Useful Computer Numeral Guide

written by Peter Perlsø, created 23rd of December 2002, last updated August 2009

This page is intended to explain the basics of computer numeral representation in an accessible way, and list some significant uses of certain numbers. I hope you find it useful, feel free to send additions or corrections to me.

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 and so on.

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 HD floppy diskettes.
GibiByte: GiB 1024 MebiBytes(2^30 B) The data capacity of a typical 1996 consumer PC hard drive.
TebiByte: TiB 1024 GibiBytes (2^40 B) The capacity of the largest available consumer 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).

You should use the NIST naming standard in regards to computerized data storage, as the bigger units you use, the larger discrepancies you will see between the two, which is for example evident in the controversy over differences between advertised and actual hard drive capacities in recent years. The reason you see those small-type disclaimers that "actual formatted capacity less" on the box for your hard drives are due to that the manufacturer can't be bothered to advertise the drive capacity in Gibi-bytes as they ought to.

More 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 and noteworthy uses

0 1
1 2
  • a bit (obviously, i hope?)
2 4
3 8
4 16
  • A half-byte, also known as a nibble
5 32
6 64
7 128
8 256
  • a Byte = 256 combinations
9 512
10 1024
12 4096
  • the original maximum number of colours in the Commodore Amiga's palette.
16 65536
  • "High Color" depth - aka Thousands of Colours*
  • maximum number of allocation blocks in FAT16 and HFS file systems
24 16.7 million
  • "True Color" depth - aka Millions of Colours
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 number of memory bytes for older IA32/x86 and PowerPC CPUs
  • maximum number of unique IPv4 IP addresses
36 68.7 billion**
  • maximum adressable number of memory bytes for PowerPC 7450 and Intel Pentium Xeon CPUs
48 281.4 trillion**
  • maximum number of logical blocks on ATA133 and later model hard disks
  • maximum number of unique Ethernet MAC adresses
64 18.44 pentillions**
  • 16 ExiBytes; the holy grail of storage of modern computing
  • maximum number of unique IPv6 IP addresses


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

**) Lingual oddity:

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

Thanks to Wade Theragakis for additions.

cc titancity.com