HS-PS4-2: Evaluating Questions About Digital Transmission and Storage
In plain English: HS-PS4-2 is the NGSS high school performance expectation that asks students to evaluate questions about the advantages of sending and storing information in digital form. Students test claims about noise, exact copies and error checks with data, and weigh disadvantages such as easy deletion and theft. It is usually taught in Physics or Physical Science.
Evaluate questions about the advantages of using a digital transmission and storage of information.
Clarification Statement: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft.
Next Generation Science Standards · Disciplinary Core Idea: Waves and Their Applications in Technologies for Information Transfer · Official standard
Students learn how information such as a photo, a song or a text message becomes a string of bits, how those bits travel as pulses of voltage, light or radio waves, and why a receiver that only has to tell a 1 from a 0 can recover a message that noise has distorted. They compare this with analog signals and analog copies, where every amplifier and every copy adds noise that cannot be removed. The core of the lesson is the practice named in the standard: students evaluate questions. They sort questions into ones that evidence can answer, ones that need revising because they are vague or rest on a false premise, and ones about values or policy, and they rewrite weak questions so that data can answer them.
The NGSS Clarification Statement says: "Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft." NGSS gives no Assessment Boundary for HS-PS4-2. The lesson therefore keeps the math to counting bits, transfer times, simple parity and repetition checks, and signal-to-noise ratios read from data; the details of compression methods and encryption are beyond this standard. Every data set on this page is invented for teaching and labeled as invented, with values chosen to match real devices.
Learning Objectives
By the end of this lesson, students will be able to:
Describe how an image or a sound is digitized into bits and sent as a series of wave pulses
Explain with a threshold model why digital signals can be regenerated after noise while analog signals keep the noise they pick up
Use data on copy generations, transfer times and error checks to evaluate claims about digital storage and transmission
Evaluate questions about digital information as testable, in need of revision, or about values, and rewrite weak questions so evidence can answer them
Weigh advantages of digital information against disadvantages such as easy deletion, security and theft
Prior Knowledge Required
Students should already be comfortable with:
Digitized signals sent as wave pulses are a reliable way to encode and transmit information MS-PS4-3
Waves carry energy and information, and a wave can be described by its amplitude and frequency
Using units to guide multi-step calculations HSN.Q.A.1
Multiplying probabilities of independent events HSS.CP.A.2
Show two versions of the same family photo: a print from 1990 that has been photocopied five times in a row, and a phone photo that has been forwarded by text message five times. Ask students to look closely at both before any explanation.
Warm-Up Prompt
"Write three questions you would want answered before deciding how a family should store and share its photos for the next 50 years. Put a star next to the question you think evidence could answer."
Collect the questions on sticky notes and keep them: students return to them in Guided Practice and at Closure. Expect a mix of testable questions ("Does the photo lose detail each time it is forwarded?"), vague ones ("Is digital better?") and value questions ("Is it sad to lose printed albums?"). All three kinds are useful to discuss.
Direct Instruction15-20 minutes
From information to bits to pulses. A picture is digitized by dividing it into pixels and storing each color as a number; a sound is digitized by measuring the pressure (sampling) many thousands of times per second and rounding each sample to one of 2n levels, where n is the number of bits per sample. The numbers are written in binary, and each bit is sent as a pulse: a high or low voltage in a copper wire, a flash of light in an optical fiber, or a change in a radio wave. Noise from heat, nearby wires or other signals changes the height of each pulse a little. The receiver only asks one question per pulse, "above or below the threshold?", so as long as the noise stays smaller than half the gap between the two levels, it reads every bit correctly and can send out a fresh, clean pulse (Diagram 1). An analog signal has no threshold: the exact voltage is the message, so an amplifier boosts the noise together with the signal, and the noise from every stage adds up. The same is true of copies: each analog copy adds its own noise (Diagram 2), while a digital copy reproduces the bits themselves.
Signal-to-noise ratio (SNR) compares signal power with noise power and is usually given in decibels (dB). When the noise power doubles, the SNR drops by about 3 dB; when it grows ten times, the SNR drops by 10 dB. If every copy or cable segment adds the same amount of independent noise, the noise power after k stages is k times that of one stage, so the SNR falls by 10 log10(k) dB.
Digitizing a photo (storage)
A phone camera takes a 4000 × 3000 pixel photo and stores 8 bits for each of red, green and blue (24 bits per pixel) before compression.
Result: 4000 × 3000 × 24 = 288,000,000 bits. Dividing by 8 bits per byte gives 36,000,000 bytes = 36 MB. Question worth asking: how much of that detail does compression keep?
Transfer time (transmission)
The same photo is uploaded over a home connection of 100 Mbit/s (megabits per second), first uncompressed and then as a 3.0 MB compressed file.
Result: Uncompressed: 288,000,000 bits ÷ 100,000,000 bits/s = 2.88 s. Compressed: 3.0 MB × 8 = 24,000,000 bits, so 0.24 s. Watch the units: file sizes are usually in bytes, link speeds in bits.
A chain of 100 cable segments
An analog signal leaves the first segment with an SNR of 60 dB, and each of 100 segments adds the same amount of noise. A digital version uses pulses of 0 V and 1.0 V, and a repeater at the end of each segment reads and resends every pulse; the noise per segment never exceeds 0.2 V.
Result: Analog: noise power × 100, so SNR = 60 - 10 log10(100) = 40 dB after 100 segments. Digital: 0.2 V is less than the 0.5 V margin, so every repeater reads every bit correctly and the message arrives unchanged.
Copies of copies (storage)
A first-generation cassette copy of a master tape measures an SNR of 56 dB. Each new copy is made from the previous copy and adds the same amount of tape noise.
Result: Sixth generation: 56 - 10 log10(6) = 48.2 dB, a loss of 7.8 dB (Diagram 2). A digital file copied six times has the same bits as the first file, which a checksum can confirm.
Detecting an error with a parity bit
The letter S is stored as the 7-bit code 1010011. An even-parity bit is added so that every byte has an even number of 1s. The receiver gets 10110110.
Result: 1010011 has four 1s, so the parity bit is 0 and the byte sent is 10100110. The received byte has five 1s (odd), so the receiver knows a bit flipped and asks for the byte again.
After each example, ask two evaluation questions: "What question does this example answer?" and "What question does it leave open?" For example, the parity example shows that one flipped bit is detected, but it leaves open what happens when two bits flip. Keep a running list of open questions on the board.
Guided Practice15 minutes
Pairs learn three tests for a question and apply them to five questions about digital information. Then they revise the weakest ones and return to their warm-up sticky notes.
Three tests for evaluating a question
Test
Ask
A question that fails it
Answerable with evidence
Could a measurement, data set or calculation answer it?
Should everyone stop using paper?
Clear and specific
Does it name what is compared, under what conditions, and what counts as the answer?
Is digital storage good?
Fair premise
Is everything the question assumes actually true?
Why are digital copies perfect?
Evaluate question (a): "Is digital storage good?" It is vague: good for what, compared with what? A revision: "Over ten years, which loses fewer family photos: a single hard drive or prints in an album?"
Evaluate question (b): "How many copy generations does it take before an analog audio copy falls below 48 dB, if the first copy measures 56 dB and each copy adds equal noise?" It is testable and specific. Use Diagram 2 to answer it (generation 7).
Evaluate question (c): "Why are digital copies perfect?" The premise is not always true: a copy is exact only when every bit is read correctly, which is why systems use checksums. Rewrite it so that it asks how often copies fail and how failures are detected.
Evaluate question (d): "Does a file downloaded 1,000 times from a server have the same checksum every time?" It is testable; describe the data you would collect.
Evaluate question (e): "Should everyone stop using paper?" It is a value and policy question. Science can inform it (by answering questions like (a) and (d)) but cannot settle it alone.
Pick two of your warm-up questions, apply the three tests, and rewrite one so data could answer it.
Independent Practice10-15 minutes
Each student analyzes an invented test of a long cable link. The same message was sent through 1, 2, 4, 8 and 16 cable segments, once as an analog signal and once as digital pulses with a regenerating repeater after each segment. Each segment adds the same amount of noise.
Independent practice data (invented): analog and digital links of different lengths
Segments
Analog SNR at the end (dB)
Digital bits misread (out of 1,000,000)
1
62.0
0
2
59.0
0
4
56.0
0
8
53.0
0
16
50.0
0
Students answer and evaluate three questions. (1) "How much does the analog SNR fall each time the number of segments doubles?" This is answerable from the table: 3.0 dB per doubling, because the noise power doubles. (2) "Did the digital link make any errors?" The table answers it only for these 1,000,000 bits; a zero count does not prove the error rate is exactly zero. (3) "Would the digital link still be error-free with 1,000 segments?" The data cannot answer it; students describe the investigation that could. They finish with two sentences stating which advantage of digital transmission the data support.
Closure5 minutes
Exit ticket: "Write one question that could test an advantage of storing a school yearbook digitally and one that probes a disadvantage. For each, name the evidence that would answer it." Strong answers name a measurement (copies compared by checksum, the time to send the files, how long a lost file takes to restore) rather than an opinion. Return the warm-up sticky notes and ask students to mark each one as testable, needs revising, or value question.
Differentiation Strategies
For Struggling Students
Give a sorting mat with three columns (testable, needs revising, value or policy) and one example card already placed in each column
Provide a unit ladder on a card: 1 byte = 8 bits, 1 MB = 1,000,000 bytes, Mbit/s = 1,000,000 bits per second
Start the threshold model with whole-number voltages (0 V and 10 V, threshold 5 V) before moving to 0 V and 1.0 V
For Advanced Students
Ask students to design a code that can correct, not just detect, a single flipped bit, and compare its extra bits with a repetition code
Have students estimate how many generations of analog copies it takes to lose 10 dB and check the answer against 10 log10(k)
Ask students to write a question that challenges the premise of a claim in a technology advertisement and describe the data that would answer it
Assessment Guidance
What to Look For
Check that students can say why a threshold lets a receiver recover bits, instead of saying only that "digital is better." Look for questions that name what is compared and what would be measured. Listen for the false premise that digital copies can never fail, and for confusion between bits and bytes in transfer-time problems. Strong evaluations mention at least one disadvantage (deletion, security, theft) and say what evidence would show how serious it is.
02
Classroom Activities
3 Activities
1
Light-Pulse Messages: Analog Versus Digital
25 minGroups of 3
Groups send the digits of a phone-style number across the room with a phone flashlight, first as an analog signal (the digit is the brightness) and then as a digital signal (the digit is four on-off pulses). A second phone with a light-meter app is the receiver. Groups add noise and compare how many digits arrive correctly.
Procedure
Analog: the sender covers the flashlight with 0 to 9 sheets of wax paper to show the digits 9 down to 0, and the receiver reads the light meter and converts the reading with a calibration table made at 1 m in a dark room.
Digital: the sender writes each digit in 4-bit binary (4 bits give 16 patterns, enough for the 10 digits; 3 bits give only 8) and sends it as four 1-second slots, light on for 1 and off for 0. The receiver reads each slot as above or below a threshold halfway between the dark and bright readings.
Send the same 20 digits each way in three conditions: lights off at 1 m, room lights on at 1 m, room lights on at 3 m.
Safety: never shine the flashlight into anyone's eyes, and keep walkways clear of cords and bags.
Sample Data (invented)
Digits received correctly out of 20. Analog: 20 (lights off, 1 m), 11 (lights on, 1 m), 4 (lights on, 3 m). Digital: 20, 20 and 19; the one wrong digit came when a student walked through the beam during a pulse.
Discussion Questions
The analog method lost the most digits at 3 m with the room lights on. Why does extra background light spoil the calibration table but not the threshold?
The digital method took 4 seconds per digit instead of 1. Evaluate this question from a classmate: "Is digital always faster?" What would you need to know to answer it?
Write one question the data cannot answer yet, and describe the trial that would answer it.
Modification for Distance Learning
Students run the digital version at home with a family member and one phone, or analyze the sample data above and post their evaluation of the "Is digital always faster?" question to the class board.
2
Question Sort and Upgrade
20 minGroups of 3-4
Each group gets 12 question cards about digital information. They sort the cards with the three tests from Guided Practice, then upgrade every card that needs revising into a question that evidence could answer.
The 12 Cards
How many times can an MP3 file be copied before any of its bits changes?
Is digital music better than analog music?
After five photocopy generations, how many of the 20 gray steps on a test chart can still be told apart?
Why is digital storage perfect?
How long does it take to send a 25 MB file over a 10 Mbit/s link?
Should the school library throw away its printed yearbooks after scanning them?
How does the fraction of misread bits change as the light-pulse receiver moves from 1 m to 5 m?
Can a deleted file be recovered from a cloud backup, and for how many days?
Are hackers a problem?
How many bits does one second of telephone-quality audio (8,000 samples per second, 8 bits per sample) take?
Does adding a parity bit let a receiver detect every error?
Which is safer, a hard drive or a shoebox?
Teacher Key
Testable with evidence or calculation: cards 1, 3, 5, 7, 8, 10 and 11 (7 cards). Needs revising: 2 and 12 (vague: better or safer in what way, against what?), 4 (false premise) and 9 (vague) (4 cards). Value or policy: card 6 (1 card), although questions like card 8 can inform it. Card 5 works out to 20 s and card 10 to 64,000 bits, so students see that some testable questions are answered by calculation, not only by experiment.
Discussion Questions
Which of your upgraded questions tests a disadvantage of digital information (deletion, security or theft)?
Card 4 and card 1 are about the same idea. Why can data answer card 1 but not card 4?
Pick the card your group would investigate first and explain why its answer matters to a real decision.
Challenge Variation
Groups write a thirteenth card that challenges the premise of an advertisement for a cloud storage service, then trade cards with another group for evaluation.
3
Museum Archive Decision Stations
25 minGroups of 3-4
An invented town museum owns 800 glass-plate photographs from about 1900 and is deciding whether to scan them and how to keep the files. Four stations hold invented data. At each station, groups write two questions the data can answer and one it cannot, then answer what they can. Groups rotate every 6 minutes.
Station Data (invented)
Station 1, storage: each plate is scanned at 6000 × 4000 pixels with 16 bits for each of three colors (48 bits per pixel), which is 144 MB per scan and 115.2 GB for all 800.
Station 2, copies: the files were copied to four drives, and a checksum of each copy was compared with the original. Copies 1, 2 and 4 matched; copy 3, on an old USB stick, did not match because of a read error, and was made again.
Station 3, risks: a five-year log from a similar invented museum: 2 accidental deletions (one restored from a backup, one lost), 1 stolen laptop holding unencrypted copies, 1 failed hard drive (no loss, because a second copy existed) and 3 glass plates cracked during handling.
Station 4, sharing: a university asks for the whole collection. Over a 200 Mbit/s connection the 115.2 GB takes 4,608 s, about 77 minutes; mailing a drive takes 2 days.
Discussion Questions
Station 2 shows one digital copy failing. Does this weaken or support the claim that digital information can be copied reliably? Consider what the checksum did.
Station 3 lists risks for both the files and the glass plates. Which risks exist only because the information is digital?
Write one question the museum board should ask before deciding, and explain which station would help answer it.
Modification for Distance Learning
Post each station as a slide. Groups work in breakout rooms and add their questions to a shared document with one column per station, then vote on the most useful question.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Reading Noisy Digital Pulses with a Threshold
Eight bits sent as pulses of 0 V and 1.0 V (dashed line) arrive with noise (dots). The receiver reads each dot as 1 if it is above the 0.5 V threshold and 0 if it is below, so all eight bits are recovered even though no received voltage equals the voltage sent. The largest error here is 0.27 V, smaller than the 0.5 V margin. Values are invented and drawn to scale.
Diagram 2: Analog Copies of Copies Lose Signal-to-Noise Ratio
Invented model data for cassette copies, each made from the one before and each adding equal tape noise, drawn to scale. The SNR falls from 56.0 dB for the first copy by 10 log10(k) dB, so the noise can never be removed by later copies. A digital file copied the same way keeps the same bits.
04
Homework Assignment
~30 min
HS-PS4-2 Homework: Evaluating Questions About Digital Information
Directions: All data are invented for practice, with values chosen to match real devices. Use 1 byte = 8 bits, 1 MB = 1,000,000 bytes and 1 GB = 1,000 MB. Show units in every calculation. Where a problem asks you to evaluate a question, say whether evidence can answer it, whether it is clear, and whether its premise is true.
Part 1: Digitizing and Sending Information (Problems 1-2)
A security camera records 1280 × 720 pixel frames with 24 bits per pixel at 30 frames per second. (a) Find the bit rate of the uncompressed video in Mbit/s. (b) The building's upload link carries 20 Mbit/s. By what factor must the video be compressed to fit? (c) A classmate asks, "Why do cameras compress video?" Rewrite the question so that data could answer it.
A signal travels through 50 cable segments that each add the same amount of noise. (a) The analog version has an SNR of 74 dB after the first segment. Find its SNR after all 50. (b) The digital version is regenerated after each segment, and each segment misreads a bit with probability 1 in 1,000,000,000. Find the probability that a given bit is misread somewhere along the link, and the expected number of wrong bits in a 1,000,000,000-bit file. (c) Evaluate the question "Is the digital link error-free?" and say what the link designer should ask instead.
Part 2: Copies, Errors and Checks (Problems 3-4)
The letters H and I have the 7-bit codes 1001000 and 1001001. (a) Add an even-parity bit to each and write the two bytes sent. (b) The receiver gets 10010000 and 10011011. Which byte shows an error, and how can the receiver tell? (c) Can the receiver tell which bit flipped? What could it do next?
A class photocopies a printed 20-step gray chart again and again and counts how many steps can still be told apart (invented data): generations 1 to 6 give 20, 18, 15, 13, 11 and 9 steps. A scanned file of the chart, copied six times, still shows all 20 steps. (a) Graph both data sets on one set of axes. (b) Find the average number of steps lost per photocopy generation from generation 1 to 6. (c) A classmate asks, "Will generation 10 show zero steps?" Evaluate the question: can the data answer it, and what assumption would you need?
Part 3: Evaluating Questions and Trade-offs (Problems 5-6)
A historical society wants to digitize 1,500 cassette tapes of interviews, each holding 60 minutes of sound, at 44,100 samples per second and 16 bits per sample in mono. (a) Find the bit rate. (b) Find the storage needed for one tape and for all 1,500 tapes in GB. (c) The society plans to keep 3 copies. How much storage is that in TB (1 TB = 1,000 GB)? (d) Evaluate these board members' questions: "Will the digital files sound exactly like the tapes do today?", "Who will be able to read the files?", "Is digitizing worth it?" Revise the weakest one.
An office keeps its files on hard drives. Suppose each drive has a 3% chance of failing in a given year (an invented but realistic figure) and failures are independent. (a) Find the chance of losing the files in a year with one drive, two drives holding the same files and three drives. (b) A manager says the calculation answers the question "Are our files safe?" Evaluate this claim: name two risks from the Clarification Statement that the calculation ignores, and explain why the independence assumption may fail (for example, all drives in one room).
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Calculations with Units
Bits, bytes, rates and probabilities computed correctly with units shown
Correct method with one unit or arithmetic error
Evaluating Questions
Each question judged on evidence, clarity and premise, with a reason
Questions judged without reasons, or only one test applied
Revised Questions
Revised questions name what is compared and the evidence that would answer them
Revision is clearer but still cannot be answered with data
Advantages and Disadvantages
Uses data to support an advantage and names a relevant disadvantage (deletion, security or theft)
Mentions advantages or disadvantages without tying them to data
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data sets are invented, with values chosen to match real devices. Use 1 byte = 8 bits and 1 MB = 1,000,000 bytes. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A student wants to investigate digital storage. Which question can be answered with evidence from an investigation?
Answer: B
Choice B names what is copied, how many times and what is measured, so a checksum or pixel comparison answers it. Choice A uses "better" without saying better in what way. Choice C is a value question. Choice D rests on a false premise: digital files can be lost or corrupted.
Question 2 of 20 · Multiple Choice
An uncompressed image is 1920 × 1080 pixels with 24 bits per pixel. How much storage does it need?
Answer: C
1920 × 1080 × 24 = 49,766,400 bits, and dividing by 8 gives 6,220,800 bytes, about 6.2 MB. Choice A is the number of bits labeled as bytes. Choice B forgets the three color channels (3 bytes per pixel). Choice D divides by 8 a second time.
Question 3 of 20 · Multiple Choice
How long does it take to send a 400 MB video over a 50 Mbit/s connection, ignoring delays?
Answer: D
400 MB × 8 = 3,200 Mbit, and 3,200 Mbit ÷ 50 Mbit/s = 64 s. Choice A divides megabytes by megabits per second without converting bytes to bits. Choice B divides the rate by the size, and choice C multiplies them.
Question 4 of 20 · Multiple Choice
Why can a repeater on a digital line send out a clean signal while an amplifier on an analog line cannot?
Answer: A
Noise changes the height of every pulse, but as long as it is smaller than half the gap between levels, the bit is read correctly and regenerated. Choice C is false: digital pulses pick up noise too, as in Diagram 1. Choice B confuses the form of the signal with its speed. Choice D is wrong because an amplifier cannot tell noise from signal.
Question 5 of 20 · Multiple Choice
A first-generation analog copy has an SNR of 48 dB. Each later copy is made from the previous one and adds the same amount of noise. What is the SNR of the fourth-generation copy?
Answer: B
After four generations the noise power is 4 times that of one copy, so the SNR drops by 10 log10(4) ≈ 6.0 dB, to 42.0 dB. Choice A subtracts 3 dB for each of the four copies instead of using the total noise. Choice C drops only 3 dB, and choice D assumes analog copies do not add noise, which is true only of digital copies.
Question 6 of 20 · Multiple Choice
Each byte below was sent with an even-parity bit, so it should contain an even number of 1s. Which received byte shows that an error happened?
Answer: D
11100011 has five 1s, an odd number, so at least one bit flipped. Choices A, B and C each have four 1s, which passes the parity test. Passing the test does not prove that a byte is correct.
Question 7 of 20 · Multiple Choice
A receiver uses an even-parity bit to check each byte. Which error will it NOT detect?
Answer: C
Two flips change the count of 1s by an even number, so the byte still passes the test. One flip or three flips change the count by an odd number and are detected (choices A and D), and a flipped parity bit (choice B) makes the count odd as well.
Question 8 of 20 · Multiple Choice
A sender repeats every bit three times, and the receiver decodes each group of three by majority vote. It receives 110 001 111 010. What message does it decode?
Answer: A
Majority vote: 110 → 1, 001 → 0, 111 → 1, 010 → 0, so the message is 1010. Choice B reads the last group as 1. Choice C takes the minority bit in every group, and choice D reads each group by its last bit only.
Question 9 of 20 · Multiple Choice
The Clarification Statement names easy deletion, security and theft as disadvantages. Which question best tests one of these disadvantages?
Answer: D
Choice D asks about deletion and names data that would answer it. Choice B is vague (expensive compared with what?) and is about cost, not one of the named disadvantages. Choices A and C ask about capacity and speed, which relate to advantages.
Question 10 of 20 · Multiple Choice
A sound card stores each sample with 5 bits. How many different levels can each sample take?
Answer: B
n bits give 2n patterns, and 25 = 32. Choice A counts the bits themselves. Choice C multiplies 5 by 2, and choice D squares 5 instead of raising 2 to the fifth power.
Question 11 of 20 · Multiple Choice
Light in an optical fiber loses 0.2 dB of power per kilometer. What fraction of the light power is left after 50 km?
Answer: A
The total loss is 0.2 × 50 = 10 dB, and a 10 dB loss leaves one tenth of the power, 10%. Choice B treats the 10 dB as a 10% loss. Choice C is the fraction left after 20 dB (100 km). Choice D is roughly a 3 dB loss, which is 15 km.
Question 12 of 20 · Multiple Choice
A student asks: "Since digital files never degrade, why do libraries bother keeping backup copies?" What is the best evaluation of this question?
Answer: C
Evaluating a question includes checking what it assumes. The bits of a correct copy are exact, but files can still be deleted, stolen or lost when a drive fails, which is the reason for backups. Choice D repeats the false premise. Choice B is wrong because the revised question can be answered with data. Choice A judges the topic, not the question.
Question 13 of 20 · Multiple Choice
A team copies an audio recording five times by analog tape and five times as a digital file (invented data). The analog SNR is 58.0, 55.0, 53.2, 52.0 and 51.0 dB for generations 1 to 5; every digital copy has the same checksum as the original. Which conclusion do the data best support?
Answer: B
Choice B describes only what was measured: a drop from 58.0 to 51.0 dB and matching checksums. Choice A is about listeners, which the data do not test. Choice C goes far beyond five copies. Choice D is false: the losses shrink (3.0, 1.8, 1.2, 1.0 dB) because each copy adds a smaller share of the total noise.
Question 14 of 20 · Multiple Choice
A memory card holds 128 GB (1 GB = 1,000 MB). About how many 6 MB photos fit on it?
Answer: D
128 GB = 128,000 MB, and 128,000 ÷ 6 ≈ 21,333 photos. Choice A multiplies instead of dividing. Choice B uses 1 GB = 100 MB. Choice C multiplies by 8 as if converting to bits, which does not apply because both sizes are in bytes.
Question 15 of 20 · Short Answer
A parent asks: "Is digital better for keeping our family photos?" Evaluate the question, then write two revised questions that evidence could answer.
The question is vague: "better" could mean cheaper, longer-lasting, easier to share or safer, and it does not say what digital is compared with. Model revisions: "After 10 copies, does a digital photo still have the same checksum as the original, and how much detail does a print lose after 10 photocopies?" and "Over five years, how many photos does a family lose with one phone and no backup, compared with photos kept in an album?" Each names what is compared and what would be measured.
Question 16 of 20 · Short Answer
A studio records at 48,000 samples per second with 24 bits per sample in stereo (2 channels). Find the bit rate and the size of a one-minute uncompressed recording in MB.
Bit rate = 48,000 × 24 × 2 = 2,304,000 bits per second (2.304 Mbit/s). One minute: 2,304,000 × 60 = 138,240,000 bits, and dividing by 8 gives 17,280,000 bytes ≈ 17.3 MB.
Question 17 of 20 · Short Answer
A radio link flips each bit with probability 0.02. To protect the data, every bit is sent three times and decoded by majority vote. Assuming flips are independent, find the probability that a decoded bit is wrong, and compare it with sending each bit once.
A decoded bit is wrong when at least two of the three copies flip: 3(0.02)²(0.98) + (0.02)³ = 0.001176 + 0.000008 = 0.001184. That is about 17 times smaller than 0.02. The cost is that the link carries three times as many bits, so the useful transfer rate is one third as large.
Question 18 of 20 · Short Answer
A city says: "Moving our property records from paper to a database makes them safer." Write two questions that challenge this claim, one about security or theft and one about deletion, and say what evidence would answer each.
Model answer: "How many people can read or copy the database, and how many unauthorized access attempts were logged last year?" Evidence: the access list and security logs; theft of a digital file leaves the original in place, so the city may not notice it. "If a record is deleted by mistake, how quickly can it be restored, and from how many separate backups?" Evidence: a test restore of deleted records. Good answers note that the paper records have their own risks (fire, water damage), so the questions should compare both.
Question 19 of 20 · Short Answer
Pulses of 0 V and 1.0 V are read with a 0.5 V threshold. The sent bits were 101011, and the receiver measured 0.82, 0.31, 0.64, 0.12, 0.47 and 0.93 V. Decode the bits, find any error, and explain what the error tells you about the noise.
Reading each value against 0.5 V gives 101001. The fifth bit is wrong: a 1 was sent but 0.47 V was received. The noise on that pulse was 1.0 - 0.47 = 0.53 V, larger than the 0.5 V margin, so the threshold could not protect it. A parity bit or a repeated transmission could reveal the error.
Question 20 of 20 · Short Answer
Explain why a digital song can be copied 1,000 times, each copy made from the last, with no loss, while an analog tape copied the same way gets noisier. Then describe one situation in which a digital copy could still fail.
Each analog copy records the exact shape of the signal, including the noise already there, and adds its own noise, so the noise builds up with every generation. A digital copy only has to read each bit as 0 or 1; if every bit is read correctly, the new file has the same bits, and a checksum can confirm it. A digital copy can fail when a drive or memory card has a read error, when the medium is damaged, or when noise is larger than the threshold margin; systems detect this with checksums and copy the file again.
0 of 20 answered · 0 correct
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Frequently Asked Questions
10 Questions
What does HS-PS4-2 mean?
HS-PS4-2 asks students to evaluate questions about why information is sent and stored in digital form. Students learn how information becomes bits sent as wave pulses, then judge which questions about digital reliability, copying and sharing evidence can answer. The code means High School, Physical Science, core idea 4 (Waves and Their Applications in Technologies for Information Transfer), performance expectation 2.
Is HS-PS4-2 taught in physics or physical science?
It is usually taught in Physics or Physical Science, often in a unit on waves and communication technology that also covers HS-PS4-1 and HS-PS4-5. The math is light: multiplying to count bits, converting bits and bytes, and simple probability, so it also fits integrated science courses in grades 9-10.
What does "evaluate questions" mean in HS-PS4-2?
It means judging whether a question is useful for finding out something real. Students ask whether evidence could answer the question, whether it is specific about what is compared, and whether its premise is true, and then they revise weak questions. For example, "Is digital better?" becomes a question that names what is measured and under what conditions.
Why is digital information more reliable than analog?
Because a receiver only has to tell a 1 from a 0. Noise changes the size of each pulse, but as long as it stays below half the gap between the two levels, every bit is read correctly and can be resent as a clean pulse. In an analog signal the exact voltage carries the message, so noise added along the way or in each copy stays in the signal.
Does HS-PS4-2 include disadvantages of digital storage?
Yes, through the Clarification Statement, which names easy deletion, security and theft. The performance expectation itself asks about advantages, but a fair evaluation weighs both. Good classroom questions compare risks, such as who can open the files on a stolen laptop, or whether a copy can be taken without the owner knowing.
Do students need to know binary for HS-PS4-2?
Only the basic idea. Students should know that information is stored as bits, that n bits give 2n patterns, and that 8 bits make a byte. Converting a few letters or small numbers to binary helps make parity checks concrete, but long conversions and number-system arithmetic are not the goal of the standard.
What is the difference between an analog and a digital signal?
An analog signal varies smoothly, and its exact size carries the information, like the groove of a vinyl record. A digital signal carries information as a sequence of distinct values, usually two, so each part of the signal only has to be read as one value or the other. Many devices convert between the two: a microphone produces an analog signal that is then sampled and stored as bits.
Is a digital copy really identical to the original?
Yes, when every bit is read and written correctly, which is why a checksum of the copy matches the checksum of the original. Copies can still fail because of a damaged drive, a read error or a failed transfer, so good systems check copies and repeat the ones that fail. This is a useful example of a premise students should question rather than assume.
Is there an assessment boundary for HS-PS4-2?
No. NGSS gives no Assessment Boundary for HS-PS4-2, only the Clarification Statement. Most classes keep the math to counting bits, transfer times and simple error checks, and treat compression algorithms and encryption as topics beyond this standard.
How does HS-PS4-2 connect to other standards?
It builds on MS-PS4-3, where students first learn that digitized signals are a reliable way to send information, and it sits beside HS-PS4-5 on how devices use waves to carry information. The probability of independent errors links to HSS.CP.A.2, and weighing digital storage against its risks leads into HS-ETS1-3, evaluating solutions by trade-offs.
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Related Standards
5 standards
These standards connect to HS-PS4-2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS4-3Prerequisite
Support the claim that digitized signals are more reliable for encoding and sending information
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