1.1.2 Binary Magnitudes and Data Prefixes
Computer systems often handle quantities that are inconvenient to write in full, such as file sizes, memory capacities, and storage volumes. Prefixes provide a shorter and clearer way to express these values.
In this section, you will compare decimal and binary prefixes, convert between units, and choose suitable units for presenting data quantities accurately.
By the end of this section, you should be able to:
- Explain why prefixes are useful when presenting data quantities.
- Use decimal prefixes: kilo, mega, giga, and tera.
- Use binary prefixes: kibi, mebi, gibi, and tebi.
- Explain the difference between units such as MB and MiB.
- Convert values between bytes and larger decimal or binary units.
- Choose a suitable unit and show calculations clearly.
Exam focus
Always include the unit in your answer. A value such as 24 is incomplete unless it is identified as 24 MB, 24 MiB, or another appropriate unit.
Why Prefixes Are Needed
A quantity combines a numerical value with a unit. The number shows the amount, while the unit explains what is being measured. For example, 640 has no clear meaning by itself, but 640 bytes and 640 seconds describe different quantities.
Large values can be written in full, using exponential notation, or with a prefix. The prefix changes how the value is presented, but not the underlying quantity.
| Presentation | Example | Interpretation |
|---|---|---|
| Written in full | 86 400 000 bytes | The complete value is shown. |
| Exponential notation | 86.4 × 106 bytes | The value is written using a power of 10. |
| Using a decimal prefix | 86.4 MB | The prefix mega represents 106. |
Exam tip
Use a unit that makes the value easy to interpret. For example, 86.4 MB is usually clearer than 86 400 000 bytes.
Decimal Magnitudes
Decimal prefixes are based on powers of 10. They are widely used in measurement and are commonly used by storage manufacturers when advertising device capacity.
| Prefix | Symbol | Factor | Equivalent value |
|---|---|---|---|
| kilo | k | 103 | 1 kB = 1000 bytes |
| mega | M | 106 | 1 MB = 1 000 000 bytes |
| giga | G | 109 | 1 GB = 1 000 000 000 bytes |
| tera | T | 1012 | 1 TB = 1 000 000 000 000 bytes |
Worked example: bytes to MB
A media file contains 72 000 000 bytes. To convert the value to megabytes, divide by 1 000 000.
72 000 000 ÷ 1 000 000 = 72 MB
Common mistake
Prefix symbols are case-sensitive. Use lowercase k for kilo and uppercase M, G, and T for mega, giga, and tera.
Binary Magnitudes
Binary prefixes are based on powers of 2. They are useful when describing quantities connected with memory and storage calculations that use binary groupings.
The first important binary factor is 210 = 1024. Although 1024 is close to 1000, the two values are not equal, so a different set of prefix names is used.
| Prefix | Symbol | Factor | Equivalent value |
|---|---|---|---|
| kibi | Ki | 210 | 1 KiB = 1024 bytes |
| mebi | Mi | 220 | 1 MiB = 1 048 576 bytes |
| gibi | Gi | 230 | 1 GiB = 1 073 741 824 bytes |
| tebi | Ti | 240 | 1 TiB = 1 099 511 627 776 bytes |
Worked example: bytes to MiB
A software package contains 7 340 032 bytes. Since 1 MiB = 1 048 576 bytes:
7 340 032 ÷ 1 048 576 = 7 MiB
Why MB and MiB Are Different
The symbols MB and MiB describe different quantities because they use different bases.
| Unit | System | Bytes |
|---|---|---|
| 1 MB | Decimal | 1 000 000 |
| 1 MiB | Binary | 1 048 576 |
The numerical difference may appear small for one unit, but it becomes more noticeable when the values reach gigabytes or terabytes.
Common misconception
GB and GiB are not interchangeable. GB uses powers of 10, while GiB uses powers of 2.
Exam tip
Before calculating, identify whether the question uses decimal or binary prefixes. Do not assume that MB means the same as MiB.
Choosing the Correct Unit
A good unit makes a value easier to read without hiding its meaning. Small quantities may be best expressed in bytes or KiB, while larger values may be clearer in MiB, GiB, GB, or TB.
| Quantity | Possible presentation | Why it is suitable |
|---|---|---|
| 3072 bytes | 3 KiB | The binary conversion is exact and compact. |
| 26 000 000 bytes | 26 MB | The decimal value is easy to read. |
| 6 442 450 944 bytes | 6 GiB | The binary unit gives an exact whole-number result. |
Exam tip
Choose the unit requested by the question. When no unit is specified, use one that keeps the answer clear and avoids an unnecessarily long number.
Converting Between Units
First identify the prefix system being used. Then apply the correct factor.
Example 1: bytes to KiB
A configuration file has a size of 92 160 bytes.
92 160 ÷ 1024 = 90 KiB
Example 2: MiB to bytes
An application uses 14 MiB of memory.
14 × 1 048 576 = 14 680 064 bytes
Example 3: converting to a common unit
A storage area has 6 GiB available. Each backup file uses 3 MiB. Convert the available space to MiB first.
6 GiB = 6 × 1024 MiB = 6144 MiB
Then calculate the number of files:
6144 ÷ 3 = 2048 files
Common mistake
Do not calculate with two different units. Convert both values to the same unit before multiplying or dividing.
Exam tip
Show the unit conversion as a separate line. This makes your method clear and helps prevent errors caused by mixing prefixes.
Interactive: Decimal and Binary Prefix Converter
Enter a file size in bytes. The tool shows how the same value looks using decimal prefixes and binary prefixes. This helps explain why, for example, MB and MiB do not always give the same number.
How to use this tool for revision
Try values such as 1024, 1 048 576, and 1 000 000 000. Compare the decimal and binary results and explain why the displayed values are different.
Practice and Misconceptions
Try these questions
- State the difference between MB and MiB.
- Convert 65 536 bytes into KiB.
- Convert 18 MiB into bytes.
- A storage area contains 5 GiB. Each file uses 2.5 MiB. How many complete files can be stored?
- A drive is labelled using GB, while an operating system reports capacity using GiB. Explain why the displayed number may be smaller even though no storage has been lost.
- Explain why selecting an appropriate prefix makes a technical answer easier to understand.
Final misconception check
A prefix does not change the stored data. It changes only the unit used to describe the quantity.
Self-check
Check that you used the correct factor, converted values to matching units, and included the final unit in every numerical answer.