📐 Scientific Units (1 video)

  1. Kilobytes, Kibibytes, and Why 1 TB ≈ 931 GiB. Transcript: web, PDF.

SI rocks my socks! (Mini-essay)

There are billions of users of computing devices who do NOT care for some cutesy historical convention where kilo somehow means 1,024. In every sphere of science and indeed life, kilo simply means 1,000. Whatever the merits of the 1,024 interpretation of kilo, the lesser evil is to clear the confusion and converge on a single standard – the sooner the better. And whaddyaknow? It so happens that there is already a standard that has been endorsed by MANY bodies (e.g. the EU, the ISO, the IEC, the US NIST, the BIPM).

The SI uses kilo, mega, giga, etc. as decimal prefixes meaning 10³,  10⁶,  10⁹, etc. From these are formed the so-called binary prefixes. And so we have ‘kilo’ + ‘binary’ = ‘kibi’, ‘mega’ + ‘binary’ = ‘mebi’, ‘giga’ + ‘binary’ = ‘gibi’, etc. meaning 2¹⁰, 2²⁰, 2³⁰, etc. (At least in English, the second syllable ‘bi’ should be pronounced ‘bee’. )  Hence, a kilobyte (kB with lower case ‘k’) is 1,000 bytes and a kibibyte (KiB with upper case ‘K’ and lower case ‘i’) is 1,024 bytes.

ACTUALLY, IT GETS EVEN MORE CONFUSING …

Example #1. The video suggests that either 1 MB = 10⁶ B = 1,000,000 bytes or 1 MB = 2^{20} = 1,048,576 bytes. But there is a third Goldilocks possibility, where 1 MB = 2^{10} × 1000 = 1,024,000 bytes!! This third possibility explains why those 3.5” floppy disks were called 1.44 MB, even though they had only 1,474,560 = 1.44 × 1,024,000 bytes! MADNESS!

Example #2. In an effort to clear the confusion, but in fact only adding to it, many other suggestions have been made over the years. For example, it has been suggested that:

(i) the Greek letter kappa \kappa = 2^{10} B = 1,024 B, \kappa2 = 2^{20} B= 1,048,576 B, etc.;

(ii) bK = 2^{10} = 1,024, bK2 = 2^{20} = 1,048,576, etc.;

(iii) 3B20 = 3 × 2^{20}, 5B30 = 3 × 330, etc.;

(iv) dikilo = k2 = 2^{10} = 1,024, dimega = m2 = 2^{20} = 1,048,576, etc.

(v) 1 large kilobyte = 1 KKB = 1,024 B, 1 large megabyte = 1 MMB = 1,048,576 B, etc.

Bonus fun fact (to be included in the DVD release)!

Under the SI, use the lower case for prefixes ≤ kilo (so k for kilo, m for milli, etc.) and the upper case for prefixes ≥ mega (M for mega, G for giga, etc.). So 1 mHz is a millihertz, while 1 MHz is a megahertz.