How many values n bits can store
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. How many different values can 1 bit store?
2. How many different values can 2 bits store?
3. What happens to the number of values when you add one extra bit?
4. Which formula gives the number of values that n bits can store?
5. How many different values can 3 bits store?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 12^n | AThe number of different values that n bits can store | |
| 22^3 = 8 | BThe rule is 2^n, not n x 2. Each extra bit doubles the values rather than adding 2. | |
| 31 bit can only be 0 or 1, so it stores 2 values | C3 bits can store 8 different values | |
| 4Adding one more bit doubles the number of values (3 bits = 8, so 4 bits = ?) | D2 x 2 equals 4, not 2. Two bits can store 4 values: 00, 01, 10 and 11. | |
| 52 bits can store 2 x 2 = 2 values | E2^1 = 2 | |
| 6n bits can store n x 2 values | F8 x 2 = 16 |
C
Definitions
2^n
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
1 bit can store _ different values
2.
2 bits: 2 x 2 = _ different values
3.
Each extra bit _______ the number of values
4.
8 bits can store 2^_ = 256 values
5.
More bits means ____ detail can be stored
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
1 bit = 2 values
B
2 bits = 4 values
C
3 bits = 8 values
D
4 bits = 12 values
Question 2
A
bits ← 3
B
values ← 1
C
REPEAT bits TIMES
D
values ← values + 2
E
DISPLAY values
Question 3
A
bits ← 3
B
values ← 2 * bits
C
DISPLAY values
Question 4
A
values ← 1 ^ 1
B
DISPLAY values
C
// 1 bit: the values 0 and 1
Question 5
A
bits ← 4
B
values ← 2 ^ bits
C
maxNumber ← values + 1
D
DISPLAY maxNumber
Answer Key
How many values n bits can store
Section A: Quick Questions
Q1
A — 2 values (0 and 1)
Q2
A — 4 values (00, 01, 10, 11)
Q3
A — It doubles
Q4
B — 2^n
Q5
B — 8 values
Section B: Match the Pairs
Q1
2^n → The number of different values that n bits can store
Q2
2^3 = 8 → 3 bits can store 8 different values
Q3
1 bit can only be 0 or 1, so it stores 2 values → 2^1 = 2
Q4
Adding one more bit doubles the number of values (3 bits = 8, so 4 bits = ?) → 8 x 2 = 16
Q5
2 bits can store 2 x 2 = 2 values → 2 x 2 equals 4, not 2. Two bits can store 4 values: 00, 01, 10 and 11.
Q6
n bits can store n x 2 values → The rule is 2^n, not n x 2. Each extra bit doubles the values rather than adding 2.
Section C: Definitions
Q1
2^n — The number of different values n bits can store. Each extra bit doubles it: 1 bit gives 2 values, 2 bits give 4, 3 bits give 8, and 8 bits give 256.Section D: Fill in the Blanks
Q1
1 bit can store 2 different valuesQ2
2 bits: 2 x 2 = 4 different valuesQ3
Each extra bit doubles the number of valuesQ4
8 bits can store 2^8 = 256 valuesQ5
More bits means more detail can be storedSection E: Spot the Error
Q1
D — Each extra bit doubles the number of values. 3 bits give 8 values, so 4 bits give 16 values, not 12.
Q2
D — Each bit doubles the number of values, so the loop must multiply by 2. Adding 2 would give 7 instead of 8. It should be values ← values * 2.
Q3
B — n bits store 2 to the power of n values, so it needs ^ not *. 2 * 3 gives 6, but 2 ^ 3 gives the correct 8.
Q4
A — 1 bit can be 0 or 1, which is 2 values. The base of the power is 2, so it should be 2 ^ 1. 1 ^ 1 would always give 1.
Q5
C — Values start at 0, so the biggest number is one less than the number of values. 4 bits give 16 values, so the max is 15. It should be values - 1.