Numerical Bases

This cheatsheet looks at representing numerical bases.

Different bases

The use of 10 as a base is fairly arbitary. We can use any base system for our numbers that makes sense. Some everyday examples of this you are used to seeing is minutes, which is base 60, and hours which is base 12/24. In computing, common bases are 2, 8, 10 and 16.

Prefixes for Integers

Integer literals are often written with a prefix to show the base:

Prefix	Meaning
0b	binary
0o	octal
(none)	base 10
0x	Hexadecimal
0	octal (old)

Some languages use ‘0’ as a prefix for octal, this can get confusing so some have adopted 0o to mean octal. Both are still in use.

Examples

Here are some examples of each of these conventions:

Hexadecimal	Decimal	Octal	Binary
0x0	0	0o0	0b0
0x1	1	0o1	0b1
..	..	..	..
0x9	9	0o11	0b1001
0xA	10	0o12	0b1010

Binary Notation

There are two commonly used ways of representing large binary values. One is based on SI-prefixes, the other uses a power of two.

A binary integer is formed of bits, a bit can either be 0 or 1 (in other words, its base 2). An n-bit (unsigned) binary number can store a value between 0 and 2ⁿ-1.

The number 0 in binary
Power	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Value
Binary	0	0	0	0	0	0	0	0
Decimal	0	0	0	0	0	0	0	0

Signed Values

Signed binary numbers can be stored in many possible ways:

Signed bit (the highest bit is 0 for positive, and 1 for negative)
Twos compliment (the highest bit is regarded as negative)

Representing large values

Decimal

SI-prefix based.

name	symbol	size
kilobyte	kB	1000
megabyte	MB	1000²
gigabyte	GB	1000³
terabyte	TB	1000⁴
petabyte	PB	1000⁵
exabyte	EB	1000⁶
zettabyte	ZB	1000⁷
yottabyte	YB	1000⁸

Note some operating systems (Windows) use kilo to mean 1024 bytes, due to historical tradition. This is not the SI defintion of kilo.

Binary

IEC convention.

name	symbol	size
kibibyte	KiB	1024
mebibyte	MiB	1024²
gibibyte	GiB	1024³
tebibyte	TiB	1024⁴
pebibyte	PiB	1024⁵
exbibyte	EiB	1024⁶
zebibyte	ZiB	1024⁷
yobibyte	YiB	1024⁸

Last updated 0001-01-01