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.
Time Optimal Mixed Radix Conversion for Residue Number Applications
BARSI, Ferruccio;PINOTTI, Maria Cristina
1994
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
