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Bits, bytes, and their multiples

Posted on January 16, 2023, by Sébastien

Cet article est aussi disponible en français.

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This post covers the absolute basics, and is aimed at people who aren't familiar with these concepts (yet).

Bits

The bit is the smallest unit of information.

It has only two possible values: 0 or 1.

The symbol for the bit is either simply "bit", or the lowercase letter "b".

Bytes

A byte consists of eight bits.

It's represented by the uppercase letter "B".

Capitalization is crucial, as the lowercase letter "b" represents the "bit" unit, as mentioned above.

Multiples (powers of 10)

Strictly speaking, the "kilo" prefix denotes one thousand – as in "kilogram" or "kilometer" – "mega" is one million, "giga" is one billion, "tera" is one trillion, and so on.

Therefore:

1 kB (kilobyte) = 1000 bytes
1 MB (megabyte) = 1000 kB = 1,000,000 bytes
1 GB (gigabyte) = 1000 MB = 1,000,000 kB = 1,000,000,000 bytes
1 TB (terabyte) = 1000 GB = 1,000,000 MB = 1,000,000,000 kB = 1,000,000,000,000 bytes

Again, capitalization is important:

Interpreted literally, 1 mb/s would be 1 millibit per second.

That is to say, 0.001 bit/s, instead of the intended 1,000,000 bit/s (1 Mbit/s).

Multiples (powers of 2)

Sometimes, multiples of 1024 are used instead of multiples of 1000.

This number was chosen because 1024 is a power of 2 (namely, 2¹⁰).

Strictly speaking – again – multiples of 1024 should use different prefixes than multiples of 1000:

1 KiB (kibibyte) = 1024 bytes
1 MiB (mebibyte) = 1024 KiB = 1,048,576 bytes
1 GiB (gibibyte) = 1024 MiB = 1,048,576 KiB = 1,073,741,824 bytes
1 TiB (tebibyte) = 1024 GiB = 1,048,576 MiB = 1,073,741,824 kB = 1,099,511,627,776 bytes

However, there's a catch:

Operating systems such as Windows use the metric prefixes… to represent binary multiples!

This can lead to some confusion:

Your brand new HDD (or SSD), marketed as 1 TB, does indeed contain 1,000,000,000,000 bytes
Windows will report a capacity of only 931 GB (even though it's technically 931 GiB)

Common uses of bits, bytes, and their multiples

As mentioned above, storage device manufacturers use decimal multiples of bytes (e.g. 1 TB = 1,000,000,000,000 bytes)…
…whereas Windows uses binary multiples of bytes (e.g. 1 GB = 1,073,741,824 bytes) for file sizes and drive sizes
RAM sticks use binary multiples of bytes (e.g. 8 GB = 8,589,934,592 bytes)
Network interface speeds are typically expressed as decimal multiples of bits
=> Example 1: Gigabit Ethernet (1 Gbit/s or 1 Gbps) can transmit up to 1,000,000,000 bits per second
=> Example 2: Until 2008, Wi-Fi had a maximum theoretical data rate of 54 Mbit/s, i.e. 54,000,000 bits per second
File transfers – as displayed in your browser, or your operating system – may use multiple of bytes. Therefore, your download speed won't ever show more than 125 MB/s (or 119 MiB/s) when you're on Gigabit Ethernet.

A note about internationalization

In some languages, the word "byte" is not used, and a different letter may be assigned to represent it.

In particular, the French word for "byte" is "octet", and the symbol is "o".

This causes quite some confusion when a native French speaker sees a label such as "32 GB" for the first time (on a USB flash drive, typically).

They might think they received a 32 gigabit device, which would be 8 times smaller than the 32 gigabytes they wanted ("32 Go").