Bytes, MB, GB: How to Navigate Computer Storage?

Computing uses units of measurement that can be confusing. Between the language of hard drive manufacturers and that of your operating system (Windows, macOS), there is a mathematical gap often misunderstood.

1. Bit and Byte: The Basis of Everything

The bit is the smallest unit of information (0 or 1). A byte is composed of 8 bits.

$1 \text{ byte} = 8 \text{ bits}$

2. The War of Powers: Base 10 vs Base 2

This is where calculation errors occur.

• The decimal system (SI): Used by manufacturers, it follows powers of 10.
• The binary system: Used by computers, it follows powers of 2 ($2^{10}$).

Conversion in base 10 (International standard)

$1 \text{ KB} = 10^3 = 1\ 000 \text{ bytes}$ $1 \text{ MB} = 10^6 = 1\ 000\ 000 \text{ bytes}$

Conversion in base 2 (Computer reality)

To be precise, we should speak of Kibibytes (KiB) or Mebibytes (MiB): $1 \text{ KiB} = 2^{10} = 1\ 024 \text{ bytes}$ $1 \text{ MiB} = 2^{20} = 1\ 048\ 576 \text{ bytes}$

3. The Mystery of the "Missing" Hard Drive

When you buy a $1 \text{ TB}$ drive ($10^{12}$ bytes), your computer divides this number by $1\ 024^3$ to display the size in GB.

The actual conversion formula seen by your PC is: $Capacity_{PC} = \frac{Capacity_{Manufacturer}}{(1.024)^3}$

This is why a 1000 GB drive actually displays only 931 GB on screen.

4. Internet Speed: Mbps vs MB/s

Another common confusion concerns download speed. Providers advertise Megabits per second (Mbps), but your browsers display Megabytes per second (MB/s).

To convert from one to the other, divide by 8: $Speed_{(MB/s)} = \frac{Speed_{(Mbps)}}{8}$

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