Units of Data Storage: Bits, Bytes, Kilobytes and File Size Calculations

A bit is a single binary digit, 0 or 1 — the smallest unit of data a computer stores. Eight bits make a byte, and larger units scale up from there. GCSE questions ask you to convert between units and to calculate the size of text, image and sound files from first principles.

The units, from smallest to largest

A nibble is worth remembering because it maps exactly onto one hexadecimal digit — which is precisely why hexadecimal is used as shorthand for binary.

Why is a byte eight bits?

Eight bits give 2⁸ = 256 different combinations, which was enough to represent every letter, digit and punctuation mark in the early character sets with room to spare. The byte became the standard unit of addressable memory, and everything since has been built around it. When you see a specification say "8-bit", "16-bit" or "64-bit", it is counting bits in multiples of that same byte.

Powers of ten versus powers of two

There is a genuine ambiguity here, and exam boards deal with it explicitly.

Historically, a kilobyte meant 1,024 bytes (2¹⁰), because computers work in powers of two. Modern convention, and current GCSE specifications, use the decimal definition: 1 kB = 1,000 bytes. The binary quantities have their own names — kibibyte (KiB) = 1,024 bytes, mebibyte (MiB) = 1,024 KiB, and so on.

For exams, use 1,000 unless the question tells you otherwise. It is worth knowing the binary prefixes exist, because they explain why a "1 TB" drive shows as roughly 931 GB in an operating system that is quietly counting in powers of two.

Converting between units

To go up a unit, divide by 1,000. To go down, multiply by 1,000. To move between bits and bytes, divide or multiply by 8.

Example 1 — how many bits in 3 kB? 3 kB × 1,000 = 3,000 bytes. 3,000 × 8 = 24,000 bits.

Example 2 — express 6,500,000 bytes in megabytes. 6,500,000 ÷ 1,000 = 6,500 kB. 6,500 ÷ 1,000 = 6.5 MB.

Example 3 — a broadband connection runs at 40 Mbps. How many megabytes per second is that? Note the lower-case b: megabits, not megabytes. 40 ÷ 8 = 5 MB per second. This trap appears constantly in networking questions and in real-world broadband advertising.

Calculating file sizes

Text files

File size (bits) = number of characters × bits per character

A plain text file of 500 characters using 8-bit ASCII: 500 × 8 = 4,000 bits = 500 bytes = 0.5 kB.

With 16-bit Unicode, the same 500 characters take 1,000 bytes — twice the space, because each character needs twice as many bits.

Bitmap images

File size (bits) = width × height × colour depth

A 200 × 300 pixel image with a colour depth of 24 bits: 200 × 300 = 60,000 pixels. 60,000 × 24 = 1,440,000 bits. 1,440,000 ÷ 8 = 180,000 bytes = 180 kB.

Colour depth is the number of bits used per pixel. A depth of n bits gives 2ⁿ possible colours, so 1 bit gives black and white, 8 bits gives 256 colours, and 24 bits gives over 16 million.

Real image files are slightly larger than this calculation suggests, because they also store metadata — dimensions, colour depth, creation date — in a header. Exam questions usually ask for the pixel data only unless the header size is given.

Sound files

File size (bits) = sample rate × duration (seconds) × bit depth × number of channels

A 30-second mono recording at 44,100 Hz with a 16-bit sample depth: 44,100 × 30 = 1,323,000 samples. 1,323,000 × 16 = 21,168,000 bits. 21,168,000 ÷ 8 = 2,646,000 bytes ≈ 2.6 MB.

In stereo, multiply by 2 — around 5.3 MB. This is why uncompressed audio is so large, and why compressed formats came to dominate.

Common mistakes to avoid

• Mixing up bits and bytes. Lower-case b is bits, upper-case B is bytes. Broadband speeds are quoted in bits; file sizes in bytes.
• Forgetting to divide by 8 at the end of an image or sound calculation. The formula produces bits; the answer is usually wanted in bytes.
• Multiplying by 1,024 when the question expects 1,000. Follow the convention your specification uses.
• Missing the number of channels in a stereo sound calculation.
• Not stating units. An answer of "180,000" without "bytes" cannot be given full marks.

Frequently asked questions

Why does a 1 TB hard drive show as less than 1 TB on my computer?

The manufacturer counts a terabyte as 1,000,000,000,000 bytes, using decimal prefixes. Many operating systems divide by 1,024 at each step, effectively reporting tebibytes while still writing "TB". The same physical drive therefore appears as roughly 931 of those units. No storage is missing — it is two different definitions of the same word. Some of the difference is also accounted for by the file system's own structures.

What is the difference between a kilobyte and a kibibyte?

A kilobyte is 1,000 bytes; a kibibyte is 1,024 bytes. The kibibyte (KiB) and its relatives — mebibyte, gibibyte, tebibyte — were introduced to remove the ambiguity that arose when "kilo" was used loosely for both. Current GCSE specifications use the decimal definitions, so answer in multiples of 1,000 unless a question says otherwise.

How do I calculate the size of a compressed file?

You cannot calculate it exactly from the formulas above, because compression removes redundancy in a way that depends on the specific content. What you can calculate is the uncompressed size, and questions often ask you to compare that with a stated compressed size to work out the compression ratio. If a 180 kB bitmap compresses to 45 kB, the ratio is 4:1 and 75% of the original size has been saved.

Why do image files get bigger when you increase the colour depth?

Colour depth is the number of bits stored for every single pixel. Doubling it from 8 bits to 16 bits doubles the storage needed for every pixel in the image, so the file size doubles too. The benefit is a much larger palette: 8 bits gives 256 colours, 16 bits gives 65,536, and 24 bits gives over 16 million — enough that photographs look continuous to the human eye.

For Socratic GCSE Computer Science tutoring — data representation, file sizes and beyond — visit aitutors.me.