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 to PiB using the IEC system.
2. Calculate the file size of a bitmap image.
3. Calculate the file size of a sound sample.

Recap / Warm-Up 5 min

Last lesson you saw that higher resolution and colour depth make bigger files. Now we put numbers to it.

Quick starter

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

Key Concept 14 min

1 · Units of storage (IEC)

A bit is a single 0 or 1. A nibble is 4 bits and a byte is 8 bits. Because memory is built in powers of 2, the syllabus uses the IEC units, where each step is × 1024 (2¹⁰):

2 · The two formulas

Both formulas give an answer in bits. Divide by 8 for bytes, then by 1024 for each unit step (KiB → MiB → GiB).

Worked Example 12 min

(a) Image: 2048 × 2048 pixels, colour depth 16 bits — size in MiB?

1. Total pixels = 2048 × 2048 = 4 194 304
2. Bits = 4 194 304 × 16 = 67 108 864 bits
3. Bytes = 67 108 864 ÷ 8 = 8 388 608 bytes
4. MiB = 8 388 608 ÷ (1024 × 1024) = 8 MiB

(b) Sound: 44 100 Hz, 16-bit, 60 min, stereo — size in MiB?

1. Bits = 44 100 × 16 × (60 × 60) = 2 540 160 000
2. Stereo ×2 = 5 080 320 000 bits
3. Bytes = 5 080 320 000 ÷ 8 = 635 040 000
4. MiB = 635 040 000 ÷ (1024 × 1024) ≈ 605 MiB

The image calculation as code

Cambridge pseudocode

// Work out the size of a bitmap image
DECLARE Width, Height, ColourDepth : INTEGER
DECLARE Bits, Bytes : INTEGER
Width ← 2048
Height ← 2048
ColourDepth ← 16
Bits ← Width * Height * ColourDepth
Bytes ← Bits DIV 8
OUTPUT "Image size in bytes: ", Bytes

The same calculation in Python (IDLE)

# File size of a bitmap image, converted to MiB
width = 2048
height = 2048
colour_depth = 16
bits = width * height * colour_depth
size_bytes = bits // 8
size_mib = size_bytes / (1024 * 1024)
print("Image is", size_mib, "MiB")

Output

Image is 8.0 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…). An image's size is resolution × colour depth; a sound's size is sample rate × resolution × seconds (× 2 for stereo). Both give bits — divide by 8 for bytes, then by 1024 per unit.

Bit / nibble / byte

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

Kibibyte (KiB)

1024 bytes (2¹⁰) — the IEC unit one step above a byte.

Image file size

Resolution (pixels) × colour depth (bits).

Sound file size

Sampling rate × sampling resolution × seconds (× 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 1 decimal place).