Useful Computer Numeral Guide

by Peter Perlsø, 23rd of December 2002, updated March 2007 (last update: Jan, 2005)

The purpose of this page is to explain the basics of computer numeral representation, and list some significant numbers used frequently in computing. I hope you find it useful.

The basics

All modern computing is based on binary numbers:

Bit: b - Binary Digit; a single digit that can have two values: '0' or '1' - hence "Binary" ("Bi-" means "Two-something" in Latin). All numbers stored in computers are represented in strings of bits. Thus, all "round" numbers are in some way divisible by two, asuch as: (2^n)... 2,4,8,16,32,64 etc.

Byte: B - A clump of 8 bits. Normally this is the smallest chunk of memory that a computer can address (access or store in memory). Also known as an "octet", especially in Francophile tounge.

The Big Ones

KiloByte: KB	1000 Bytes (1e3 B)
MegaByte: MB	1000 KiloBytes (1e6 B)
GigaByte: GB	1000 MegaBytes(1e9 B)
TeraByte: TB	1000 GigaBytes (1e12 B)
Petabyte: PB	1000 TeraBytes (1e15 B)
Exabyte: EB	1000 PetaBytes (1e18 B)
Avabit: Ab	~ 6.022e23 bits

KibiByte: KiB	1024 Bytes (2^10)
MebiByte: MiB	1024 KibiBytes (2^20 B)	Slightly less than the data capacity of old floppy diskettes.
GibiByte: GiB	1024 MebiBytes(2^30 B)	The data capacity of an average 1996 hard drive.
TebiByte: TiB	1024 GibiBytes (2^40 B)	The capacity of the largest singular hard drive unit in 2007.
PebiByte: PiB	1024 TebiBytes (2^50 B)	The projected typical size of a prosumer RAID array by 2020.
ExiByte: EiB	1024 PebiBytes (2^60 B)	~ 1.15 pentillion combinations; less than one percent of the data capacity of one cubic centimetre of concentrated human DNA material.

Kilo- or Kibi- ?!?

In 1998, the US NIST (National Institute of Standards and Technology) decided to rename the existing standards, so that instead of kilo-, mega- and giga- bytes, we would have kibi-, mebi- and gibi-bytes (as in KIlo-BInary, MEga-BInary and GIga-BInary).

It is suggested that you use the NIST naming standard in regards to computerized data storage, as the discrepancy between "kilo-" and "kibi-" size types become larger, the larger units you use. The incorrect naming of storage sizes today, for example, is the reason that you get less storage space on your hard disk compared to what the manufacturer advertises.

Further info here.

Computerized representation of numbers:

decimal (base 10 - human)	binary (base 2 - raw digital)	hexadecimal (base 16)
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
6	110	6
7	111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F
16	10000	10
32	100000	20
64	1000000	40
100	1100100	64
128	10000000	80
200	11001000	C8
255	11111111	FF
256	100000000	100

Bits and combinations:

n (# of bits)	2^n (# of combos)	Comments
0	1
1	2	a bit (obviously, i hope?)
2	4
3	8
4	16	also known as a nibble - half a byte
5	32
6	64
7	128
8	256	a Byte = 256 combinations
9	512
10	1024
16	65536	High Color depth* maximum number of allocation blocks in FAT16 and HFS file systems
24	16.7 million	True Color depth
28	268.4 million	maximum number of logical blocks on ATA100 or older hard disks
32	4.29 billion**	CMYK color depth (for professional graphics and printing) maximum number of allocation blocks in FAT32/NTFS and HFS+ file systems maximum adressable amount of memory for older IA32 and PPC CPUs maximum number of unique IPv4 IP addresses
36	68.7 billion**	maximum adressable amount of memory for PPC 7450 and Intel Pentium Xeon CPUs
48	281.4 trillion**	maximum number of logical blocks on ATA133 and newer hard disks maximum number of unique Ethernet MAC adresses
64	18.44 pentillions**	16 ExiBytes; the holy grail of storage of modern computing maximum numbeer of unique IPv6 IP addresses

*) On Macs, Thousands of Colors correspond to 32768 colours (15 bits = 5+5+5) and one alpha channel (transparency).

**) Please note:

US billions = danish "milliarder" = 10^9
US trillions = danish "billioner" = 10^12
US quadrillions = danish "billiarder" = 10^15
US pentillions = danish "trillioner" = 10^18