira?

    • No, since 0.6 is still less than a full pulse of 1.0
    • Yes, since a 0 pushed up by 0.6 reads above 0.5
    • No, since the receiver ignores noise
    • Yes, but a 1 is the sole pulse that can be misread

  8. Use this

    Two cables (example data). Pulses are sent as 0 or 1. Cable A adds noise of up to 0.35, up or down. Cable B adds noise of up to 0.55, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  9. Cable A adds noise of up to 0.35 and cable B up to 0.55. Full pulse is 1, empty is 0. Which cable can cause a misread, Luz?

    • Cable B only, since 0.55 is more than the 0.5 gap
    • Cable A only, since it is closer to the halfway line
    • Neither, since digital signals ignore noise
    • Both, since any noise can cause a misread

  10. 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.

  11. A classmate says digital copies can never contain an error. Which sentence limits that claim, Milo?

    • Sentence 7
    • Sentence 9
    • Sentence 6
    • Sentence 8

  12. Which claim do the report's numbers support best, Noah?

    • Tape drifted further each copy; the digital file did not
    • Digital files stay exact on a cable with any amount of noise
    • Tape is simply a worse material than a digital file
    • Tape copies get worse by the same amount on each copy

  13. Use this

    Investigation card (test results). Changed: kind of copy (tape or digital file). Measured: difference from the original (%). Kept the same: same recording, same room, 1 copy made of each. Tape: 2. Digital file: 0.

  14. Tala says tape copies are only 2% worse, so noise barely matters. Why can't this test show that?

    • Tape is exactly 2% worse, in any test
    • A digital file should have been measured at 2% too
    • The recording was the same for both, which is not fair
    • It checked one copy; analog noise builds up over many

  15. Use this

    Investigation card (test results). Changed: cable length. Measured: bits misread out of 1000 sent. Kept the same: same signal, same receiver, one trial per cable. 5 m: 0. 50 m: 1. 200 m: 3.

  16. Zee says longer cables always cause more errors. How strong is the evidence from this one test?

    • Strong: digital errors come from long cables alone
    • Strong: the counts rise with length, so the claim is proven
    • Useless: digital signals cannot be misread
    • Weak: tiny counts from one trial each, so repeat it
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Digital and analog signals

Answer Key - Grade 8 Science Worksheet - Challenge Me

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

  1. Ari's recorder takes 2000 samples a second at 8 bits each and records 6 seconds. A link sends 8000 bits each second. How many seconds to send it all?

    12 s

  2. Bo's phone records 5 seconds at 1000 samples a second, 16 bits each. A weak connection sends 4000 bits each second. How many seconds to send the clip?

    20 s

  3. Esme's mic takes 4000 samples a second at 8 bits each and records 3 seconds. The link sends 16000 bits each second. How many seconds to send it all?

    6 s

  4. Read this first

    Use this

    Cable noise (example data). Pulses are sent as 0 or 1. The cable adds noise of up to 0.3, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  5. A cable adds noise of up to 0.3, up or down, to each pulse. Full pulse is 1, empty is 0. Can it make the receiver misread a bit, Jun?

    • No, since digital signals cannot be misread
    • Yes, since 0.3 is more than the 0 that was originally sent
    • No, since a 0 stays at most 0.3 and a 1 at least 0.7
    • Yes, since any noise changes the pulse heights

  6. Use this

    Cable noise (example data). Pulses are sent as 0 or 1. The cable adds noise of up to 0.6, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  7. A different cable adds noise of up to 0.6, up or down. Full pulse is 1, empty is 0. Can it make the receiver misread a bit, Kira?

    • No, since 0.6 is still less than a full pulse of 1.0
    • Yes, since a 0 pushed up by 0.6 reads above 0.5
    • No, since the receiver ignores noise
    • Yes, but a 1 is the sole pulse that can be misread

  8. Use this

    Two cables (example data). Pulses are sent as 0 or 1. Cable A adds noise of up to 0.35, up or down. Cable B adds noise of up to 0.55, up or down. The receiver reads above 0.5 as 1 and below 0.5 as 0.

  9. Cable A adds noise of up to 0.35 and cable B up to 0.55. Full pulse is 1, empty is 0. Which cable can cause a misread, Luz?

    • Cable B only, since 0.55 is more than the 0.5 gap
    • Cable A only, since it is closer to the halfway line
    • Neither, since digital signals ignore noise
    • Both, since any noise can cause a misread

  10. 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.

  11. A classmate says digital copies can never contain an error. Which sentence limits that claim, Milo?

    • Sentence 7
    • Sentence 9
    • Sentence 6
    • Sentence 8

  12. Which claim do the report's numbers support best, Noah?

    • Tape drifted further each copy; the digital file did not
    • Digital files stay exact on a cable with any amount of noise
    • Tape is simply a worse material than a digital file
    • Tape copies get worse by the same amount on each copy

  13. Use this

    Investigation card (test results). Changed: kind of copy (tape or digital file). Measured: difference from the original (%). Kept the same: same recording, same room, 1 copy made of each. Tape: 2. Digital file: 0.

  14. Tala says tape copies are only 2% worse, so noise barely matters. Why can't this test show that?

    • Tape is exactly 2% worse, in any test
    • A digital file should have been measured at 2% too
    • The recording was the same for both, which is not fair
    • It checked one copy; analog noise builds up over many

  15. Use this

    Investigation card (test results). Changed: cable length. Measured: bits misread out of 1000 sent. Kept the same: same signal, same receiver, one trial per cable. 5 m: 0. 50 m: 1. 200 m: 3.

  16. Zee says longer cables always cause more errors. How strong is the evidence from this one test?

    • Strong: digital errors come from long cables alone
    • Strong: the counts rise with length, so the claim is proven
    • Useless: digital signals cannot be misread
    • Weak: tiny counts from one trial each, so repeat it