Binary prefixes and magnitudes

By the end of this lesson

By the end you can tell a kibibyte from a kilobyte (and mebi from mega, gibi from giga, tebi from tera), and convert between them in your head.

Bits, nibbles and bytes

Everything a computer stores is a pattern of bits (binary digits), each one a 0 or a 1.

Unit	Size
bit (b)	one binary digit
nibble	4 bits
byte (B)	8 bits

Real files run to millions of bytes, so we need prefixes. The catch: there are two families of prefix, and they don't agree.

Definition

Decimal prefix

A prefix that multiplies by a power of 10: kilo (k) $= 10^3$ , mega (M) $= 10^6$ , giga (G) $= 10^9$ , tera (T) $= 10^{12}$ . Each step up multiplies by 1000.

Definition

Binary prefix

A prefix that multiplies by a power of 2: kibi (Ki) $= 2^{10}$ , mebi (Mi) $= 2^{20}$ , gibi (Gi) $= 2^{30}$ , tebi (Ti) $= 2^{40}$ . Each step up multiplies by $2^{10} = 1024$ .

The two ladders, side by side

Decimal unit	Bytes	Binary unit	Bytes
1 kB (kilobyte)	1 000	1 KiB (kibibyte)	1 024
1 MB (megabyte)	1 000 000	1 MiB (mebibyte)	1 048 576
1 GB (gigabyte)	1 000 000 000	1 GiB (gibibyte)	1 073 741 824
1 TB (terabyte)	1 000 000 000 000	1 TiB (tebibyte)	1 099 511 627 776

The "bi" in kibi, mebi, gibi and tebi stands for binary. See "bi", think 1024.
Watch the symbols: kilo is a lower-case k; kibi is Ki.
The only number you must know cold is $2^{10} = 1024$ . Every other step is "times 1024 again".

Quick check

Multiple choiceQuestion 1 · Recall

One-line answerQuestion 2 · Recall

Answer the 2 questions above to continue.