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24-Ruby IV

## Bit, byte, kB, MB, GB etc in SI and in Mathcad

We are obliged to use only SI when writing textbooks, reference books, articles, technical reports atc. And in this system there are no units of information. How to solve this problem? That's how!

4 REPLIES 4
23-Emerald III
(To:ValeryOchkov)

In your unit system 1 MB = 56 kB.

And the ratio becomes less (worse) for the higher multiples until 1 YB is little more than 3 times a ZB.

Fortunately in my computer 1 MB = 1024 kB, and that 1024:1 ratio holds up to the highest multple.

I guess you need to define MB := 2^20 * B, GB := 2^30 *B etc.

Success!

Luc

P.S.

The SI have not included bit and Byte as units. The IEC, in Standard IEC 80000-13, acknowledge that bit and Byte are not units, but are often used as such. They propose for power-of-2 muliples to put an i after each prefix, so megabyte is:

MiB= 1024*1024 Byte     in words: One mebibyte

then you get 1024 MiB= 1GiB (gibibyte), 1024*GiB = 1 TiB (tebibyte) etc.

Interestingly the 1000 prefix, normally a lower case k (as in kg), becomes Ki to mean 1024; that's a capital K.

23-Emerald II
(To:LucMeekes)

@LucMeekes wrote:

The SI have not included bit and Byte as units. The IEC, in Standard IEC 80000-13, acknowledge that bit and Byte are not units, but are often used as such.

Well, they're right, but they're also wrong.  Technically, "bit" and "byte" are not non-SI units that are accepted for use under the SI.  However, the SI Brochure (Edition 9, current at the date of this message) tacitly recognizes that the bit and byte are units when it discusses decimal and multiples.

page 143, sidenote: The SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits). The names and symbols for prefixes to be used with powers of 2 are recommended as follows: kibi ...

Under the auspices of the VIM (International Vocabulary of Metrology), anybody can define their own system of quantities or extend an existing one.  Hence, for "accounting" purposes, one may define the "unit of information" as a quantity within an extended SI and define the bit as its unit.   This is effectively what is done with Money in Mathcad.

As long as these Cinderella units are magically converted back to dimension one at the end of the unit bookkeeping, everyone should be happy.

As an aside, I'm not sure that the SIUnitsOf function is behaving correctly.  I think that it should drop the Money unit.

Definition: SIUnitsOf(x)—Returns the dimension (magnitude and unit) of the unit of x scaled to the default SI unit, regardless of your chosen unit system. Returns 1 if x has no units.

Additional Information: Divide a value by the SIUnitsOf function to make it unitless, scaled in SI.

@LucMeekes wrote:
The IEC, in Standard IEC 80000-13,  ... propose for power-of-2 muliples to put an i after each prefix, so megabyte is:

MiB= 1024*1024 Byte     in words: One mebibyte

then you get 1024 MiB= 1GiB (gibibyte), 1024*GiB = 1 TiB (tebibyte) etc.

Interestingly the 1000 prefix, normally a lower case k (as in kg), becomes Ki to mean 1024; that's a capital K.

I've occasionally used these as units.  If we subvert the mole, we can have:

Stuart

24-Ruby IV
(To:LucMeekes)

24-Ruby IV
(To:LucMeekes)

@LucMeekes wrote:

In your unit system 1 MB = 56 kB.

And the ratio becomes less (worse) for the higher multiples until 1 YB is little more than 3 times a ZB.

Fortunately in my computer 1 MB = 1024 kB, and that 1024:1 ratio holds up to the highest multple.

I guess you need to define MB := 2^20 * B, GB := 2^30 *B etc.

So?

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