# Binary counterpart to decade

In logarithms, a decade is a range of values from N up to 1o×N.

What term should be used to describe a range from N to 2×N, when using binary numbers?

A musical octave covers such a range of audible frequencies, but that term is probably too foreign.

Googling "binade" turns up a Wikipedia page, but also evidence that it's not a real word, but rather a neologism that's happened to get coined a few times.

I feel like I'm forgetting something from engineering school.

Octave is apparently the proper word in electronics as well as music:

In electronics, an octave is a doubling or halving of a frequency. The term is derived from the Western musical scale (an octave is a doubling in frequency) and is therefore common in audio electronics. (The prefix octa-, denoting eight, refers to the eight notes of a diatonic scale.) Along with the decade, it is a unit used to describe frequency bands or frequency ratios.

A similar note is posted in the opening paragraph of the corresponding entry on decade:

One decade is a factor of 10 difference between two numbers (an order of magnitude difference) measured on a logarithmic scale. Along with the octave, it is a unit used to describe frequency bands or frequency ratios.

I wouldn't worry that octave is too domain-specific, as you are already using decade in a domain-specific way. (In lay English, it refers to a period of 10 years.)

If you really want to avoid the association with frequencies, then it's reasonable to go with binary decade, in parallel formation with binary digit. This is generalizable to other bases than just 10 and 2. For example, while we do have the term bit for binary digit, there is no commonly used single-word term for hexadecimal digit.

• Binary decade would seem to be the accepted term. Jul 14 '14 at 5:47
• @Gnawme In that source, "binary decade counter" is only a decade counter (counts by ten) which happens to be implemented in binary logic. Jul 14 '14 at 7:15
• I'd like "binary decade" to be a real term, but Googling it only turns up references like Gnawme's, referring to decimal arithmetic implemented in binary technology. I'll accept this answer given a reference mentioning logarithms as opposed to logic circuits. Jul 15 '14 at 2:12
• @Potatoswatter: The references I quoted (for decade and octave) specifically mention frequency ratios (which are inherently suited to be represented graphically on a logarithmic scale) and have nothing to do with logic circuits. As of this writing, there aren't any readily available references for binary decade the way you want it to be used, because it's simply not (yet) an established term. I only suggested it (as a neologism) because it would work, if you really can't bear to use octave. But you mention engineering school. Engineers definitely use octave. Jul 16 '14 at 5:11
• @JohnY Yep, it's possible that's all that was "ringing a bell," no pun intended :) . I'll select this answer, I just invented my own specific terminology for my application. It's a numeric software library, with no relation to frequency or electronics. Jul 16 '14 at 23:04

This is interesting. If there is a word or phrase for this, it's not immediately obvious to me. There does seem a use for such a word.

The closest I can come up with would be order of magnitude, but that is probably more commonly meant to express different powers of ten. One could be more specific I suppose, saying binary order of magnitude.

It seems related to frequency band. You'd want a word that can transfer to other bases, so that you don't need to think about ternades, etc. I wonder what the people on math.stackexchange and Math Overflow could contribute to this? For example, what would you call the range between powers of e in natural logarithms?

Binary decade would be understandable, and transferable to other bases, even though it is etymologically impure.

Base two is funny because adding another digit is the same as increasing the power of two that's referred to. Within a power of two of 2^12 or between 2^5 and 2^6 (where ^ is "to the") cover decade like ranges.

• So the answer here is "power"? Given a context where many similar words are being used canonically, coining such a new definition, however closely related to existing usage, would be very confusing. Jul 17 '14 at 23:30
• How does this make base-2 "funny"? Adding another digit in any base is the same as increasing the power (exponent) in that base. "10^5 to 10^6" is a decade. The phrase "within a power of 10 of 10^12" means "within a decade of 10^12". Jul 18 '14 at 3:44