Talk:Octal

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snip:

For example, the binary representation for decimal 74 is 1001010, which groups into 1 001 010 — so the octal representation is 112.

-end-

Can anyone explain this "representation?" -- Anonymous

It may help to first understand the binary numeral system. Put simply, 1001010 binary is equivalent to 1 × 2⁶ + 1 × 2³ + 1 × 2¹ = 64 + 8 + 2 = 74. Since each octal digit directly corresponds to a group of three binary digits, any binary representation can be condensed into an octal form. The octal numeral 112 above can be expanded to mean 1 × 8² + 1 × 8¹ + 2 × 8⁰ = 64 + 8 + 2 = 74. -- Wapcaplet 01:40, 10 Dec 2004 (UTC)

I changed the above quoted paragraph to be slightly clearer, I hope.

I'm not sure about a couple of things in the article though. First, Knuth/TAOCP says Karl ("Charles") XII "hit on the idea of radix-8 arithmetic about 1717" and that this "was probably his own invention, although he had met Leibniz briefly in 1707". The article makes it sound like Knuth is certain about this, and forgets the .. well, qualified statement. Perhaps it should not even mention it at all?

Second, novem/novus. Any specific reason to believe this is true? Most of these kind of similarities are entirely random.

Third, fractions. Why should octal be better for fractions? (I'm assuming the author really meant numbers like 0.25, not fractions like 1/4, but then English is not my first language.) It has all the advantages and disadvantages of binary, but if anything it is worse than most bases: it has fewer divisors, so more numbers would tend to "expand into infinity". (Compare with radix 12, that would be nice considering how common 1/3 is.)

Fourth, does the "8" in "base 8 number system" really need to be an article link?

magetoo 16:36, 12 Dec 2004 (UTC)

• I can't answer for the Knuth reference or novem/novus, but I agree on the matter of fractions; I don't think fractions should even be brought into the picture. When octal is the preferred numeral system, fractions aren't likely to be of much interest. I raised a similar question about the hexadecimal article a while back (the author in that case had claimed that hexadecimal was "quite good" for fractions, which is only true if one considers infinitely repeating expansions desirable). If it were up to me, discussion of fractions would be removed from both articles. In fact, I think I will go ahead and do so... -- Wapcaplet 17:48, 12 Dec 2004 (UTC)

[edit] Number prefixes

Please add description of 0x = hexadecimal, 0b = binary, 0 = octal. - Omegatron 16:48, Jun 23, 2005 (UTC)

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This is just a C rule. Why then not use the '$' prefix, as in Pascal? ;)

[edit] move Knuth?

Seems like that reference to Knuth (that King Charles XII of Sweden was the inventor of octal in Europe) should be removed from the "By Native Americans" section and placed in its own section. Perhaps "Historically" or "In History"? Meonkeys 01:00, 14 November 2006 (UTC)