Data Storage Calculations

AQA 4.5 — Data storage calculations

Retrieval: every lesson in this sequence has produced a file size in bits, then converted it to bytes. This lesson makes that conversion chain — and every larger unit beyond it — fully explicit, and applies it across images, sound and mixed storage scenarios together.

Key vocabulary

Bit — a single binary digit (0 or 1); the smallest unit of digital storage.
Byte — exactly 8 bits, the standard unit for measuring file and storage sizes.
Kilobyte (KB), Megabyte (MB), Gigabyte (GB), Terabyte (TB) — progressively larger units, each 1024 times the one before, in the binary convention this course uses.

Understand — why 1024, not 1000

Storage units scale in powers of 2, because that's the natural counting system for binary hardware: 2¹⁰ = 1024, which is why 1 KB is conventionally 1024 bytes in a computing (as opposed to marketing) context, not a round 1000.

See it — the full conversion ladder

8 bits        = 1 byte
1024 bytes    = 1 kilobyte (KB)
1024 KB       = 1 megabyte (MB)
1024 MB       = 1 gigabyte (GB)
1024 GB       = 1 terabyte (TB)

Each rung is exactly 1024 times the rung below it — to convert down a rung (e.g. MB → KB), multiply by 1024; to convert up a rung (e.g. KB → MB), divide by 1024.

Calculate it — three worked examples

Example 1 (bits to a human-readable unit): the 24-bit, 100×100 image from the Image Representation lesson was 240,000 bits. In bytes: 240,000 ÷ 8 = 30,000 bytes. In KB: 30,000 ÷ 1024 ≈ 29.3 KB.

Example 2 (converting upward through multiple rungs): a 5,000,000-byte file, expressed in MB: first to KB (5,000,000 ÷ 1024 ≈ 4,882.8 KB), then to MB (4,882.8 ÷ 1024 ≈ 4.77 MB) — or equivalently, dividing by 1024² in one step.

Example 3 (a mixed, realistic estimate): estimating storage for 200 photos, each averaging 6 MB: 200 × 6 = 1,200 MB. Converting to GB: 1,200 ÷ 1024 ≈ 1.17 GB — a genuinely useful real-world estimate, of exactly the kind a device's "storage full" warning depends on.

Check your understanding — calculate it yourself

A USB drive holds 4 GB. Roughly how many 3 MB songs can it store? (4 GB = 4 × 1024 MB = 4096 MB. 4096 ÷ 3 ≈ 1365 songs.)

Apply it — a mixed storage scenario

A school wants to estimate storage needed for a new set of class resources: 50 photos averaging 4 MB each, 20 minutes of mono audio recorded at 44,100 Hz/16-bit (use the formula from the Sound Representation lesson), and a batch of text documents totalling 15 MB. Calculate the total storage required, in GB, showing each component's contribution separately before summing.

(Photos: 50 × 4 = 200 MB. Audio: 44,100 × 16 × (20×60) × 1 bits = 846,720,000 bits = 105,840,000 bytes ≈ 100.9 MB. Documents: 15 MB. Total: 200 + 100.9 + 15 = 315.9 MB ≈ 0.31 GB.)

Common mistake

Forgetting that a step change from bits to bytes (divide by 8) is a completely different operation from a step change between byte-based units like KB→MB (divide by 1024) — mixing these up (e.g. dividing by 1024 when you meant to divide by 8) is one of the most common calculation errors in this whole topic, and always worth double-checking explicitly.

Challenge

A cloud storage plan offers 100 GB. Estimate how many 24-bit, 4000×3000 pixel photos (using the Image Representation formula) it could store, showing your full working from pixels through to GB, and state one simplifying assumption your estimate relies on (e.g. ignoring metadata, assuming no compression).

Looking ahead: Sequence 8 (Computer Systems & Architecture) moves from how data is represented to what physically processes it — the same binary values calculated throughout this sequence are exactly what the processor you'll study next actually fetches, decodes and executes.