← Years 7–8 Data & Information

How many values n bits can store

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.

Part of: 7-8 Digital Technologies: Representing data with binary — Module 11, IGCSE Computer Science 0478 — 1.1 Number Systems — Module 9, IGCSE Computer Science 0478 — 1.2 Text, Sound and Images — Module 2, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 13, ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 9

Understanding How many values n bits can store in Years 7–8 Data & Information

What it does: With one bit there are only two choices, 0 or 1, which matches 2^1 = 2. Each extra bit doubles the count. 3 bits give 8 values, so 4 bits give 8 x 2 = 16 values. A single bit can be 0 or 1, so 1 bit gives 2 values. This is 2^1 = 2. More bits means more possible values, so more shades or colours can be shown. 2 bits only gives 4 values, but 8 bits gives 256. 2^8 = 256 values. The number of values is not the same as the number of bits. The expression 2^n means 2 multiplied by itself n times, which is how many different bit patterns n bits can make.

Common mistakes: Each extra bit doubles the number of values. 3 bits give 8 values, so 4 bits give 16 values, not 12. 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.

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Learning
Duo
How many different values can 1 bit store?
1 value2 values (0 and 1)
Matches
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.
Applying
Meanings
Term
2^n
Meaning
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.
Practice
1 bit = 2^1 = 2 values
Testing
Gaps
1 bit can store different values
Check Answer
Spots
33 bits = 8 values
44 bits = 12 values

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Quick Questions

1. How many different values can 1 bit store?
A. 2 values (0 and 1) ✓
B. 1 value
A single bit can be 0 or 1, so 1 bit gives 2 values. This is 2^1 = 2.
2. How many different values can 2 bits store?
A. 4 values (00, 01, 10, 11) ✓
B. 3 values (00, 01, 10)
Each bit has 2 choices, so 2 bits give 2 x 2 = 4 values. Don't forget 00 counts as a value!
3. What happens to the number of values when you add one extra bit?
A. It doubles ✓
B. It goes up by 1
Each extra bit doubles the number of values. 2 bits give 4 values, 3 bits give 8, 4 bits give 16.
4. Which formula gives the number of values that n bits can store?
A. n^2
B. 2^n ✓
The formula is 2^n, because each bit has 2 choices. For 3 bits, 2^3 = 8, but 3^2 would wrongly give 9.
5. How many different values can 3 bits store?
A. 6 values
B. 8 values ✓
3 bits give 2 x 2 x 2 = 8 values. Doubling from 4 values (2 bits) gives 8.

Match the Pairs

2^n → The number of different values that n bits can store
2^3 = 8 → 3 bits can store 8 different values
1 bit can only be 0 or 1, so it stores 2 values → 2^1 = 2
Adding one more bit doubles the number of values (3 bits = 8, so 4 bits = ?) → 8 x 2 = 16
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.
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.

Key Term

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.

Fill in the Blanks

1. 1 bit can store 2 different values
Hint: Type how many values a single bit can hold (think 0 and 1).
2. 2 bits: 2 x 2 = 4 different values
Hint: Type the total number of values that 2 bits can store.
3. Each extra bit doubles the number of values
Hint: Type the word for what happens to the number of values when you add one bit.
4. 8 bits can store 2^8 = 256 values
Hint: Type the power, which is the number of bits used.
5. More bits means more detail can be stored
Hint: Type the word that describes how much detail you get when you use extra bits.

Spot the Error

Question 1
A 1 bit = 2 values
B 2 bits = 4 values
C 3 bits = 8 values
D 4 bits = 12 values
Line D — Each extra bit doubles the number of values. 3 bits give 8 values, so 4 bits give 16 values, not 12.
Question 2
A bits ← 3
B values ← 1
C REPEAT bits TIMES
D values ← values + 2
E DISPLAY values
Line 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.
Question 3
A bits ← 3
B values ← 2 * bits
C DISPLAY values
Line 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.
Question 4
A values ← 1 ^ 1
B DISPLAY values
C // 1 bit: the values 0 and 1
Line 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.
Question 5
A bits ← 4
B values ← 2 ^ bits
C maxNumber ← values + 1
D DISPLAY maxNumber
Line 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.

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