Orders of magnitude (data)

From Wikipedia the free encyclopedia

An order of magnitude is usually a factor of ten. Thus, four orders of magnitude is a factor of 10,000 or 104.

This article presents a list of multiples, sorted by orders of magnitude, for units of information measured in bits and bytes.

The byte is a common unit of measurement of information (kilobyte, kibibyte, megabyte, mebibyte, gigabyte, gibibyte, terabyte, tebibyte, etc.). For the purpose of this article, a byte is a group of 8 bits (octet), a nibble is a group of four bits. Historically, neither assumption has always been true.

The decimal SI prefixes kilo, mega, giga, tera, etc., are powers of 103 = 1000. The binary prefixes kibi, mebi, gibi, tebi, etc. respectively refer to the corresponding power of 210 = 1024.

In casual usage, when 1024 is a close enough approximation of 1000, some of the decimal prefixes have been used in relation to computer memories to mean the binary power, but increasingly from 1998, standards bodies have chosen to limit the resultant confusion by disallowing when software displays a binary quantity with a decimal prefix.[1][2] Microsoft operating systems still report file and free spaces on a storage device in this casual sense.

Orders of magnitude (data)
Binary
[bits] 		Decimal Item
Factor Term Factor Term
2−1 10−1 0.415 bits (log2 4/3) – amount of information needed to eliminate one option out of four.
0.6–1.3 bits – approximate information per letter of English text.[3]
20 bit 100 bit 1 bit – 0 or 1, false or true, Low or High (a.k.a. unibit)
1.442695 bits (log2 e) – approximate size of a nat (a unit of information based on natural logarithms)
1.5849625 bits (log2 3) – approximate size of a trit (a base-3 digit)
21 2 bits – a crumb (a.k.a. dibit) enough to uniquely identify one base pair of DNA
3 bits – a triad(e), (a.k.a. tribit) the size of an octal digit
22 nibble 4 bits – (a.k.a. tetrad(e), nibble, quadbit, semioctet, or halfbyte) the size of a hexadecimal digit; decimal digits in binary-coded decimal form
5 bits – the size of code points in the Baudot code, used in telex communication (a.k.a. pentad)
6 bits – the size of code points in Univac Fieldata, in IBM "BCD" format, and in Braille. Enough to uniquely identify one codon of genetic code. The size of code points in Base64; thus, often the entropy per character in a randomly-generated password.
7 bits – the size of code points in the ASCII character set

– minimum length to store 2 decimal digits

23 byte (B) 8 bits – (a.k.a. octet or octad(e)) on many computer architectures.

– equivalent to 1 "word" on 8-bit computers (Apple II, Atari 8-bit computers, Commodore 64, etc.).
– the "word size" for 8-bit console systems including: Atari 2600, Nintendo Entertainment System

101 decabit 10 bits

– minimum bit length to store a single byte with error-correcting computer memory
– minimum frame length to transmit a single byte with asynchronous serial protocols

12 bits – wordlength of the PDP-8 of Digital Equipment Corporation (built from 1965 to 1990)
24 16 bits

– the Basic Multilingual Plane of Unicode, containing character codings for almost all modern languages, and a large number of symbols
– the basic unit in UTF-16; the full Universal Character Set (Unicode) can be encoded in one or two of these
– commonly used in many programming languages, the size of an integer capable of holding 65,536 different values
– equivalent to 1 "word" on 16-bit computers (IBM PC, Commodore Amiga)
– the "word size" for 16-bit console systems including: Sega Genesis, Super Nintendo, Mattel Intellivision

25 32 bits (4 bytes)

– size of an integer capable of holding 4,294,967,296 different values
– size of an IEEE 754 single-precision floating point number
– size of addresses in IPv4, the current Internet Protocol
– equivalent to 1 "word" on 32-bit processors, including those for the Apple Macintosh, Pentium-based PC, PlayStation, GameCube, Xbox, Wii

36 bits – size of word on Univac 1100-series computers and Digital Equipment Corporation's PDP-10
56 bits (7 bytes) – cipher strength of the DES encryption standard
26 64 bits (8 bytes)

– size of an integer capable of holding 18,446,744,073,709,551,616 different values
– size of an IEEE 754 double-precision floating point number
– equivalent to 1 "word" on 64-bit computers (Power, PA-RISC, Alpha, Itanium, SPARC, x86-64 PCs and Macintoshes).
– the "word size" for 64-bit console systems including: Nintendo 64, PlayStation 2, PlayStation 3, Xbox 360

80 bits (10 bytes) – size of an extended precision floating point number, for intermediate calculations that can be performed in floating point units of most processors of the x86 family.
102 hectobit 100 bits
27 128 bits (16 bytes)

– size of addresses in IPv6, the successor protocol of IPv4
– minimum cipher strength of the Rijndael and AES encryption standards, and of the widely used MD5 cryptographic message digest algorithm
– size of an SSE vector register, included as part of the x86-64 standard

160 bits (20 bytes) – maximum key length of the SHA-1, standard Tiger (hash function), and Tiger2 cryptographic message digest algorithms
28 256 bits (32 bytes)

– minimum key length for the recommended strong cryptographic message digests as of 2004
– size of an AVX2 vector register, present on newer x86-64 CPUs

29 512 bits (64 bytes)

– maximum key length for the standard strong cryptographic message digests in 2004
– size of an AVX-512 vector register, present on some x86-64 CPUs

103 kilobit
(kbit) 		1,000 bits (125 bytes)
210 kibibit
(Kibit) 		1,024 bits (128 bytes) - RAM capacity of the Atari 2600
1,288 bits (161 bytes) – approximate maximum capacity of a standard magnetic stripe card
211 2,048 bits (256 bytes) – RAM capacity of the stock Altair 8800
212 4,096 bits (512 bytes)

– typical sector size, and minimum space allocation unit on computer storage volumes, with most file systems
– approximate amount of information on a sheet of single-spaced typewritten paper (without formatting)

4,704 bits (588 bytes) – uncompressed single-channel frame length in standard MPEG audio (75 frames per second and per channel), with medium quality 8-bit sampling at 44,100 Hz (or 16-bit sampling at 22,050 Hz)
kilobyte
(kB, KB) 		8,000 bits (1,000 bytes)
213 kibibyte
(KiB) 		8,192 bits (1,024 bytes) – RAM capacity of a ZX81 and a ZX80.
9,408 bits (1,176 bytes) – uncompressed single-channel frame length in standard MPEG audio (75 frames per second and per channel), with standard 16-bit sampling at 44,100 Hz
104 15,360 bits – one screen of data displayed on an 8-bit monochrome text console (80x24)
214 16,384 bits (2 kibibytes) – one page of typed text,[4] RAM capacity of Nintendo Entertainment System
215 32,768 bits (4 kibibytes)
216 65,536 bits (8 kibibytes)
105 100,000 bits
217 131,072 bits (16 kibibytes) – RAM capacity of the smallest ZX Spectrum.
218 262,144 bits (32 kibibytes) - RAM capacity of Matra Alice 90
393,216 bits (48 kibibytes) - RAM capacity of 48K ZX Spectrum
506 kilobits – approximate size of this article as of 20 May 2019
219 524,288 bits (64 kibibytes) – RAM capacity of popular 8-bit computers like the C-64, Amstrad CPC etc.
106 megabit
(Mbit) 		1,000,000 bits
220 mebibit
(Mibit) 		1,048,576 bits (128 kibibytes) – RAM capacity of popular 8-bit computers like the C-128, Amstrad CPC etc. Or a 1024 x 768 pixel JPEG image.
1,978,560 bits – a one-page, standard-resolution black-and-white fax (1728 × 1145 pixels)
221 2,097,152 bits (256 kibibytes)
4,147,200 bits – one frame of uncompressed NTSC DVD video (720 × 480 × 12 bpp Y'CbCr)
222 4,194,304 bits (512 kibibytes)
4,976,640 bits – one frame of uncompressed PAL DVD video (720 × 576 × 12 bpp Y'CbCr)
5,000,000 bits – Typical English book volume in plain text format of 500 pages × 2000 characters per page and 5-bits per character.
5,242,880 bits (640 kibibytes) – the maximum addressable memory of the original IBM PC architecture
megabyte
(MB) 		8,000,000 bits (1,000 kilobytes) – the preferred definition of megabyte
8,343,400 bits – one "typical" sized photograph with reasonably good quality (1024 × 768 pixels).
223 mebibyte
(MiB) 		8,388,608 bits (1,024 kibibytes), one of a few traditional meanings of megabyte
107 11,520,000 bits – capacity of a lower-resolution computer monitor (as of 2006), 800 × 600 pixels, 24 bpp
11,796,480 bits – capacity of a 3.5 in floppy disk, colloquially known as 1.44 megabyte but actually 1.44 × 1000 × 1024 bytes
224
16,777,216 bits (2 mebibytes)
25,000,000 bits – amount of data in a typical color slide
30,000,000 bits – The first commercial harddisk IBM 350 in 1956 could store 3.75 MiB for a cost of US$50,000,[5] equivalent to $560,343 in 2023.
225 33,554,432 bits (4 mebibytes) – RAM capacity of stock Nintendo 64 and average size of a music track in MP3 format.
41,943,040 bits (5 mebibytes) – approximate size of the Complete Works of Shakespeare[4]
80,000,000 bits – In 1985 a 10 MB harddisk cost US$710,[5] equivalent to $2,011 in 2023.
98,304,000 bits – capacity of a high-resolution computer monitor as of 2011, 2560 × 1600 pixels, 24 bpp
50 – 100 megabits – amount of information in a typical phone book
226 108 67,108,864 bit (8 mebibytes)
227 134,217,728 bits (16 mebibytes)
150 megabits – amount of data in a large foldout map
228 268,435,456 bits (32 mebibytes)
144,000,000 bits: In 1980 an 18 MB hard disk cost US$4,199,[5] equivalent to $15,527 in 2023.
423,360,000 bits: a five-minute audio recording, in CDDA quality
229 536,870,912 bits (64 mebibytes)
109 gigabit
(Gbit) 		1,000,000,000 bits
230 gibibit
(Gibit) 		1,073,741,824 bits (128 mebibytes)
231 2,147,483,648 bits (256 mebibytes)
232 4,294,967,296 bits (512 mebibytes)
5.45×109 bits (650 mebibytes) – capacity of a regular compact disc (CD)
5.89×109 bits (702 mebibytes) – capacity of a large regular compact disc
6.4×109 bits – capacity of the human genome (assuming 2 bits for each base pair)
6,710,886,400 bits – average size of a movie in Divx format in 2002.[6]
gigabyte
(GB) 		8,000,000,000 bits (1,000 megabytes) – In 1995 a 1 GB harddisk cost US$849,[5] equivalent to $1,698 in 2023.
233 gibibyte
(GiB) 		8,589,934,592 bits (1,024 mebibytes) – The maximum disk capacity using the 21-bit LBA SCSI standard introduced in 1979.
1010 10,000,000,000 bits
234 17,179,869,184 bits (2 gibibytes). The storage limit of IDE standard for harddisks in 1986, also the volume size limit for the FAT16B file system (with 32 KiB clusters) released in 1987 as well as the maximum file size (2 GiB-1) in DOS operating systems prior to the introduction of large file support in DOS 7.10 (1997).
235 34,359,738,368 bits (4 gibibytes) – maximum addressable memory for the Motorola 68020 (1984) and Intel 80386 (1985), also the volume size limit for the FAT16B file system (with 64 KiB clusters) as well as the maximum file size (4 GiB-1) in MS-DOS 7.1-8.0.
3.76×1010 bits (4.7 gigabytes) – capacity of a single-layer, single-sided DVD
236 68,719,476,736 bits (8 gibibytes)
79,215,880,888 bits – 9.2 GiB size of Wikipedia article text compressed with bzip2 on 2013-06-05
1011 100,000,000,000 bits
237 137,438,953,472 bits (16 gibibytes).
1.46×1011 bits (17 gigabytes) – capacity of a double-sided, dual-layered DVD
2.15×1011 bits (25 gigabytes) – capacity of a single-sided, single-layered 12-cm Blu-ray
238 274,877,906,944 bits (32 gibibytes)
239 549,755,813,888 bits (64 gibibytes)
1012 terabit
(Tbit) 		1,000,000,000,000 bits
240 tebibit
(Tibit) 		1,099,511,627,776 bits (128 gibibytes) – estimated capacity of the Polychaos dubium genome, the largest known genome. The storage limit for ATA-1 compliant disks introduced in 1994.
1.6×1012 bits (200 gigabytes) – capacity of a hard disk that would be considered average as of 2008. In 2005 a 200 GB harddisk cost US$100,[5] equivalent to $156 in 2023. As of April 2015, this is the maximum capacity of a fingernail-sized microSD card.
241 2,199,023,255,552 bits (256 gibibytes) – As of 2017, this is the maximum capacity of a fingernail-sized microSD card
242 4,398,046,511,104 bits (512 gibibytes)
terabyte
(TB) 		8,000,000,000,000 bits (1,000 gigabytes) – In 2010 a 1 TB hard disk cost US$80,[5] equivalent to $112 in 2023.
243 tebibyte
(TiB) 		8,796,093,022,208 bits (1,024 gibibytes)
1013 10,000,000,000,000 bits (1.25 terabytes) – capacity of a human being's functional memory, according to Raymond Kurzweil in The Singularity Is Near, p. 126
16,435,678,019,584 bits (1.9 terabytes) – Size of all multimedia files used in the English Wikipedia in May 2012
244 17,592,186,044,416 bits (2 tebibytes) – Maximum size of MBR partitions used in PCs introduced in 1983, also the maximum disk capacity using the 32-bit LBA SCSI introduced in 1987
245 35,184,372,088,832 bits (4 tebibytes)
246 70,368,744,177,664 bits (8 tebibytes)
1014 100,000,000,000,000 bits
247 140,737,488,355,328 bits (16 tebibytes). NTFS volume capacity in Windows 7, Windows Server 2008 R2 or earlier implementation.[7]
1.5×1014 bits (18.75 terabytes)
248 281,474,976,710,656 bits (32 tebibytes)
(approximately) 4×1014 bits – as of 2022, data of π to the largest number of decimal digits ever calculated (1×1014).
249 562,949,953,421,312 bits (64 tebibytes)
1015 petabit
(Pbit) 		1,000,000,000,000,000 bits
250 pebibit
(Pibit) 		1,125,899,906,842,624 bits (128 tebibytes)
251 2,251,799,813,685,248 bits (256 tebibytes)
252 4,503,599,627,370,496 bits (512 tebibytes)
petabyte
(PB) 		8,000,000,000,000,000 bits (1,000 terabytes)
253 pebibyte
(PiB) 		9,007,199,254,740,992 bits (1,024 tebibytes)
1016 10,000,000,000,000,000 bits
254 18,014,398,509,481,984 bits (2 pebibytes)
255 36,028,797,018,963,968 bits (4 pebibytes) – theoretical maximum of addressable physical memory in the AMD64 architecture [citation needed]
4.5×1016 bits (5.625 petabytes) – estimated hard drive space in Google's server farm as of 2004 [citation needed]
256 72,057,594,037,927,936 bits (8 pebibytes)
10 petabytes (1016 bytes) – estimated approximate size of the Library of Congress's collection, including non-book materials, as of 2005.[8] Size of the Internet Archive topped 10 PB in October 2013[9]
1017 100,000,000,000,000,000 bits
257 144,115,188,075,855,872 bits (16 pebibytes)
2×1017 bits (25 petabytes) – Storage space of Megaupload file-hosting service at the time it was shut down in 2012[10]
258 288,230,376,151,711,744 bits (32 pebibytes)
259 576,460,752,303,423,488 bits (64 pebibytes)
8 ×1017, the storage capacity of the fictional Star Trek character Data
1018 exabit
(Ebit) 		1,000,000,000,000,000,000 bits
260 exbibit
(Eibit) 		1,152,921,504,606,846,976 bits (128 pebibytes). The storage limit using the 48-bit LBA ATA-6 standard introduced in 2002.
1.6×1018 bits (200 petabytes) – total amount of printed material in the world [citation needed]
2×1018 bits (250 petabytes) – storage space at Facebook data warehouse as of June 2013,[11] growing at a rate of 15 PB/month.[12]
261 2,305,843,009,213,693,952 bits (256 pebibytes)
2.4×1018 bits (300 petabytes) – storage space at Facebook data warehouse as of April 2014, growing at a rate of 0.6 PB/day.[13]
262 4,611,686,018,427,387,904 bits (512 pebibytes)
exabyte
(EB) 		8,000,000,000,000,000,000 bits (1,000 petabytes)
263 exbibyte
(EiB) 		9,223,372,036,854,775,808 bits (1,024 pebibytes)
1019 10,000,000,000,000,000,000 bits
264 18,446,744,073,709,551,616 bits (2 exbibytes).
265 36,893,488,147,419,103,232 bits (4 exbibytes)
50,000,000,000,000,000,000 bits (50 exabit)
266 73,786,976,294,838,206,464 bits (8 exbibytes)
1020 100,000,000,000,000,000,000 bits
1.2×1020 bits (15 exabytes) – estimated storage space at Google data warehouse as of 2013[14]
267 147,573,952,589,676,412,928 bits (16 exbibytes) – maximum addressable memory using 64-bit addresses without segmentation.[15] Maximum file size for ZFS filesystem.
268 295,147,905,179,352,825,856 bits (32 exbibytes)
3.5 × 1020 bits – increase in information capacity when 1 joule of energy is added to a heat-bath at 300 K (27 °C)[16]
269 590,295,810,358,705,651,712 bits (64 exbibytes)
1021 zettabit
(Zbit) 		1,000,000,000,000,000,000,000 bits
270 zebibit
(Zibit) 		1,180,591,620,717,411,303,424 bits (128 exbibytes)
271 2,361,183,241,434,822,606,848 bits (256 exbibytes)
3.4×1021 bits (0.36 zettabytes) – amount of information that can be stored in 1 gram of DNA[17]
4.7×1021 bits (0.50 zettabytes) – amount of digitally stored information in the world as of May 2009[18]
4.8×1021 bits (0.61 zettabytes) – total hard drive capacity shipped in 2016[19]
272 4,722,366,482,869,645,213,696 bits (512 exbibytes)
zettabyte
(ZB) 		8,000,000,000,000,000,000,000 bits (1,000 exabytes)
273 zebibyte
(ZiB) 		9,444,732,965,739,290,427,392 bits (1,024 exbibytes)
1022 10,000,000,000,000,000,000,000 bits
276 276 bits – Maximum volume and file size in the Unix File System (UFS) and maximum disk capacity using the 64-bit LBA SCSI standard introduced in 2000 using 512-byte blocks.[20]
1023 1.0×1023 bits – increase in information capacity when 1 joule of energy is added to a heat-bath at 1 K (−272.15 °C)[21]
277 6.0×1023 bits – information content of 1 mole (12.01 g) of graphite at 25 °C; equivalent to an average of 0.996 bits per atom.[22]
1024 yottabit
(Ybit) 		1,000,000,000,000,000,000,000,000 bits
7.3×1024 bits – information content of 1 mole (18.02 g) of liquid water at 25 °C; equivalent to an average of 12.14 bits per molecule.[23]
280 yobibit
(Yibit) 		1,208,925,819,614,629,174,706,176 bits (128 zebibytes)
yottabyte
(YB) 		8,000,000,000,000,000,000,000,000 bits (1,000 zettabytes)
283 yobibyte
(YiB) 		9,671,406,556,917,033,397,649,408 bits (1,024 zebibytes)
1025 1.1×1025 bits – entropy increase of 1 mole (18.02 g) of water, on vaporizing at 100 °C at standard pressure; equivalent to an average of 18.90 bits per molecule.[24]
1.5×1025 bits – information content of 1 mole (20.18 g) of neon gas at 25 °C and 1 atm; equivalent to an average of 25.39 bits per atom.[25]
Beyond standardized SI / IEC (binary) prefixes
2127 N/A 1038 N/A 2127 bits, 2124 bytes – IBM Eagle
2131 1039 2131 bits, 2128 bytes – theoretical maximum volume size of the ZFS filesystem.[26][27][28]
2150 1042 ~ 1042 bits – the number of bits required to perfectly recreate the natural matter of the average-sized U.S. adult male human brain down to the quantum level on a computer is about 2.6×1042 bits of information (see Bekenstein bound for the basis for this calculation).
2193 1058 ~ 1058 bits – thermodynamic entropy of the sun[29] (about 30 bits per proton, plus 10 bits per electron).
2230 1069 ~ 1069 bits – thermodynamic entropy of the Milky Way Galaxy (counting only the stars, not the black holes within the galaxy) [citation needed]
2255 1077 1.5×1077 bits – information content of a one-solar-mass black hole.[30]
2305 1090 The information capacity of the observable universe, according to Seth Lloyd (not including gravitation)[31]

Note: this page mixes between two kinds of entropies:

  1. Entropy (information theory), such as the amount of information that can be stored in DNA
  2. Entropy (thermodynamics), such as entropy increase of 1 mole of water

These two definitions are not entirely equivalent, see Entropy in thermodynamics and information theory.

For comparison, the Avogadro constant is 6.02214076×1023 entities per mole, based upon the number of atoms in 12 grams of carbon-12 isotope.

In 2012, some hard disks used ~984,573 atoms to store each bit. In January 2012, IBM researchers announced they compressed 1 bit in 12 atoms using antiferromagnetism and a scanning tunneling microscope with iron and copper atoms. This could mean a practical jump from a 1 TB disk to a 100 TB disk.[5][32]

See also

[edit]

References

[edit]
  1. ^ "Definitions of the SI units: The binary prefixes". physics.nist.gov. Retrieved 17 June 2020.
  2. ^ "quantifiers". www.catb.org. Retrieved 24 January 2022.
  3. ^ Mark Nelson (24 August 2006). "The Hutter Prize". Retrieved 27 November 2008.
  4. ^ a b "A special report on managing information: All too much". The Economist. 25 February 2010. Retrieved 4 March 2010.
  5. ^ a b c d e f g "Cost of Hard Drive Space". 11 May 2013. Retrieved 23 June 2013.
  6. ^ "How much does DivX shrink a file?". 18 April 2002. Retrieved 24 June 2013.
  7. ^ Microsoft TechNet (28 March 2003). "How NTFS Works". Windows Server 2003 Technical Reference. Retrieved 12 September 2011.
  8. ^ Hickey, Thom (OCLC Chief Scientist) (21 June 2005). "Entire Library of Congress". Outgoing. Retrieved 5 May 2010.
  9. ^ The Internet Archive Has Now Saved a Whopping 10,000,000,000,000,000 Bytes of Data, retrieved October 2nd 2013
  10. ^ 25 petabyte on Megaupload. Archived 1 August 2012 at archive.today Retrieved 16 February 2012
  11. ^ "Facebook unveils Presto engine for querying 250 PB data warehouse". 7 June 2013. Archived from the original on 13 April 2014. Retrieved 29 March 2014.
  12. ^ "100 Petabytes of Cloud Data". 18 March 2014.
  13. ^ "Scaling the Facebook data warehouse to 300 PB". 10 April 2014.
  14. ^ Estimated storage space at Google
  15. ^ "A brief history of virtual storage and 64-bit addressability". Retrieved 17 February 2007.
  16. ^ [citation needed] J K−1
  17. ^ http://www.tmrfindia.org/ijcsa/V2I29.pdf [bare URL PDF]
  18. ^ "Internet data heads for 500bn gigabytes", The Guardian, 18 May 2009. Retrieved on 23 April 2010.
  19. ^ 424 Million HDDs Shipped in 2016 – Trendfocus
  20. ^ "Working Draft T10, American National Standard Project 1417-D, Revision 4, 28 July 2001" (PDF). o3one.org. 8 January 2002. p. 72. Retrieved 23 June 2013.
  21. ^ 1 J K−1. Equivalent to 1/(k ln 2) bits, where k is the Boltzmann constant
  22. ^ Equivalent to 5.74 J K−1. Standard molar entropy of graphite.
  23. ^ Equivalent to 69.95 J K−1. Standard molar entropy of water.
  24. ^ Equivalent to 108.9 J K−1
  25. ^ Equivalent to 146.33 J K−1. Standard molar entropy of neon. An experimental value, see [1] for a theoretical calculation.
  26. ^ "What Is ZFS? - Oracle Solaris ZFS Administration Guide". docs.oracle.com. Retrieved 6 May 2021.
  27. ^ Lloyd, Seth (August 2000). "Ultimate physical limits to computation". Nature. 406 (6799): 1047–1054. arXiv:quant-ph/9908043. Bibcode:2000Natur.406.1047L. doi:10.1038/35023282. ISSN 0028-0836. PMID 10984064. S2CID 75923.
  28. ^ "To Boil the Oceans". Harder, Better, Faster, Stronger. 10 February 2009. Retrieved 6 May 2021.
  29. ^ Given as 1042 erg K−1 in Bekenstein (1973), Black Holes and Entropy[permanent dead link], Physical Review D 7 2338
  30. ^ Entropy = in nats, with for a Schwarzschild black hole. 1 nat = 1/ln(2) bits. See Jacob D. Bekenstein (2008), Bekenstein-Hawking entropy, Scholarpedia.
  31. ^ Lloyd, Seth (24 May 2002). "Computational Capacity of the Universe" (PDF). Physical Review Letters. 88 (23): 237901. arXiv:quant-ph/0110141. Bibcode:2002PhRvL..88w7901L. doi:10.1103/PhysRevLett.88.237901. PMID 12059399. S2CID 6341263. Archived (PDF) from the original on 11 November 2017.
  32. ^ "IBM Smashes Moore's Law, Cuts Bit Size to 12 Atoms". 12 January 2012. Archived from the original on 29 September 2013. Retrieved 23 June 2013.
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