Number of volume levels from sample resolution
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. How many volume levels can a 1-bit sample have?
2. What happens to the number of volume levels each time you add one more bit of sample resolution?
3. Which formula gives the number of volume levels for n bits?
4. How many volume levels does an 8-bit sample have?
5. How many volume levels does a 16-bit sample (the CD standard) have?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1levels = 2^n | AThis is backwards. Fewer levels means each volume is rounded to a more distant level. More levels means rounding to a closer level and a more accurate sound. | |
| 22^8 = 256 | BThe levels were found by multiplying 2 by the number of bits. The correct way is 2^8, which is 2 multiplied by itself 8 times, giving 256 levels. | |
| 3Each extra bit doubles the number of volume levels, so 16 bits give far more levels than 8 bits | CAn 8-bit sample can be stored as any one of 256 different volume levels | |
| 4A sample resolution of 1 bit can only store two volume levels, like off and on | DThe number of volume levels equals 2 multiplied by itself n times, where n is the sample resolution in bits | |
| 5levels = 2 x 8 = 16 levels for 8 bits | E2^16 = 65536 | |
| 6With more levels, each sample is rounded more roughly | F2^1 = 2 |
C
Definitions
levels = 2^n
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
levels = 2^_
2.
1 bit: levels = 2^1 = _
3.
8 bits: levels = 2^_ = 256
4.
16 bits: levels = 2^__ = 65536
5.
stored = _____(volume)
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
bits = 1
B
levels = 2 ** bits
C
print("Levels:", bits)
Question 2
A
bits = 65536
B
levels = 2 ** bits
C
print(levels)
Question 3
A
levels = 2 * 8
B
print(levels)
C
print("That is 256 levels")
Question 4
A
bits = 3
B
levels = bits ** 2
C
print(levels)
Question 5
A
SET bits TO 8
B
SET levels TO bits * 2
C
DISPLAY levels
Answer Key
Number of volume levels from sample resolution
Section A: Quick Questions
Q1
B — 2 levels
Q2
B — It doubles
Q3
A — 2^n
Q4
A — 256 levels
Q5
A — 65,536 levels
Section B: Match the Pairs
Q1
levels = 2^n → The number of volume levels equals 2 multiplied by itself n times, where n is the sample resolution in bits
Q2
2^8 = 256 → An 8-bit sample can be stored as any one of 256 different volume levels
Q3
Each extra bit doubles the number of volume levels, so 16 bits give far more levels than 8 bits → 2^16 = 65536
Q4
A sample resolution of 1 bit can only store two volume levels, like off and on → 2^1 = 2
Q5
levels = 2 x 8 = 16 levels for 8 bits → The levels were found by multiplying 2 by the number of bits. The correct way is 2^8, which is 2 multiplied by itself 8 times, giving 256 levels.
Q6
With more levels, each sample is rounded more roughly → This is backwards. Fewer levels means each volume is rounded to a more distant level. More levels means rounding to a closer level and a more accurate sound.
Section C: Definitions
Q1
levels = 2^n — A sample resolution of n bits gives 2^n volume levels, so each extra bit doubles the levels. 8 bits give 256 levels and 16 bits give 65,536. Fewer levels means more rounding.Section D: Fill in the Blanks
Q1
levels = 2^nQ2
1 bit: levels = 2^1 = 2Q3
8 bits: levels = 2^8 = 256Q4
16 bits: levels = 2^16 = 65536Q5
stored = round(volume)Section E: Spot the Error
Q1
C — The program should print the number of levels (2), not the number of bits. It should be print("Levels:", levels).
Q2
A — 65,536 is the number of levels, not the number of bits. A 16-bit sample resolution should be bits = 16.
Q3
A — Levels are 2 to the power of the bits, so 8 bits need 2 ** 8 = 256. Multiplying gives only 16.
Q4
B — The base must be 2 and the exponent must be the bits. bits ** 2 gives 9, but 2 ** bits gives the correct 8 levels.
Q5
B — Each extra bit doubles the levels, so levels = 2 ^ bits. Multiplying bits by 2 gives 16, not 256.