Conclusions
In a DBS the average time for algebraic addition of complementary codes is reduced by comparison with addition in a PBS of inverse codes by (1/2)τΣ and of complementary codes by (1/3)τΣ.
The general time of addition in a PBS of inverse codes is 2τΣ, and of complementary codes with superposition of the cycle of addition with the addition of the complementary unit, (11/6)τΣ [1, 3].
In addition, in a DBS with equally probable appearance of numbers in a given array, taking into accoupt the exclusion of binary transitions with prohibited combinations, the time for addition of whole numbers is reduced by 2l(n−1) τ and for numbers of a proper fraction by 2n(h−1) τ. This reduction of time amounts on the average to 10 or 15%.
Consequently, in a DBS the average addition time may be reduced by 20 or 30%.
The anticipated areas of use of a DBS could be in digital differential analyzers for automatic control and in various arithmetic chains of specialized devices where the main operation is algebraic addition.
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Literature Cited
M. A. Kartsev, The Arithmetic of Digital Machines [in Russian], Izd. Nauka, Moscow (1969).
Z. L. Rabinovich, Elementary Operations in Computing Machines [in Russian], Kiev (1966).
D. A. Pospelov, Arithmetical Basis of Discrete-Operation Computing Machines [in Russian], Izd. Vysshaya Shkola, Moscow (1970).
A. I. Zhuk, “The circulation of signals in a carry chain in inverse-code adders,” Voprosy Radioélektroniki, Part 4, Moscow (1968).
Additional information
Translated from Kibernetika, No. 4, pp. 148–149, July–August, 1972.
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Cherkashin, F.A. Addition of binary numbers in a system with an artificial order of weights. Cybern Syst Anal 8, 700–702 (1972). https://doi.org/10.1007/BF01068297
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DOI: https://doi.org/10.1007/BF01068297