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Computers store and process vast amounts of data, measured in units that range from individual bits to petabytes and beyond. This lesson covers the standard units used to measure data storage and how to convert between them.
The bit is the smallest unit of data in computing. It stores a single binary value: 0 or 1.
The word "bit" is short for binary digit.
On its own, a single bit can represent only two values (0 or 1), but when combined with other bits, it can represent much more complex data.
A nibble is a group of 4 bits. It can represent 2⁴ = 16 different values (0–15 in denary, or 0–F in hexadecimal).
A nibble corresponds to exactly one hexadecimal digit, which is why nibbles are useful when working with hex.
A byte is a group of 8 bits (or 2 nibbles). It is the standard unit of data storage and is the smallest addressable unit in most computer systems.
A byte can represent 2⁸ = 256 different values (0–255 in unsigned binary).
One byte can store:
flowchart LR
A[Bit] --> B[Nibble: 4 bits]
B --> C[Byte: 8 bits]
C --> D[KB: 1024 B]
D --> E[MB: 1024 KB]
E --> F[GB: 1024 MB]
F --> G[TB: 1024 GB]
G --> H[PB: 1024 TB]
As data sizes grow, larger units are used. In computing, each unit is 1024 times the previous one (because 1024 = 2¹⁰):
| Unit | Symbol | Size in Bytes | Approximate Size |
|---|---|---|---|
| 1 Byte | B | 1 | A single character |
| 1 Kilobyte | KB | 1,024 | A short text document |
| 1 Megabyte | MB | 1,024 × 1,024 = 1,048,576 | A photo or short song |
| 1 Gigabyte | GB | 1,024³ = 1,073,741,824 | A movie or large application |
| 1 Terabyte | TB | 1,024⁴ | A large hard drive |
| 1 Petabyte | PB | 1,024⁵ | Data centre-scale storage |
Note: Some specifications use 1000 instead of 1024 for these conversions (e.g. the SI definition of kilobyte). For the GCSE exam, use 1024 unless told otherwise.
To convert from a larger unit to a smaller unit, multiply by 1024 for each step down.
Worked Example: Convert 3 MB to bytes.
Worked Example: Convert 2.5 GB to MB.
To convert from a smaller unit to a larger unit, divide by 1024 for each step up.
Worked Example: Convert 5,242,880 bytes to MB.
Worked Example: Convert 512 KB to MB.
To convert bits to bytes, divide by 8.
To convert bytes to bits, multiply by 8.
Worked Example: How many bytes is 2048 bits?
Worked Example: How many bits is 4 KB?
| From | To | Operation |
|---|---|---|
| Bits → Bytes | Divide by 8 | 16 bits = 2 bytes |
| Bytes → Bits | Multiply by 8 | 3 bytes = 24 bits |
| Bytes → KB | Divide by 1024 | 2048 bytes = 2 KB |
| KB → Bytes | Multiply by 1024 | 5 KB = 5120 bytes |
| KB → MB | Divide by 1024 | 2048 KB = 2 MB |
| MB → KB | Multiply by 1024 | 3 MB = 3072 KB |
| MB → GB | Divide by 1024 | 4096 MB = 4 GB |
| GB → MB | Multiply by 1024 | 2 GB = 2048 MB |
| GB → TB | Divide by 1024 | 2048 GB = 2 TB |
| TB → GB | Multiply by 1024 | 1 TB = 1024 GB |
The number of different values that can be represented by n bits is:
Number of values = 2ⁿ
| Number of Bits | Number of Values |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
| 8 | 256 |
| 10 | 1024 |
| 16 | 65,536 |
| 24 | 16,777,216 |
Exam Tip: Data unit conversion questions appear frequently. Practise converting in both directions (up and down) and between bits and bytes. Show every step of your working in the exam to earn method marks.
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