The Miser Project

Notes Folio n010202
Homage to the Bit


0.16 2017-08-29 16:40

The bit, taken to be shorthand for "binary digit," is the fundamental element of modern digital technology.  Bits are used in telecommunication, in the workings of computers, and in the digital representation of video, audio, and other signals.

The bit is also fundamental in another sense.  Since the foundation of information theory by Claude Shannon in 1948, it is understood that the most efficiently-achievable representations of data are in binary forms [Shannon2014].

The prevalence of bitness, binary-ness, and just plain bits is exemplified by the Art of Computer Programming section "7.1. Zeros and Ones" consisting of 234 dense pages plus an additional 145 pages discussing the exercises [Knuth2011].

Bits, although not know as such at the time, also figure in Boolean logic, where the two values 0 and 1 are regarded as values of logical propositions cast in mathematical terms [Boole1854].

In this note, bits are examined not so much as simply 0 and 1 values but as abstractions where 0 and 1 are merely one representation.  The idea is to dig into what constitutes bitness and how that is manifest in computational procedures, especially ones that come into play in Miser.

-- Dennis E. Hamilton
Seattle, Washington



George Boole.  An Investigation of the Laws of Thought: on which are founded the mathematical theories of logic and probabilities.  Macmillan (London: 1854).  Dover (New York: 1858) reprint, ISBN 0-486-60028-9 pbk.


Donald E. Knuth.  The Art of Computer Programming, volume 4A: Combinatorial Algorithms Part 1.  Addison-Wesley (New Jersey: 2011).  ISBN 0-201-03804-8.


Claude Shannon.  Wikipedia entry, 2014-03-25 accessed at <>.


Related Material


0.16 2014-03-30-09:44 Transposition to Folio Cover Page
The original single-page note is branched to an Initial Notes page and this folio cover.
0.15 2002-12-07-22:32 Latest Asserted Version
This may be the version inherited from r010101a, but it is the version shown on the page before transposition to folio form,
0.00 2002-12-07-22:31 Split off from Orcmid Reading r010101a to provide initial material (orcmid).
The original too-comprehensive note is pasted here as a boilerplate to be distilled down to the basic Homage to the Bit topic.  It provides a basic sketch of  how types might be realized in a Miser, expanding on a key idea of Peter Landin and his mentors.  Manifest abstractions, Miser style, are employed in a way that gives power to the notion of "type" in the rich sense of "typical."

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