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How 1024 Bytes Became 1000.
Lets get right to the point; you just bought a 200GB hard drive, installed it and are now looking at its properties as reported by the computer. Computer says there's only 186.26GB even though besides that it says there is 200,000,000,000 Bytes. Where did the other 13.74GB go?
NO WHERE! This topic, if not explained right can be very very hard on the mind and cause quite a headache, as it did for mee when I was trying to get my head around it. It's actually quite simple. The hard drive does infact have 200,000,000,000 Bytes, that using SI (metric system units) you can shorten that to 200GB (giga = one billion). The computer on the other hand doesn't count bytes like that. To put it very simply: the computer counts memory to the power of 2, theres whole lot behind WHY, but that doen't matter, you can look into that in detail later.
2 x 2 = 4 (22 = 4)
2 x 2 x 2 = 8 (23 = 8) 2 x 2 x 2 x 2 = 16 (24 = 16) 2 x 2 x 2 x 2 x 2 = 32 (25 = 32) 2 x 2 x 2 x 2 x 2 x 2 = 64 (26 = 64) 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 (27 = 128) 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 (28 = 256) 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 (29 = 512) 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 (210 = 1024)
You see that last string there is 2 to the power of 10, it equals 1024. In the early days of computing the geeks thought it'd be a good idea to shorten 1024 by calling it 1 kilo byte. It was so close to 1000 that it didnt seem to matter, as long as they knew what they were talking about. Decades later everyone is still using the WRONG measument for ease of use. As the numbers grow, the differences are becoming more obvious. 1024 vs 1000 isnt a huge difference, but now we're in the age of the terabyte, that trillions show much more of a difference then the simple thousands. Because there was never a special unit given to count data properly, we have stuck with the original fake way of counting. It's starting so show it ugly face now that larger files and hard drives are common place in everyday life.
1000 x 1000 x 1000 = 1,000,000,000. A real SI metric Gigabyte, whis is what we expect a GB to be because Giga mean a billion. 1024 x 1024 x 1024 = 1,073,741,824. A computer will count tis as exactly 1 Gigabyte because it's counted in binary, even though it's not a gigabyte as the SI unit suggests. The sinple fact is they never made a proper unit for counting binary data which are always 2 to the power of something. So now we're in the shit. Until this problem is resolved you can work true data capacities for yourself, I'll show you how. If 1000 x 1000 x 1000 = 1,000,000,000. (10003) (109) A Real SI GigaByte. And 1024 x 1024 x 1024 = 1,073,741,824. (10243) (230) A Binary GigaByte. Hard drive capacity as measured in SI metric devided by the real binary unti value used to measure the capacity in the first place will reveal the true capacity. 200,000,000,000 / 1,073,741,824 = 186.2645149 Billion Binary Bytes. On a scientific calculator this can be worked out easily: 2009 / 10243 = 186.2645149 Billion Binary Bytes. 200GB devided by a real binary GB = true binary value as seen by the computer. On the calc it will look like this... "2" "0" "0" "10x" "9" " / " (Devided by) "1" "0" "2" "4" "Yx" "3" " = " 186.2645149 Lets do another one, take my 2TB hard drive (RAID) for example: 2,000,000,000,000 / 1,073,741,824 = 1.818989404 Trillion Binary Bytes. Again on the scientific calculator: 2 12 / 10244 = 1.818989404 Trillion Binary Bytes. On the calc it will look like this... "2" "10x" "12" " / " (Devided by) "1" "0" "2" "4" "Yx" "4" " = " 1.818989404 A new system has been devised to replace the troublesome way of measuing we have today, its called the IEC 20027-2. So now 1000 Bytes can safely be called 1KB and the KB we know of today will now be called a kibibyte which is 1024. So instead of saying my RAID has 1.82 Trillion Binary Bytes, I can say it has 1.82 Tibibytes (TiB). It is infact 2 Terabytes (TB) as the label on the disc says it will be (500GB x4), because it's measured in the metric SI system. So if you want to know how much capacity if have I can say I have 1.82 Tib which is the real capacity as used by the computer. 2TB is also correct but a usless value because it has nothing to do with computing. In the end, I was never short of 13.74GB when i got my 200GB drive. 13.74GB is the differenece between the real metric SI system and the true binary value. Its like having $1US and $0.6NZ cents, ITS THE SAME VALUE! I didn't loose 40 cents. We were never cheeted, we we're just very confused by the way large data values were measured, it's all doen to lazyness. 
See also:
When One Billion does not equal One Billion by James Wiebe, CEO WiebeTech LLC www.wiebetech.com (c) 2003 WiebeTech LLC |