Answers · Communicating with waves

Analogue and digital signals — answer key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. CQ12 · Practice

Options as numbered on the pupil sheet: 1 — A digital signal; 2 — A digital signal that has picked up noise; 3 — An analogue signal.

Model answer. Signal A varies continuously and takes any value in its range, so it is an analogue signal. Signal B jumps between just two values, on and off, so it is a digital signal. Signal C is the same pulses as B with small wiggles of noise on them: a digital signal that has picked up noise, as it arrives at a repeater. Each pulse is still clearly above or below the half-height line, so it can be regenerated.

A full answer includes

I matched A to an analogue signal.
I matched B to a digital signal.
I matched C to a digital signal that has picked up noise.
I did not match C to an analogue signal because its line is wiggly.

Also accept

A analogue; B digital; C digital with noise

Watch for

“C is analogue, because its line is wiggly.” — C still has only two levels, on and off; the wiggles are noise on the pulses.
“B is analogue, because it copies the sound.” — B has only two values, on and off: that is digital.
“A is digital, because it goes up and down.” — A can take any value in its range, not just a few: it is analogue.

2. CQ13 · Practice

Model answer. An analogue signal varies continuously and can take any value in its range. A digital signal has only a few values, usually just on and off (1 and 0), sent as pulses. Both are carried by the same waves at the same speed, and both pick up noise on the way. Row B.

A full answer includes

I chose row B.
I did not choose row A, where the two descriptions are swapped.

Also accept

Row B

Watch for

“Row A.” — The descriptions are swapped. It is the analogue signal that can take any value, and the digital signal that has only a few.
“Row C.” — Both kinds of signal are carried by the same waves, at the same speed. The difference is in the values they can take.
“Row D.” — A digital signal picks up noise too. The difference is in the values the signals can take.

3. CQ14 · Practice

Options as numbered on the pupil sheet: 1 — Digital; 2 — Analogue.

Model answer. The voltage from the guitar pickup and the height of the water in the rain gauge vary continuously and can take any value, so they are analogue. The remote’s infrared beam is either on or off, and the data wire is either 0 V or 3.3 V, with nothing in between: they have only two values, so they are digital.

A full answer includes

I matched the guitar pickup’s voltage to analogue.
I matched the water in the rain gauge to analogue.
I matched the remote’s flashing infrared beam to digital.
I matched the data wire’s voltage to digital.
I did not match the remote to analogue because infrared is a wave.

Also accept

guitar analogue; rain gauge analogue; remote beam digital; data wire digital

Watch for

“The guitar pickup’s voltage is digital, because it comes from an electric guitar.” — The voltage rises and falls smoothly with the string, by any amount: that is analogue.
“The rain gauge is digital, because its scale has numbers on it.” — The water can stop at any height, between the marks too: it varies continuously.
“The remote’s beam is analogue, because infrared is a wave.” — What matters is the signal: the beam is only on or off, so the signal is digital.
“The data wire is analogue, because a voltage can take any value.” — This voltage is only ever 0 V or 3.3 V, with nothing in between: digital.

4. CQ15 · Practice

Model answer. The voltage can never be 1.5 V, or any other value between the four levels, so it does not vary continuously, as an analogue signal would. A digital signal has only a few possible values: usually two, on and off, but sometimes more. So this signal is digital. What matters is that no value in between is possible, not that there are exactly two.

A full answer includes

I wrote that this signal can take only four values, so it cannot vary continuously.
I wrote that a digital signal has only a few values, not always two.
I wrote that this signal is digital.
I did not write that a digital signal must have exactly two values.

Also accept

only four values, nothing in between, so it is digital; a digital signal has a few values, not always two

Watch for

“The signal is analogue because it changes over time.” — Both kinds of signal change over time. What matters is whether the signal can take any value in its range, or only a few.
“A digital signal must have exactly two values.” — Two is the usual number, but a digital signal can have a few values. What matters is that nothing in between is possible.

5. CQ16 · Practice

Options as numbered on the pupil sheet: 1 — The voltage is measured thousands of times a second; 2 — A laser flashes the code along the fibre as pulses of light; 3 — At the far end the pulses are turned back into a varying voltage; 4 — The microphone turns the voice into a varying voltage; 5 — Each measurement is turned into a code of 1s and 0s.

Model answer. The microphone turns the voice into a varying voltage, an analogue signal. To send it digitally, the voltage is measured many thousands of times a second, and each measurement is turned into a short code of 1s and 0s. A laser flashes the code along the fibre as pulses of light. At the mast, the pulses are turned back into a varying voltage, ready to be sent out.

A full answer includes

I put the microphone first.
I put measuring the voltage second.
I put the codes of 1s and 0s third.
I put the laser flashing the code fourth.
I put turning the pulses back into a varying voltage last.
I did not put the laser before the measuring.

Also accept

microphone; measured; codes of 1s and 0s; laser pulses; turned back into a varying voltage

Watch for

“The microphone gives out pulses directly.” — The microphone gives a varying voltage. It is measured, and the measurements are sent as pulses.
“The laser flashes before the voltage is measured.” — The laser can only flash a code once there is one: first measure, then make the code, then send it.

6. CQ17 · Practice

Model answer. The older monitor sends an analogue signal: the strength of its radio wave varies continuously, copying the cry. The newer monitor sends the same cry as a digital signal. Its microphone’s voltage is measured 8 000 times a second, and each measurement is sent as a code of 1s and 0s. The parent’s unit turns the codes back into a varying voltage, and its speaker turns that into the cry. So a sound can be sent as a digital signal as well as an analogue one, and the pupil is incorrect.

A full answer includes

I wrote that the older monitor sends the cry as an analogue signal.
I wrote that the newer monitor sends the same kind of sound as a digital signal.
I wrote that each code stands for one measurement of the microphone’s voltage.
I wrote that the parent’s unit turns the codes back into a varying voltage for its speaker.
I did not write that the older monitor sends pulses.

Also accept

the older monitor sends the cry as an analogue signal; the newer one sends the same sound as a digital signal: each code is a measurement, turned back into a varying voltage at the parent’s unit

Watch for

“A sound can only be sent as an analogue signal, because it varies smoothly.” — The newer monitor sends the cry as codes of 1s and 0s, each one a measurement of the smoothly varying voltage. A sound can be sent either way.
“The older monitor sends the cry as pulses.” — Its radio wave rises and falls smoothly with the cry: an analogue signal. Only the newer one sends pulses.

7. CQ18 · Practice

Model answer. In each stretch the signal picks up noise. A repeater amplifies an analogue signal, but it cannot tell the noise from the message, so it amplifies both and the noise builds up. A digital signal is regenerated: the repeater decides whether each pulse is on or off and sends a fresh, clean pulse, leaving the noise behind. So a digital signal has an increased range, due to accurate signal regeneration.

A full answer includes

(1) I wrote noise.
(2) I wrote amplified (or boosted).
(3) I wrote regenerated.
(4) I wrote range (or distance).
I did not swap amplified and regenerated.

Also accept

noise; amplified; regenerated; range
noise; boosted; regenerated; distance

Watch for

“The repeater adds the noise.” — The noise is picked up along each stretch of cable; the repeater amplifies it (analogue) or leaves it behind (digital).
“An analogue signal is regenerated and a digital signal is amplified.” — Only a signal with a few values can be read and sent on fresh. An analogue signal is amplified, noise and all.

8. CQ19 · Practice

Model answer. Digital pulses can be rebuilt clean at every repeater, so they can be sent much further without getting noisier: an increased range, due to accurate signal regeneration. And because the receiver only has to tell on from off, the pulses can be very short and close together, so more data is sent every second: an increased rate of transmission of data. The pulses do not travel faster, and they still pick up noise on the way.

A full answer includes

I chose: it can go further, as each repeater rebuilds clean pulses.
I chose: more data can be sent along the same link each second.
I did not choose that the pulses move faster.

Also accept

it can go further, as each repeater rebuilds clean pulses; more data each second

Watch for

“Its pulses move along the link faster than analogue ones.” — They travel at the same speed; more data arrives each second.
“Its pulses pick up no noise at all along the whole link.” — They pick up noise in every stretch; each repeater leaves it behind while it is small enough.

9. CQ20 · Practice

Model answer. The receiver of link Y must measure the exact brightness of the light at every moment. The receiver of link X only has to tell on from off, so the pulses can be made very short and packed very close together: many more of them arrive each second, and so does the data. The light of both links travels at the same speed, both pick up noise, and glass is transparent to both.

A full answer includes

I chose: each pulse need only be read as on or off, so pulses can be short and close together.
I did not choose the reason about speed: both kinds of light travel at the same speed in the fibre.

Also accept

each pulse need only be read as on or off, so pulses can be short and close together

Watch for

“The pulses travel along the fibre faster than the smoothly varying light.” — Light in the same glass travels at the same speed, however it is switched. More pulses arrive each second, not faster ones.
“The pulses pick up no noise at all in the fibre, so no data ever has to be sent twice.” — Digital pulses pick up noise too. The gain is that very short pulses, close together, can still be read as on or off.
“The glass absorbs light whose brightness varies, but lets pulses through.” — Glass is transparent to the light of both links. The difference is in what the receiver has to read.

10. CQ21 · Practice

Options as numbered on the pupil sheet: 1 — Off; 2 — On.

Model answer. (a) Each height above 0.5 becomes on, and every other height becomes off: off, on, off, off, on, on, on, on. (b) Pulse 3 was sent on but arrived at 0.45, below half height, so it was regenerated as off; pulse 6 was sent off but arrived at 0.55, above half height, so it was regenerated as on. The noise was big enough to push them across the half-height line, and the repeater cannot know. (c) The changes are 0.1, 0.2, 0.55, 0.3, 0.1, 0.55, 0 and 0.3: pulse 3 fell from 1.0 to 0.45, and pulse 6 rose from 0 to 0.55. The largest change is 0.55, more than half the full height, and only those two pulses are wrong.

A full answer includes

(a) I matched pulses 2, 5, 6, 7 and 8 to on.
(a) I matched pulses 1, 3 and 4 to off.
(b) I identified pulse 3 as wrong: sent on, regenerated off.
(b) I identified pulse 6 as wrong: sent off, regenerated on.
(b) I wrote that noise pushed them across the half-height line.
(c) Method: for each pulse, I found the difference between the height it left with (1.0 or 0) and the height it arrived with.
(c) Answer: I wrote 0.55.
(a) I did not regenerate the 0.45 pulse as on because it is nearly half.

Also accept

(a) off, on, off, off, on, on, on, on (b) pulses 3 and 6; noise pushed them across half height (c) 0.55

Watch for

“Pulse 3, at 0.45, is regenerated as on, because it is nearly half.” — Below 0.5 means off, however close.
“Pulse 6, at 0.55, is regenerated as off, because it was sent off.” — The repeater cannot know what was sent. Above 0.5 means on.
“Regeneration always gives the pulses that were sent.” — Only while the noise is too small to push a pulse across the half-height line.
“(c) The largest change is 0.45.” — That is the height pulse 3 arrived with. It left at 1.0, so it changed by 1.0 − 0.45 = 0.55.

11. CQ22 · Practice

Model answer. (a) The noise picked up along each stretch arrives at the repeater mixed with the voice. The repeater cannot tell the noise from the voice, so it amplifies both by the same amount: amplifying more makes the hiss louder too, and the next stretch adds more noise on top. Only a digital signal, regenerated at each repeater, leaves the noise behind. (b) Whether a signal is analogue or digital depends on the values it can take, not on what carries it. A voltage on a wire that is only ever 0 V or 5 V is digital; light whose brightness varies smoothly with a sound is analogue. Light and electricity can each carry either kind of signal.

A full answer includes

(a) I wrote that the repeater cannot tell the noise from the voice.
(a) I wrote that it amplifies the noise as much as the voice, so the hiss stays.
(b) I wrote that analogue or digital depends on the values the signal can take, not on what carries it.
(b) I gave an example, such as a voltage that is only on or off (digital), or light whose brightness varies smoothly (analogue).
(a) I did not write that amplifying more makes the voice louder than the hiss.

Also accept

(a) the repeater amplifies the noise with the voice, so the hiss stays (b) it depends on the values the signal can take, not on light or electricity

Watch for

“(a) Amplifying more makes the voice louder than the hiss.” — The hiss is amplified by the same amount as the voice, so it stays just as loud compared with the voice.
“(b) Light is digital because it can be flashed on and off.” — Light can also vary smoothly in brightness, carrying an analogue signal. What matters is the values the signal can take.

12. CQ23 · Practice

Model answer. (a) With repeaters 40 km apart, an on pulse arrives at 1.0 − 0.2 = 0.8 or more, and an off pulse at 0.2 or less. Every on pulse is above half height and every off pulse below it, so each is regenerated right. (b) With repeaters 120 km apart, an on pulse could arrive as low as 1.0 − 0.6 = 0.4, below half height, and be regenerated as off; an off pulse could arrive as high as 0.6 and be regenerated as on. Some pulses would be wrong, and the next repeater cannot know. (c) An on pulse leaves at 1.0 and is read as off once it is no longer above half height, 0.5. So the smallest change that could do it is 1.0 − 0.5 = 0.5. The repeaters must be close enough together that the noise always stays below this.

Checked automatically

(c) Smallest change that could turn an on pulse off: 0.5 (exact value)
- Common wrong answer 0.6 : A change of 0.6 does turn an on pulse off, but a smaller change already does. Where is the half-height line?
- Common wrong answer 0.2 : A change of 0.2 leaves an on pulse at 0.8, still above half height, so it is still read as on.
- Common wrong answer 1 : A change of 1.0 takes an on pulse right down to 0, but a smaller change already makes it off.

A full answer includes

(a) I wrote that an on pulse arrives at 0.8 or more, above half height.
(a) I wrote that an off pulse arrives at 0.2 or less, below half height.
(b) I predicted that some pulses could be regenerated wrongly.
(b) I wrote that an on pulse could arrive as low as 0.4, below half height, and become off.
(b) I wrote that an off pulse could arrive as high as 0.6, above half height, and become on.
(c) Method: I worked out the drop from full height to half height: 1.0 − 0.5.
(c) Answer: I wrote 0.5.
(b) I did not write that regeneration always gives the pulses that were sent.

Also accept

(a) on at 0.8 or more, off at 0.2 or less (b) some pulses wrong: on as low as 0.4, off as high as 0.6 (c) 0.5

Watch for

“Every pulse is lost with repeaters 120 km apart.” — Most pulses still arrive clearly on or off; only those pushed across the half-height line are wrong.
“Nothing changes, because digital signals are always regenerated perfectly.” — Regeneration is accurate only while the noise is too small to push a pulse across the half-height line.
“(c) The smallest change is 0.6.” — A change of 0.6 does turn an on pulse off, but a change of 0.5 already brings it down to half height, which is not above half height.

13. CT2 · Apply

Model answer. (a) The groove varies continuously, copying the sound, so the record stores an analogue signal; the file has only two values, 1 and 0, so it stores a digital signal. (b) Each tape copy copied everything, music and hiss, and added a little more hiss of its own, so after eight copies the hiss had built up, just as noise builds up when an analogue signal is amplified at every repeater. (c) Copying a file reads each 1 or 0 and writes it again cleanly, like a repeater regenerating each pulse. A copy may store a 1 slightly weak or a 0 slightly strong, small changes (noise), but each is still read as the right 1 or 0, so the small changes are left behind and the eighth copy is exactly the same as the first: this is accurate regeneration, the reason for the increased range of digital signals.

A full answer includes

(a) I identified the record as analogue.
(a) I identified the file as digital.
(b) I wrote that each copy copied the hiss already there.
(b) I wrote that each copy added more hiss, so the hiss built up.
(c) I wrote that each copy reads every 1 or 0 and writes it again cleanly.
(c) I wrote that this is like regenerating pulses, so nothing builds up.
(c) I did not write that the file picks up no noise at all.

Also accept

(a) record analogue; file digital (b) hiss copied and added each time (c) regenerated accurately each time

Watch for

“The record is digital, because it is a recording.” — The groove varies continuously, copying the sound: analogue.
“Digital copies are exact because digital signals pick up no noise.” — A copy can pick up small changes (noise), but each 1 or 0 is still read right and written again cleanly, so the noise is left behind.