Storage Units & File-Size Calculations

Syllabus & Goals 3 min

Cambridge 1.3 · Data storage and file compression Paper 1 · Computer Systems

By the end of this lesson you can:

1. State the units of storage from bit and nibble up to PiB, using the IEC (× 1024) system.
2. Calculate the file size of a bitmap image and how many images fit on a device.
3. Calculate the file size of a mono or stereo sound file, in KiB, MiB or GiB.

Textbook: Chapter 1, §1.3.1–1.3.2 (pp. 32–34)

Recap / Warm-Up 5 min

Last lesson you saw that more pixels, more colour depth, a higher sample rate or a larger resolution all make bigger files. Now you put numbers on it.

Quick starter

How many bits are in one byte? How many bits in a nibble?

Key Concept 14 min

1 · Units of storage

A bit (0 or 1) is the basic unit. A nibble is 4 bits. A byte is 8 bits — the smallest unit of memory a computer addresses. Bigger sizes are measured in multiples of bytes.

Memory is built in powers of 2, so the IEC (International Electrotechnical Commission) units step up by 2¹⁰ = 1024 each time. The syllabus uses only these units.

2 · Why a "64 GB" card shows less space

Some manufacturers still label storage in SI units, where a gigabyte (GB) is 1 000 000 000 bytes. Computers measure in GiB (1 073 741 824 bytes). The two do not match.

3 · The two formulas

Both formulas give an answer in bits. Then walk down the ladder:

Worked Example 12 min

Worked example 1 · image size in MiB

Question: a photo is 2 560 × 1 440 pixels with a colour depth of 24 bits. Calculate its size in MiB.

1. Pixels = 2 560 × 1 440 = 3 686 400.
2. Bits = 3 686 400 × 24 = 88 473 600 bits.colour depth is bits per pixel, so this is the total number of bits.
3. Bytes = 88 473 600 ÷ 8 = 11 059 200 bytes.
4. KiB = 11 059 200 ÷ 1024 = 10 800 KiB.
5. MiB = 10 800 ÷ 1024 = 10.55 MiB (to 2 d.p.).each ÷ 1024 moves one rung down the IEC ladder.

Worked example 2 · how many photos fit?

Question: photos are 1 600 × 1 200 pixels with 24-bit colour. How many fit on a 16 GiB memory card?

1. Pixels = 1 600 × 1 200 = 1 920 000.
2. Size of one photo = 1 920 000 × 24 ÷ 8 = 5 760 000 bytes.
3. Card = 16 × 1024 × 1024 × 1024 = 17 179 869 184 bytes.both sizes must be in the same unit before dividing.
4. 17 179 869 184 ÷ 5 760 000 = 2 982.62.
5. Answer: 2 982 photos.round down — a part-photo cannot be stored.

Worked example 3 · stereo sound in MiB

Question: a 45-second clip is recorded in stereo at 48 000 Hz with a 16-bit sample resolution. Calculate the file size in MiB.

1. One channel = 48 000 × 16 × 45 = 34 560 000 bits.
2. Stereo × 2 = 69 120 000 bits.stereo stores two channels, so twice the samples.
3. Bytes = 69 120 000 ÷ 8 = 8 640 000 bytes.
4. MiB = 8 640 000 ÷ 1 048 576 = 8.24 MiB (to 2 d.p.).

The image calculation as code

// Size of a bitmap image in MiB
DECLARE Width, Height, ColourDepth : INTEGER
DECLARE Bits, Bytes : INTEGER
DECLARE SizeMiB : REAL
Width ← 2560
Height ← 1440
ColourDepth ← 24
Bits ← Width * Height * ColourDepth
Bytes ← Bits DIV 8
SizeMiB ← Bytes / (1024 * 1024)
OUTPUT "Image size: ", SizeMiB, " MiB"

width = 2560
height = 1440
colour_depth = 24
bits = width * height * colour_depth
size_bytes = bits // 8
size_mib = size_bytes / (1024 * 1024)
print("Image size:", size_mib, "MiB")

Image size: 10.546875 MiB

Try It Yourself 12 min

📝 Exam Practice 10 min

Recap & Key Terms 3 min

Storage is measured in IEC units that step up by 1024 (KiB, MiB, GiB, TiB, PiB). An image's size is resolution × colour depth; a sound's is rate × resolution × seconds (× 2 for stereo). Both give bits: divide by 8 for bytes, then by 1024 per unit. Round down when counting how many files fit.

Bit / nibble / byte

A bit is a single 0 or 1; a nibble is 4 bits; a byte is 8 bits.

Kibibyte (KiB)

2¹⁰ = 1024 bytes.

Mebibyte (MiB)

2²⁰ = 1 048 576 bytes (1024 KiB).

Gibibyte (GiB)

2³⁰ = 1 073 741 824 bytes (1024 MiB).

Image file size

Image resolution (pixels) × colour depth (bits).

Sound file size

Sample rate (Hz) × sample resolution (bits) × length (s); × 2 for stereo.

Homework 1 min

Task (≤ 15 min): a photo is 1920 × 1080 pixels with a colour depth of 24 bits. Calculate its size in (a) bytes and (b) MiB, to 2 decimal places. (c) How many of these photos fit on a 4 GiB card? [4]