the reference about the beautiful Bachet's weighing problem using the
digits -1,0,1 in place of 0,1,2 can also be found in the Edouard Lucas's
book "Recreations Mathematiques" published in the 19th century, a new
edition has been made by Librairie Scientifique et technique Albert
Blanchard in 1992.
I've not the Knuth's book on my desk (the second volume of "The Art of
Computer Programming") but I remember there is a discussion about base
with negative and positive digits; I think that in the new edition of
this book, more can be found on these subjects.
I also remember that Pr. Algirdas A. Avizienis has proposed a
generalization of this, you
Ref: A. AVIZIENIS
"Signed-digit number representations for fast parallel arithmetic."
IRE Transactions on Electronic Computers 10 (1961), 389-400.
Hope it helps,
Robert ERRA.
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Les limites de mon langage signifie les limites du monde.
(Wittgenstein).
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