Binary Powers of 10
by Duke Ionescu
04/28/97
These are all original calculations done by myself. Please feel free to verify them
and write me about your findings.
They are meant as purely informational/fun facts to know, since I haven't found any other purpose for them yet :-)
A ?1byte & ?2byte are my picks, in lack of a better name, for the next two larger bytes. Interesting things to note
are the repeating patterns in the last 2 digits. It's also a layman's way to verify that my calculations are correct
(which they may not be).
I may decide to release the program I wrote (in C) to do these calculations to the PD, but for now its not since I'm still
tweaking it whenever I have a little time on my hands. Write me if you're interested. An _int64 stops at 18 full digits,
while my largest number is 35 digits (2^10^33*8). I am trying to decide if it makes any sense to keep on going, possibly to
[initially] 100 digits. If there is any interest in this, I'll do it.
The standard powers of 10 are 10^x, while the binary powers of 10 are in the form of 2^10^x (1024^x). Programmers and the
like should be aware of this, but I doubt many mainstream users are. Bits are 2^10^x*8 (1024^x*8).
Certain companies, like hard-drive manufacturers, use 10^x to asses their products' capacity, which is plain wrong. They
can get away with it (and do) because not enough people realize there's a difference, however small (or not so small, as
you can see below). Be binary correct!!! :-)
Bytes Bits Deviation from 10^x
1 bit = .125 byte = 1 bit
1 byte = 1 byte = 8 bits x
1 kilobyte = 1,024 bytes = 8,192 bits 3 24
1 megabyte = 1,048,576 bytes = 8,388,608 bits 6 48,576
1 gigabyte = 1,073,741,824 bytes = 8,589,934,592 bits 9 73,741,824 <- This is how many bytes you're getting cheated
1 terabyte = 1,099,511,627,776 bytes = 8,796,093,022,208 bits 12 99,511,627,776 out of, per GB, when you buy a hard drive.
1 petabyte = 1,125,899,906,842,624 bytes = 9,007,199,254,740,992 bits 15 125,899,906,842,624 That's 70.3 MBs, enough to install Win95!!!
1 exabyte = 1,152,921,504,606,846,976 bytes = 9,223,372,036,854,775,808 bits 18 152,921,504,606,846,976
1 zettabyte = 1,180,591,620,717,411,303,424 bytes = 9,444,732,965,739,290,427,392 bits 21 180,591,620,717,411,303,424
1 yottayte = 1,208,925,819,614,629,174,706,176 bytes = 9,671,406,556,917,033,397,649,408 bits 24 208,925,819,614,629,174,706,176
1 ?1byte = 1,237,940,039,285,380,274,899,124,224 bytes = 9,903,520,314,283,042,199,192,993,792 bits 27 237,940,039,285,380,274,899,124,224
1 ?2byte = 1,267,650,600,228,229,401,496,703,205,376 bytes = 10,141,204,801,825,835,211,973,625,643,008 bits 30 267,650,600,228,229,401,496,703,205,376
1 ?3byte = 1,298,074,214,633,706,907,132,624,082,305,024 bytes = 10,384,593,717,069,655,257,060,992,658,440,192 bits 33 298,074,214,633,706,907,132,624,082,305,024
1 bit = .125 byte = 1 bit Deviation from 10^x
1 byte = 1 byte = 8 bits x
1 kilobyte = 1024 bytes = 8192 bits 3 24
1 megabyte = 1048576 bytes = 8388608 bits 6 48576
1 gigabyte = 1073741824 bytes = 8589934592 bits 9 73741824
1 terabyte = 1099511627776 bytes = 8796093022208 bits 12 99511627776
1 petabyte = 1125899906842624 bytes = 9007199254740992 bits 15 125899906842624
1 exabyte = 1152921504606846976 bytes = 9223372036854775808 bits 18 152921504606846976
1 zettabyte = 1180591620717411303424 bytes = 9444732965739290427392 bits 21 180591620717411303424
1 yottabyte = 1208925819614629174706176 bytes = 9671406556917033397649408 bits 24 208925819614629174706176
1 ?1byte = 1237940039285380274899124224 bytes = 9903520314283042199192993792 bits 27 237940039285380274899124224
1 ?2byte = 1267650600228229401496703205376 bytes = 10141204801825835211973625643008 bits 30 267650600228229401496703205376
1 ?3byte = 1298074214633706907132624082305024 bytes = 10384593717069655257060992658440192 bits 33 298074214633706907132624082305024
Some interesting facts about what these various-sized bytes can store:
* 1 bit: a binary decision
* 1 byte: a character
* 5 Megabytes: The complete works of Shakespeare
* 2 Gigabytes: 20 meters of shelved books
* 10 Terabytes: The printed collection of the US Library of Congress
* 200 Petabytes: All printed material
* 5 Exabytes: All words ever spoken by human beings
From another source, with credit - documentary
Etymology of Units
by PC Hariharan
1.Kilo Greek khilioi = 1000
2.Mega Greek megas = great, e.g., Alexandros Megos
3.Giga Latin gigas = giant
4.Tera Greek teras = monster
5.Peta Greek pente = five, fifth prefix, peNta - N = peta
6.Exa Greek hex = six, sixth prefix, Hexa - H = exa Remember, in standard French, the initial H is silent, so they
would pronounce Hexa as Exa. It is far easier to call it Exa for everyone's sake, right?
7.Zetta almost homonymic with Greek Zeta, but last letter of the Latin alphabet
8.Yotta almost homonymic with Greek iota, but penultimate letter of the Latin alphabet.
The first prefix is number-derived; second, third, and fourth are based on mythology. Fifth and sixth are supposed to be
just that: fifth and sixth. But, with the seventh, another fork has been taken. The General Conference of Weights and
Measures (CGMP, from the French; they have been headquartered, since 1874, in Sevres on the outskirts of Paris) has
now decided to name the prefixes, starting with the seventh, with the letters of the Latin alphabet, but starting from the end.
Now, that makes it all clear! Remember, both according to CGMP and SI, the prefixes refer to powers of 10. Mega is
10**6, exactly 1,000,000, kilo is exactly 1000, not 1024.
End of Etymology of Units 101.