Does the concept of a fractional bit of information have any meaning?

Question

A bit is an eighth of a byte. Does, for instance, half a bit have any physical meaning?

Answer 1

There is certainly information meaning to fractional bits. Follow the links at

From Wikipedia, the free encyclopedia:
Entropy (disambiguation)
http://en.wikipedia.org/wiki/Entropy_%28disambiguation%29

to

Information entropy, in statistics, the amount of information that is contained in a random variable
http://en.wikipedia.org/wiki/Information_entropy

or to

Entropy (statistical views) - the statistical definition of entropy
http://en.wikipedia.org/wiki/Entropy_%28statistical_views%29

For example, each random roll of one fair six sided die yields log(6) / log(2) or just under 2.585 bits of entropy. Flipping a biased coin yields (see table) bits of entropy per toss.
Heads - Tails or Tails - Head ratio --> approximate entropy per flip
50% - 50% 1.000000
60% - 40% 0.970951
70% - 30% 0.881291
75% - 25% 0.811278
80% - 20% 0.721928
85% - 15% 0.609840
90% - 10% 0.468996
95% - 5% 0.286397
96% - 4% 0.242292
97% - 3% 0.194392
98% - 2% 0.141441
99% - 1% 0.080793

As another example, see various estimates of how many bits of information one letter of English text carries on average:

Search results:

http://www.google.com/search?q=entropy+of+English+text

One particular result:

Refining the Estimated Entropy of English by Shannon Game Simulation

Matt Mahoney
Florida Institute of Technology
[e-mail]

http://www.cs.fit.edu/~mmahoney/dissertation/entropy1.html

"
Abstract

Shannon (1950) estimated the entropy of written English to be between 0.6 and 1.3 bits per character (bpc), based on the ability of human subjects to guess successive characters in text. Simulations to determine the empirical relationship between the provable bounds and the known entropies of various models suggest that the actual value is 1.1 bpc or less.
"

Answer 2

Remember this, a bit is a single binary number to which we represent as 0 or 1. However, under the hood, there is a real reason why the binary system was chosed.
That reason is simple, a computer is an electrical device, and the memory, the processor and all of its parts are also electrical at some point in their operation.
Electricity can have only one of two states, on or off ( present or absent). Therefore, the bit is truly representing the electrical state, and you can not have a fractional state. It is either on or off, not 1/4 on because that would still be on simply because it is not off.
So the smallest is the bit, anything smaller than this has no meaning, significance, or interpretation in the real world. So no information would exist in a fractional bit.

Answer 3

Well, 1/8 of a byte and 1/2 of a bit indicates fractions.

See how?

Guido

Answer 4

I've checked several sites, it looks like "bit" is the smallest way to name that unit of measure. Good question! ;-)