← IGCSE Computer Science Paper 1

Calculating the size of a sound file

Uncompressed sound file size in bits is the sample rate (Hz) times the sample resolution (bits) times the length in seconds. Divide the bits by 8 to get bytes.

Part of: IGCSE Computer Science 0478 — 1.3 Data Storage and Compression — Module 26

Understanding Calculating the size of a sound file in IGCSE Computer Science Paper 1

What it does: Sample rate x sample resolution x length in seconds is 44100 x 16 x 10 = 7,056,000 bits. 8000 x 8 x 5 = 320,000 bits, and dividing by 8 gives 40,000 bytes. The three values are multiplied together. Adding them gives a meaningless number. 100 x 8 x 10 = 8000 bits. Do not forget to multiply by all three values. The formula needs the length in seconds, so convert minutes to seconds first by multiplying by 60. 1000 x 16 x 5 = 80000 bits. Divide by 8 to get 10000 bytes. Length is part of the multiplication, so doubling the length doubles the number of bits.

Common mistakes: The sound length in seconds is missing. File size in bits = sample rate x sample resolution x length in seconds, so the line should be bits = rate * res * 10. The program works out the size in bytes but then prints the size in bits. It should print the variable bytes.

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Learning
Duo
Which formula gives the size of an uncompressed sound file in bits?
sample rate + sample resolution + length in secondssample rate x sample resolution x length in seconds
Matches
size_bits = rate + resolution + seconds
↓
The three values are added instead of multiplied. The size in bits is rate x resolution x seconds.
Applying
Meanings
Term
size = sample rate x resolution x seconds
Meaning
Uncompressed sound file size in bits is the sample rate (Hz) times the sample resolution (bits) times the length in seconds. Divide the bits by 8 to get bytes.
Practice
sampleRate ← 8000
Testing
Gaps
bits = rate * * seconds
Check Answer
Spots
2res = 16
3bits = rate * res

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Quick Questions

1. Which formula gives the size of an uncompressed sound file in bits?
A. sample rate x sample resolution x length in seconds ✓
B. sample rate + sample resolution + length in seconds
The three values are multiplied together. Adding them gives a meaningless number.
2. A sound has a sample rate of 100 Hz, a sample resolution of 8 bits and lasts 10 seconds. What is the file size in bits?
A. 8000 bits ✓
B. 800 bits
100 x 8 x 10 = 8000 bits. Do not forget to multiply by all three values.
3. You have worked out a sound file is 8000 bits. How do you convert this to bytes?
A. Multiply by 8
B. Divide by 8 ✓
There are 8 bits in 1 byte, so bits divided by 8 gives bytes. 8000 / 8 = 1000 bytes.
4. A sound is 1 minute long. What length do you use in the file size formula?
A. 60 seconds ✓
B. 1 second
The formula needs the length in seconds, so convert minutes to seconds first by multiplying by 60.
5. A sound has a sample rate of 1000 Hz, a sample resolution of 16 bits and a length of 5 seconds. What is its size in bits?
A. 8000 bits
B. 80000 bits ✓
1000 x 16 x 5 = 80000 bits. Divide by 8 to get 10000 bytes.

Match the Pairs

size_bits = rate * resolution * seconds → Calculates the uncompressed sound file size in bits
size_bytes = size_bits / 8 → Converts the file size from bits to bytes
Worked example: a 10 second sound sampled at 44100 Hz with 16-bit resolution has this size in bits → 44100 * 16 * 10
Size in bytes of a 5 second sound at 8000 Hz and 8-bit resolution: multiply to get bits, then divide by 8 → 8000 * 8 * 5 / 8
size_bits = rate + resolution + seconds → The three values are added instead of multiplied. The size in bits is rate x resolution x seconds.
size_bytes = rate * resolution * seconds * 8 → The result is multiplied by 8 instead of divided by 8. Bits must be divided by 8 to get bytes.

Key Term

size = sample rate x resolution x seconds
Uncompressed sound file size in bits is the sample rate (Hz) times the sample resolution (bits) times the length in seconds. Divide the bits by 8 to get bytes.

Fill in the Blanks

1. bits = rate * resolution * seconds
Hint: Type the variable for how many bits each sample uses.
2. bits = rate * resolution * seconds
Hint: Type the operator that combines the bits per second with the length of the sound.
3. bytes = bits / 8
Hint: Type the operator that turns a number of bits into bytes.
4. bytes = bits / 8
Hint: Type the number of bits that make up one byte.
5. seconds = 2 * 60 bits = 8000 * 8 * seconds
Hint: Type the number of seconds in one minute to convert the length of 2 minutes.

Spot the Error

Question 1
A rate = 8000
B res = 16
C bits = rate * res
D print(bits)
Line C — The sound length in seconds is missing. File size in bits = sample rate x sample resolution x length in seconds, so the line should be bits = rate * res * 10.
Question 2
A bits = 8000 * 16 * 10
B bytes = bits / 8
C print(bits)
Line C — The program works out the size in bytes but then prints the size in bits. It should print the variable bytes.
Question 3
A rate = 22050
B res = 8
C secs = 60
D bits = rate * res + secs
Line D — The three values must be multiplied, not added. The correct line is bits = rate * res * secs.
Question 4
A bits = 8000 * 30
B bytes = bits / 8
C kib = bytes / 1024
D print(kib)
Line A — The sample resolution (16 bits) has been left out. The size in bits is sample rate x sample resolution x length, so it should be bits = 8000 * 16 * 30.
Question 5
A bits = 16000 * 8 * 20
B bytes = bits / 8
C kib = bytes / 1000
D print(kib)
Line C — A kibibyte is 1024 bytes, not 1000. The line should be kib = bytes / 1024.

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