Q:

Why do English volume units use base 2?

I would post this on Quora, since it is more of a "just wondering" sort of question, except that I much prefer StackExchange's platform:

As weird as Imperial units generally are, English volume units surprisingly make a lot of sense.  I'm thinking there must be a reason for this... is there?

Examples:

1 cup = 8 fluid ounces
1 pint = 2 cups (16 fluid ounces)
1 quart = 2 pints (32 fluid ounces)
1 gallon = 4 quarts (128 fluid ounces)

Compared to some other craziness in the world of non-SI units, these make a ton of sense:

They are all base-2 multiples, which is really easy for converting one unit to another, and for easily covering the "space of interest" (i.e., you'll never need to say 0.031 gallons, since you can instead say 4 fl. oz).
Even the names are suggestive / helpful:

a quart is a quarter of a gallon.

Was there a royal scientists or some-such academic responsible for this lack of insanity?

A:

The introduction of these units precedes the Royal Society by a long time, and the story of their origins is murky. Pints, pecks, gallons and quarts appeared in the so-called "Winchester Standards" instituted in England by Henry VII in 1495. A standard bushel, gallon and quart made of bronze, issued in 1497 and stamped with the mark of Henry VII are still preserved in the British Museum. Later they became the basis of the Imperial Units defined in the British Weights and Measures Act of 1824. One of the earliest documents defining the gallon, bushel and quarter, is the Tractatus de Ponderibus et Mensuris, officially listed as an "ancient statute of uncertain date", but estimated as  c. 1250 - 1305 and sometimes attributed to Henry III or Edward I: 

"By Consent of the whole Realm the King’s Measure was made, so that... Twenty-pence make an Ounce; and Twelve Ounces make a Pound, and Eight Pounds make a Gallon of Wine; and Eight Gallons of Wine make a Bushel of London; which is the Eighth Part of a Quarter."

But even in the Imperial Units the pint was still 20 fluid ounces, so it was not fully binarized even in 1824. There was no unit for 4 pints, I guess half-gallon worked well enough, but 1/4 pint was called gill.
The reason the "Winchester Standards" are so called is that c. 970, when the capital of England was Winchester, the then king Edgar the Peaceful allegedly instituted the said units already. Alas, no traces of them are found before the Norman Conquest of 1066, a century later, and most unit names (quarter, bushel, peck, gallon, pottle, quart, pint) have French roots. The units in use prior to the Norman Conquest, and even as late as 1196, were different and had Latin derived names (sester, amber, mitta, coomb, seam), although seams and sesters can be roughly equated to quarters and pints. 
As a side curiosity, the ancient Chinese units of weight went in multiples of 16, and we also do not know if some sage was behind it, see What is the most ancient civilization that used base-16 (hexadecimal) number system?

