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1.3.1 | MEASURING STORAGE
01 | HOW MUCH DATA IS THERE?
A text message, a photograph and a video all contain binary data, but they contain very different amounts. Storage units give us a way to describe and compare those amounts without writing an enormous number of bits.
Think of the units as a ladder. First we group bits into bytes. Then we group bytes into larger binary units, with 1024 of one unit making the next.
02 | BITS, NIBBLES AND BYTES
| Unit | Meaning | Example |
|---|---|---|
| Bit | One binary digit | 0 or 1 |
| Nibble | 4 bits | 1010 |
| Byte | 8 bits | 10101100 |
One byte contains two nibbles. A byte has eight bit positions and can represent 256 different patterns. That is 256 patterns, not 256 bits.
2 nibbles = 1 byte = 8 bits 4 bytes × 8 = 32 bits 40 bits ÷ 8 = 5 bytes
Use a lowercase b for bits and an uppercase B for bytes when interpreting abbreviated units. Writing the unit in full can help avoid mistakes.
03 | THE BINARY STORAGE LADDER
| Unit | Symbol | Made from | Bytes |
|---|---|---|---|
| Byte | B | 8 bits | 1 |
| Kibibyte | KiB | 1024 bytes | 1024 |
| Mebibyte | MiB | 1024 KiB | 1048576 |
| Gibibyte | GiB | 1024 MiB | 1073741824 |
| Tebibyte | TiB | 1024 GiB | 1099511627776 |
| Pebibyte | PiB | 1024 TiB | 1125899906842624 |
| Exbibyte | EiB | 1024 PiB | 1152921504606846976 |
Read the third column carefully: 1 GiB is 1024 MiB, not 1024 bytes. The prefix tells you which step you are on.
Moving towards a smaller unit: multiply by 1024 for each step. Moving towards a larger unit: divide by 1024 for each step. The separate byte-to-bit step uses 8.
04 | WHY 1024, NOT 1000?
1024 is 2¹⁰, a power of two. Binary prefixes such as kibi and mebi define units based on powers of 1024.
| Binary unit | Decimal unit |
|---|---|
| 1 KiB = 1024 bytes | 1 kB = 1000 bytes |
| 1 MiB = 1048576 bytes | 1 MB = 1000000 bytes |
| 1 GiB = 1073741824 bytes | 1 GB = 1000000000 bytes |
For these Cambridge syllabus storage calculations, use 1024 rather than 1000. Use KiB, MiB and GiB accurately in your answers. Decimal units are included here so you can recognise the distinction in everyday product labels.
05 | LARGE UNIT TO SMALL UNIT
A sound clip contains 3 MiB of data. How many KiB is that? MiB to KiB is one step towards a smaller unit.
3 × 1024 = 3072 KiB
To express the same amount in bytes, take a second step.
3 × 1024 × 1024 = 3145728 bytes
The data has not grown. You are measuring the same amount with a smaller unit, so the number increases.
06 | SMALL UNIT TO LARGE UNIT
A file contains 524288 bytes. Express its size in KiB, then MiB.
524288 ÷ 1024 = 512 KiB 512 ÷ 1024 = 0.5 MiB
A fractional result is valid. A file does not have to occupy a whole MiB. Keep full precision during the calculation and round only if the question asks you to.
07 | WHEN THE QUESTION STARTS WITH BITS
A data block contains 16384 bits. Express its size in KiB. First convert bits to bytes using 8, then bytes to KiB using 1024.
16384 ÷ 8 = 2048 bytes 2048 ÷ 1024 = 2 KiB
For the reverse journey, use the factors in reverse order.
2 KiB × 1024 = 2048 bytes 2048 bytes × 8 = 16384 bits
Do not use 1024 between bits and bytes. Write the units beside each intermediate result.
08 | WILL THE FILES FIT?
You have 8 MiB of available space. Each file uses 512 KiB. Ignoring file-system overhead, how many whole files fit?
8 × 1024 = 8192 KiB 8192 ÷ 512 = 16 files
Convert to a common unit before comparing or dividing. In a real storage device, formatting and other data may reduce the space available. In an exam, follow the assumptions stated.
09 | TRY THE STORAGE CONVERTER
Choose the starting and target units. Predict whether the numerical answer will get larger or smaller before checking. The converter uses binary units and displays a rounded decimal for recurring results.
10 | A QUICK EXAM CHECK
Start unit: bits or bytes? Target unit: what does the question request? Route: how many steps, and which factors? Sense check: smaller units should produce a larger number.
Always include the final unit. “2048” alone does not say whether you mean bits, bytes or KiB.