Converting bytes to megabytes

Question

I ve seen three ways of doing conversion from bytes to megabytes    megabytes bytes 1000000 megabytes bytes 1024 1024 megabytes bytes 1024 1000   Ok  I think  3 is totally wrong but I have seen it   I think  2 is right  but I am looking for some respected authority  like W3C  ISO  NIST  etc  to clarify which megabyte is a true megabyte   Can anyone cite a source that explicitly explains how this calculation is done   Bonus question  if  2 is a megabyte what are  1 and  3 called   BTW   Hard drive manufacturers don t count as authorities on this one

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The answer is that  1 is technically correct based on the real meaning of the Mega prefix  however  and in life there is always a however  the math for that doesn t come out so nice in base 2  which is how computers count  so  2 is what people really use

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Here is what the standard  SI  says   http   physics nist gov Pubs SP330 sp330 pdf page 34

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Megabyte means 2 20 bytes  I know that technically that doesn t mesh with the SI units  and that some folks have come up with a new terminology to mean 2 20  None of that matters  Efforts to change the language to  clarify  things are doomed to failure   Hard-drive manufacturers use it to mean 1 000 000 bytes  because that s what it means in SI so they figure technically they aren t lying  while actually they are   That falls under lies  damn lies  and marketing

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There s an IEC standard that distinguishes the terms  e g  Mebibyte   1024 2 bytes but Megabyte   1000 2  in order to be compatible to SI units like kilograms where k M     means 1000 1000000   Actually most people in the IT area will prefer Megabyte   1024 2 and hard disk manufacturers will prefer Megabyte   1000 2  because hard disk sizes will sound bigger than they are    As a matter of fact  most people are confused by the IEC standard  multiplier 1000  and the traditional meaning  multiplier 1024   In general you shouldn t make assumptions on what people mean  For example  128 kBit s for MP3s usually means 128000 bits because the multiplier 1000 is mostly used with the unit bits  But often people then call 2048 kBit s equal to 2 MBit s - confusing eh   So as a general rule  don t trust bit byte units at all

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Divide by 2 to the power of 20   1024 1024  bytes   1 megabyte    1024 1024   1 048 576    2 20   1 048 576 1 048 576 1 048 576   1     It is the same thing

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Use the computation your users will most likely expect  Do your users care to know how many actual bytes are on a disk or in memory or whatever  or do they only care about usable space  The answer to that question will tell you which calculation makes the most sense   This isn t a precision question as much as it is a usability question  Provide the calculation that is most useful to your users

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In general  it s wrong to use decimal SI prefixes  e g  kilo  mega  when referring to binary data sizes  except in casual usage   It s ambiguous and causes confusion  To be precise you can use binary prefixes  e g  1 mebibyte   1 MiB   1024 kibibytes   2 20 bytes   When someone else uses decimal SI prefixes for binary data you need to get more information before you can know what is meant

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BTW  Hard drive manufacturers don t count as authorities on this one    Oh  yes they do  and the definition they assume from the S I  is the correct one   On a related issue  see this post on CodingHorror

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Traditionally by megabyte we mean your second option -- 1 megabyte   220 bytes  But it is not correct actually because mega means 1 000 000  There is a new standard name for 220 bytes  it is mebibyte  http   en wikipedia org wiki Mebibyte  and it gathers popularity

[math] Converting bytes to megabytes

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