Orders of Magnitude (data)

An order of magnitude is generally a factor of ten. A quantity growing by four orders of magnitude implies it has grown by a factor of 10000 or 104. However, because computers are binary, orders of magnitude are sometimes given as powers of two.

This article presents a list of multiples, sorted by orders of magnitude, for digital information storage measured in bits. This article assumes a descriptive attitude towards terminology, reflecting general usage. The article assumes the following:

  • A group of 8 bits constitutes one byte. The byte is the most common unit of measurement of information (megabyte, mebibyte, gigabyte, gibibyte, etc.).
  • In 16-bit and 32-bit architectures, having processor registers of these sizes, that chunk of data is usually called a word.
  • The decimal SI prefixes kilo, mega etc., are powers of 10. The power of two equivalents are the binary prefixes kibi, mebi, etc.

Accordingly:

  • 1 kB (kilobyte) = 1000 bytes = 8000 bits
  • 1 KiB (kibibyte) = 210 bytes = 1024 bytes = 8192 bits


Orders of magnitude (data)
Binary Decimal Item
Factor Term Factor Term
20 bit 100 bit 1 bit – 0 or 1, false or true, Low or High
1.6 bits – approximate size of a trit (a base-3 digit)
21 2 bits – a crumb (rarely used term), enough to uniquely identify one base pair of genetic code
3 bits – the size of an octal digit
22 nibble 4 bits – (aka "nibble" or "semioctet", rarely used) 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
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.
7 bits – the size of code points in the ASCII character set

– minimum length to store 2 decimal digits

23 byte 8 bits – (a.k.a. "octet") on many computer architectures.

– Equivalent to 1 "word" on 8-bit computers (Apple II, Atari 800, Commodore 64, et al.).
– the "word size" (instruction length) 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 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 1965–1990)
24 16 bits

– 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" (instruction length) 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 computers (Apple Macintosh, Pentium-based PC).
– the "word size" (instruction length) for various console systems including: PlayStation, Nintendo 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" (instruction length) 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

160 bits – maximum key length of the SHA-1, standard Tiger (hash), and Tiger2 cryptographic message digest algorithms
28 256 bits (32 bytes) – minimum key length for the recommended strong cryptographic message digests as of 2004
29 512 bits (64 bytes) – maximum key length for the standard strong cryptographic message digests in 2004
103 kilobit 1000 bits
210 kibibit 1024 bits (128 bytes)
1288 bits – approximate maximum capacity of a standard magnetic stripe card
211 2048 bits (256 bytes) – RAM capacity of the stock Altair 8800
212 4096 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)

4704 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)
8000 bits (103 bytes) – one kilobyte
213 kibibyte 8192 bits (1,024 bytes) – RAM capacity of a Sinclair ZX81.
9408 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, 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 Sinclair ZX Spectrum.
160 kilobits – approximate size of this article as of 15 April 2010
218 262,144 bits (32 kibibytes)
219 524,288 bits (64 kibibytes) – RAM capacity of a lot of popular 8-bit Computers like the C-64, Amstrad CPC etc.
106 megabit 1,000,000 bits
220 mebibit 1,048,576 bits (128 kibibytes) – RAM capacity of popular 8-bit Computers like the C-128, Amstrad CPC etc.
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)
5,242,880 bits (640 kibibytes) – the maximum addressable memory of the original IBM PC architecture
8,000,000 bits (106 bytes) – the preferred definition of megabyte
8,343,400 bits – one "typical" sized photograph with reasonably good quality (1024 × 768 pixels).
223 mebibyte 8,388,608 bits (1024 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 megabits – amount of data in a typical color slide
225 33,554,432 bits (4 mebibytes) – RAM capacity of stock Nintendo 64
41,943,040 bits (5 mebibytes) – approximate size of the Complete Works of Shakespeare
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 (32 mebibytes)
423,360,000 bits: a five-minute audio recording, in CDDA quality
229 536,870,912 bits (64 mebibytes)
109 gigabit 1,000,000,000 bits
230 gibibit 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
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)
233 gibibyte 8,589,934,592 bits (1024 mebibytes)
1010 10,000,000,000 bits
234 17,179,869,184 bits (2 gibibytes)
235 34,359,738,368 bits (4 gibibytes) – maximum addressable memory on the Intel 80386
3.76×1010 bits (4.7 gigabytes) – capacity of a single-layer, single-sided DVD
236 68,719,476,736 bits (8 gibibytes)
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 disc
238 274,877,906,944 bits (32 gibibytes)
239 549,755,813,888 bits (64 gibibytes)
1012 terabit 1,000,000,000,000 bits (125 gigabytes)
240 tebibit 1.34×1012 bits – estimated capacity of the Polychaos dubium genome, the largest known genome
1.6×1012 bits (200 gigabytes) – capacity of a hard disk that would be considered average as of 2008
241 2,199,023,255,552 bits (256 gibibytes)
242 4,398,046,511,104 bits (512 gibibytes)
243 tebibyte 8,796,093,022,208 bits (1024 gibibytes)
(approximately) 8.97×1012 bits – as of 2010, data of π to the largest number of decimal digits ever calculated (2.7×1012)
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
244 17,592,186,044,416 bits (2 tebibytes)
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)
1.5×1014 bits (18.75 terabytes)
248 281,474,976,710,656 bits (32 tebibytes)
249 562,949,953,421,312 bits (64 tebibytes)
1015 petabit 1,000,000,000,000,000 bits
250 pebibit 1,125,899,906,842,624 bits (128 tebibytes)
2.4×1015 bits (300 terabytes) – size of the Internet Archive as of 2004
251 2,251,799,813,685,248 bits (256 tebibytes)
252 4,503,599,627,370,496 bits (512 tebibytes)
8,000,000,000,000,000 bits (1015 bytes) – one petabyte
253 pebibyte 9,007,199,254,740,992 bits (1024 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
4.5×1016 bits (5.625 petabytes) – estimated hard drive space in Google's server farm as of 2004
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
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
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 1,000,000,000,000,000,000 bits
260 exbibit 1,152,921,504,606,846,976 bits (128 pebibytes)
1.6×1018 bits (200 petabytes) – total amount of printed material in the world
261 2,305,843,009,213,693,952 bits (256 pebibytes)
262 4,611,686,018,427,387,904 bits (512 pebibytes)
263 exbibyte 9,223,372,036,854,775,808 bits (1024 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
267 147,573,952,589,676,412,928 bits (16 exbibytes) – maximum addressable memory using 64bit addresses without segmentation
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)
269 590,295,810,358,705,651,712 bits (64 exbibytes)
1021 zettabit 1,000,000,000,000,000,000,000 bits
270 zebibit 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
4.7×1021 bits (0.50 zettabytes) – amount of digitally stored information in the world as of May 2009
272 4,722,366,482,869,645,213,696 bits (512 exbibytes)
273 zebibyte 9,444,732,965,739,290,427,392 bits (1024 exbibytes)
1022 10,000,000,000,000,000,000,000 bits
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)
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.
1024 yottabit 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.
280 yobibit 1,208,925,819,614,629,174,706,176 bits (128 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.
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.
2 150 1045 ~ 1045 bits – the number of bits required to perfectly recreate the average-sized U.S. adult male human being down to the quantum level on a computer is about 2×1045 bits of information (see Bekenstein bound for the basis for this calculation).
1058 ~ 1058 bits – thermodynamic entropy of the sun (about 30 bits per proton, plus 10 bits per electron).
1069 ~ 1069 bits – thermodynamic entropy of the Milky Way Galaxy (counting only the stars, not the black holes within the galaxy)
1077 1.5×1077 bits – information content of a one-solar-mass black hole.
2305 1092 The information capacity of the observable universe, according to Seth Lloyd.
2332.19 10100 googol number
23.3219·googol 10googol googolplex number

For comparison, the Avogadro constant is 6.02214179(30)×1023 entities per mole, based upon the number of atoms in 12 grams of carbon-12 isotope.

Famous quotes containing the words orders and/or magnitude:

    I’ve got orders to obey, thank God.
    Robert Bolt (1924–1995)

    Although a man may lose a sense of his own importance when he is a mere unit among a busy throng, all utterly regardless of him, it by no means follows that he can dispossess himself, with equal facility, of a very strong sense of the importance and magnitude of his cares.
    Charles Dickens (1812–1870)