Why storage units use 1024, not 1000

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Why storage units use 1024, not 1000

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. How many bytes are in 1 kibibyte (KiB) in IGCSE Computer Science?
A 1024
B 1000
2. Which power of 2 equals 1024?
A 2^8
B 2^10
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
4. A student must work out how many MiB are in 3 GiB. Which calculation is correct?
A 3 × 1024
B 3 × 1000
5. Which set of prefixes are the binary prefixes?
A kilo, mega, giga
B kibi, mebi, gibi
B

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left columnRight column
12^10 = 1024 A3072 / 1024 = 3 GiB
21 KiB = 1024 bytes BThe kibi prefix is a binary prefix, so a kibibyte is 1024 bytes, not 1000 bytes
3To change 5 MiB into KiB, multiply by 1024 because each unit step is 1024 times bigger C5 * 1024 = 5120 KiB
4To change 3072 MiB into GiB, divide by 1024 because 1 GiB is 1024 MiB DUsed 1000 instead of 1024. Binary prefixes step up by 1024, so 2 KiB is 2 * 1024 = 2048 bytes.
52 KiB = 2 * 1000 = 2000 bytes E2 to the power 10 is not 1000. It is 1024, and this is the number used between storage units.
62^10 = 1000 F2 to the power 10 equals 1024, which is why each storage unit is 1024 times bigger than the one before it
C

Definitions

2^10 = 1024
D

Fill in the Blanks

Complete each line of code by filling in the missing parts.

1.
2^10 = ____
2.
_^10 = 1024
3.
bytes ← KiB _ 1024
4.
2^__ = 1024
5.
kilo is 1000, but ____ is 1024
E

Spot the Error

Shade in the letter of the line that contains an error.

Question 1
A bytesInKiB ← 2 ^ 8
B bytesInMiB ← bytesInKiB * 1024
C OUTPUT bytesInMiB
Question 2
A // 1 KiB = 10^3 bytes
B bytes ← 5 * 1024
C OUTPUT bytes
Question 3
A INPUT bytes
B OUTPUT 'Bytes to KiB'
C kib ← bytes / 1000
Question 4
A mib ← 2
B kib ← mib * 1024
C bytes ← kib * 1000
Question 5
A unit ← 2 ^ 10
B bytesInMiB ← unit ^ 2
C bytesInGiB ← unit * 3

Answer Key

Why storage units use 1024, not 1000
Section A: Quick Questions
Q1
A — 1024
Q2
B — 2^10
Q3
A — Computers count in binary, and 2^10 = 1024
Q4
A — 3 × 1024
Q5
B — kibi, mebi, gibi
Section B: Match the Pairs
Q1
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
Q2
1 KiB = 1024 bytes → The kibi prefix is a binary prefix, so a kibibyte is 1024 bytes, not 1000 bytes
Q3
To change 5 MiB into KiB, multiply by 1024 because each unit step is 1024 times bigger → 5 * 1024 = 5120 KiB
Q4
To change 3072 MiB into GiB, divide by 1024 because 1 GiB is 1024 MiB → 3072 / 1024 = 3 GiB
Q5
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.
Q6
2^10 = 1000 → 2 to the power 10 is not 1000. It is 1024, and this is the number used between storage units.
Section C: Definitions
Q1
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.
Section D: Fill in the Blanks
Q1
2^10 = 1024
Q2
2^10 = 1024
Q3
bytes ← KiB * 1024
Q4
2^10 = 1024
Q5
kilo is 1000, but kibi is 1024
Section E: Spot the Error
Q1
A — A kibibyte is 2 to the power 10 bytes, which is 1024. 2 ^ 8 is only 256. It should be bytesInKiB ← 2 ^ 10.
Q2
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.
Q3
C — To convert bytes to KiB you divide by 1024, not 1000, because 1 KiB is 1024 bytes. It should be kib ← bytes / 1024.
Q4
C — Each step between storage units is a factor of 1024. Converting KiB to bytes means multiplying by 1024, not 1000.
Q5
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.