← IGCSE Computer Science Paper 1

Why storage units use 1024, not 1000

Each storage unit is 1024 times the one before, because computers count in binary and 2 to the power 10 is 1024. So calculations use 1024, not 1000.

Part of: IGCSE Computer Science 0478 — 1.3 Data Storage and Compression — Module 10

Understanding Why storage units use 1024, not 1000 in IGCSE Computer Science Paper 1

What it does: Moving from a larger unit (MiB) to a smaller unit (KiB) means multiplying by 1024, not 1000. Each storage unit is 1024 times the one before it. 1 KiB = 1024 bytes. 2 to the power 10 is 1024. 2^8 is only 256. Computers use binary (base 2), so units go up in powers of 2. 2^10 = 1024. In exam calculations always use 1024, not 1000. 3 GiB = 3 × 1024 = 3072 MiB. Kibi, mebi and gibi are the binary prefixes and step up by 1024. Kilo, mega and giga are the decimal prefixes and step up by 1000.

Common mistakes: A kibibyte is 2 to the power 10 bytes, which is 1024. 2 ^ 8 is only 256. It should be bytesInKiB ← 2 ^ 10. Storage units step up in powers of 2, not powers of 10. 1 KiB = 2^10 = 1024 bytes, so the comment should say 2^10 bytes.

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Learning
Duo
How many bytes are in 1 kibibyte (KiB) in IGCSE Computer Science?
10001024
Matches
2 KiB = 2 * 1000 = 2000 bytes
↓
Used 1000 instead of 1024. Binary prefixes step up by 1024, so 2 KiB is 2 * 1024 = 2048 bytes.
Applying
Meanings
Term
2^10 = 1024
Meaning
Each storage unit is 1024 times the one before, because computers count in binary and 2 to the power 10 is 1024. So calculations use 1024, not 1000.
Practice
kibibytes ← 5
Testing
Gaps
2^10 =
Check Answer
Spots
1bytesInKiB ← 2 ^ 8
2bytesInMiB ← bytesInKiB * 1024

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Quick Questions

1. How many bytes are in 1 kibibyte (KiB) in IGCSE Computer Science?
A. 1024 ✓
B. 1000
Each storage unit is 1024 times the one before it. 1 KiB = 1024 bytes.
2. Which power of 2 equals 1024?
A. 2^8
B. 2^10 ✓
2 to the power 10 is 1024. 2^8 is only 256.
3. Why do storage units step up by 1024?
A. Computers count in binary, and 2^10 = 1024 ✓
B. Computers count in tens, and 10^3 = 1000
Computers use binary (base 2), so units go up in powers of 2. 2^10 = 1024.
4. A student must work out how many MiB are in 3 GiB. Which calculation is correct?
A. 3 × 1024 ✓
B. 3 × 1000
In exam calculations always use 1024, not 1000. 3 GiB = 3 × 1024 = 3072 MiB.
5. Which set of prefixes are the binary prefixes?
A. kilo, mega, giga
B. kibi, mebi, gibi ✓
Kibi, mebi and gibi are the binary prefixes and step up by 1024. Kilo, mega and giga are the decimal prefixes and step up by 1000.

Match the Pairs

2^10 = 1024 → 2 to the power 10 equals 1024, which is why each storage unit is 1024 times bigger than the one before it
1 KiB = 1024 bytes → The kibi prefix is a binary prefix, so a kibibyte is 1024 bytes, not 1000 bytes
To change 5 MiB into KiB, multiply by 1024 because each unit step is 1024 times bigger → 5 * 1024 = 5120 KiB
To change 3072 MiB into GiB, divide by 1024 because 1 GiB is 1024 MiB → 3072 / 1024 = 3 GiB
2 KiB = 2 * 1000 = 2000 bytes → Used 1000 instead of 1024. Binary prefixes step up by 1024, so 2 KiB is 2 * 1024 = 2048 bytes.
2^10 = 1000 → 2 to the power 10 is not 1000. It is 1024, and this is the number used between storage units.

Key Term

2^10 = 1024
Each storage unit is 1024 times the one before, because computers count in binary and 2 to the power 10 is 1024. So calculations use 1024, not 1000.

Fill in the Blanks

1. 2^10 = 1024
Hint: Type the value of 2 to the power 10.
2. 2^10 = 1024
Hint: Type the base, because computers count in binary.
3. bytes ← KiB * 1024
Hint: Type the operator that converts a larger unit into a smaller one.
4. 2^10 = 1024
Hint: Type the power that 2 is raised to.
5. kilo is 1000, but kibi is 1024
Hint: Type the binary prefix that matches kilo but uses 1024.

Spot the Error

Question 1
A bytesInKiB ← 2 ^ 8
B bytesInMiB ← bytesInKiB * 1024
C OUTPUT bytesInMiB
Line A — A kibibyte is 2 to the power 10 bytes, which is 1024. 2 ^ 8 is only 256. It should be bytesInKiB ← 2 ^ 10.
Question 2
A // 1 KiB = 10^3 bytes
B bytes ← 5 * 1024
C OUTPUT bytes
Line A — Storage units step up in powers of 2, not powers of 10. 1 KiB = 2^10 = 1024 bytes, so the comment should say 2^10 bytes.
Question 3
A INPUT bytes
B OUTPUT 'Bytes to KiB'
C kib ← bytes / 1000
Line C — To convert bytes to KiB you divide by 1024, not 1000, because 1 KiB is 1024 bytes. It should be kib ← bytes / 1024.
Question 4
A mib ← 2
B kib ← mib * 1024
C bytes ← kib * 1000
Line C — Each step between storage units is a factor of 1024. Converting KiB to bytes means multiplying by 1024, not 1000.
Question 5
A unit ← 2 ^ 10
B bytesInMiB ← unit ^ 2
C bytesInGiB ← unit * 3
Line C — A GiB is three steps of 1024, so it is 1024 cubed (2^30). Multiplying by 3 only gives 3072. It should be unit ^ 3.

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