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The Computer Journal 1994 37(10):907-916; doi:10.1093/comjnl/37.10.907
© 1994 by British Computer Society
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Time optimal mixed radix conversion for residue number applications

F. Barsi * and M. C. Pinotti §

1 Dipartimento di Matematica, Universita di Perugia, Via Vanvitelli 1, 06100 Perugia, Italy, 2 Istituto di Elaborazione dell'Informazione dell CNR, Via S. Maria 46, 56100 Pisa, Italy

A new method is proposed for converting residue integers into a mixed radix notation. The method is based upon a modified formulation of the Chinese Remainder Theorem, and permits both conventional logic and look-up table implementations. Moreover, it represents the first method enabling optimal, residue-to-weighted system, asymptotic conversion time. To prove this, a constructive VLSI design has been devised, exhibiting time O(log s), where s is the total number of input bits. If compared with the existing mixed radix converting techniques, the method proposed considerably enhances the conversion time. To conclude, it is shown that, at the present state of the technology, practical ECL IC's implementation achieve 35–40 ns conversion times with RAMs and 60–70 ns with logic circuitry for dynamic ranges up to 300 bits.

Received March 15, 1994. revised October 12, 1994.

* Dipartimento di Matematica, Universita di Perugia, Via Vanvitelli 1, 06100 Perugia, Italy

§ Istituto di Elaborazione dell'Informazione dell CNR, Via S. Maria 46, 56100 Pisa, Italy


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