objectives
By the end you'll be able to…
- Explain why computers store data as binary.
- Name and order every GCSE unit of data from bit to petabyte.
- Convert between units by multiplying or dividing by 8 (for bits/bytes) or 1000 (for everything bigger).
- Calculate the capacity of a storage device and how many files it can hold.
why binary?
Why does everything become 1s and 0s?
Every computer is built from billions of tiny switches called transistors. A switch has only two possible states: on or off. That's a perfect match for the binary number system, which has only two digits: 1 and 0.
- 1 = switch on / current flowing / magnetised north / laser reflected.
- 0 = switch off / no current / magnetised south / laser absorbed.
Because computers can only store on/off, every piece of data — text, images, sound, video, anything — must first be converted into binary before it can be stored or processed.
A car's accelerator has hundreds of positions between 0 and 100 mph. A computer only has two: 0 mph (0) or 100 mph (1). Anything in between has to be built up from lots of ons and offs.
units
The units of data storage
A single 1 or 0 is called a bit. That's the smallest unit of data a computer can store. It isn't very useful on its own, so bits are grouped into bigger units. These are the units you must know for GCSE:
| Unit | Symbol | Size | Example |
|---|---|---|---|
| Bit | b | 1 or 0 | — |
| Nibble | — | 4 bits | Half a byte |
| Byte | B | 8 bits | A single character (e.g. "A") |
| Kilobyte (KB) | KB | 1,000 B | A small text file |
| Megabyte (MB) | MB | 1,000 KB | A music file |
| Gigabyte (GB) | GB | 1,000 MB | A HD movie |
| Terabyte (TB) | TB | 1,000 GB | A large hard drive |
| Petabyte (PB) | PB | 1,000 TB | A large data centre |
Technically, 1 KB = 210 = 1024 bytes. In GCSE we simplify and use 1,000 to make the maths easier. Always use 1000 unless the question says otherwise.
Quick flashcards — click to reveal
converting
Converting between units
There are only two rules you ever need:
- Going between bits and bytes? Multiply or divide by 8.
- Going between any bigger units (B → KB → MB → GB → TB → PB)? Multiply or divide by 1000.
Rule of thumb:
- Going up a unit (smaller → bigger): divide.
- Going down a unit (bigger → smaller): multiply.
Convert 2000 KB into MB.
KB → MB is going up, so divide by 1000.
2000 ÷ 1000 = 2 MB
Convert 2 TB into GB.
TB → GB is going down, so multiply by 1000.
2 × 1000 = 2000 GB
Convert 24 bits into bytes.
bits → bytes is going up, so divide by 8.
24 ÷ 8 = 3 bytes
Try it yourself
Q1. How many bytes are in 6 nibbles?
Q2. How many bits are in 5 kilobytes?
Q3. Tick the equivalents: 2000 gigabytes = ? terabytes
capacity
Data capacity & calculating how much fits
Data capacity is the maximum amount of information a storage device can hold. If you know the capacity and the size of one file, you can work out how many files the device can store.
| Device | Typical capacity |
|---|---|
| CD | 700 MB |
| USB flash drive | 16 GB – 256 GB |
| SSD | 128 GB – 2 TB |
| HDD | 500 GB – 8 TB |
The three-step method
- Know the capacity of the device.
- Convert so the file size and capacity are in the same units.
- Divide capacity ÷ file size = number of files.
Lyla creates images that are 3 MB each. She stores them on a 6 GB USB stick. How many images can she save?
Step 1 — convert to the same units. 6 GB = 6 × 1000 = 6000 MB.
Step 2 — divide. 6000 ÷ 3 = 2000 images.
File-size formulas (for later topics)
You'll meet these again in the images and sound topics — bookmark them for now:
| File type | Formula |
|---|---|
| Text file | (bytes per character) × (number of characters) |
| Image file | Resolution (W × H) × colour depth (bits) |
| Sound file | Sample rate × duration × bit depth |
practice
Exam-style practice
Q1. A memory card has a capacity of 32 GB. Each video is 400 MB. How many videos fit?
Q2. A text file is 5,000 characters long using Extended ASCII (1 byte per character). What is the file size in KB?
Q3. A CD has 700 MB capacity. A song is 5 MB. How many songs fit on the CD?
// end of topic 1 — units & capacity